Experimental study of effects of air content on cavitation and pressure fluctuations

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2010,22(5):634-638 DOI: 10.1016/S1001-6058(09)60097-4

EXPERIMENTAL STUDY OF EFFECTS OF CAVITATION AND PRESSURE FLUCTUATIONS*

AIR

CONTENT

ON

YE Jin-ming, XIONG Ying, LI Fang, CHEN Shuang-qiao College of Naval Architecture and Power, Naval University of Engineering, Wuhan 430033, China, E-mail: [email protected]

(Received August 20, 2009, Revised August 18, 2010)

Abstract: This article studies the effects of air content on propeller cavitation and pressure fluctuations. The cavitation is observed while the pressure fluctuations on the hull are measured. When adjusting the air content, the sheet cavitation range does not change distinctly, but the pressure fluctuations see obvious differences. The amplitudes of the pressure fluctuations increase with the decrease of the air content. The results indicate that the air content has little effect on the sheet cavitation range but has an important effect on the bubble cavitation and the tip vortex cavitation. When the air content decreases, the water tensile force increases, which results in the instability of the bubble cavitation and the tip vortex cavitation and the increase of the pressure fluctuations. To minimize the scale effects, the experiments should be run at a high Reynolds number with a high nuclei content. The high Reynolds number is often realized by increasing the flow velocity and the propeller rotation speed, and the high nuclei content is often made by increasing the dissolved air content. Key words: cavitation, pressure fluctuations, model test, air content

1. Introduction The propeller is the most important source of the stern vibration. The cavitation on propellers makes pressure fluctuations especially serious. It is clear that the water quality has an important influence on the propeller cavitation inception process and the propeller induced pressure fluctuations[1-3]. The water quality is traditionally defined in terms of the dissolved air content level. In most numerical and pressure predictions of cavitation[4-10] [11-13] , the air content effects are not fluctuations considered. The effects of the water quality or the air content on cavitation and fluctuations are often studied by experiments.

* Project supported by the Foundation of the State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University (Grant No. 0811), the National Natural Science Foundation of China (Grant No. 51009145) and the Foundation of Ministry of Education Key Laboratory of High speed ship Engineering, Wuhan University of Technology (Grant No. HSSE 1004). Biography: YE Jin-ming (1978-), Male, Ph. D., Lecturer

Experimental studies of the influence of air on cavitation inception and dynamics over the past 20 years are reviewed by Billet[14] and Gindroz[15]. The influence of dissolved gas on the inception and development of the tip vortex cavitation was examined by Briançon and Merle[16]. They demonstrated how both free and dissolved gas content would influence the cavitation of a stationary elliptic planform hydrofoil, including the core diameter and the dynamics of the vortex. While the size of the incident nuclei was not taken as an independently varying parameter in the study, it was shown that the dynamics and the fragmentation of larger bubbles in the vortex can influence the noise that the bubbles emit upon collapse. In order to correlate the water quality measurements with both visual and acoustic inception for several types of propeller cavitation, Grand Tunnel Hydrodynamic (GTH) offered a correlation for the propeller leading-edge sheet, between the bubble and tip vortex cavitation inception and water quality data as determined by the liquid tension and the microbubble event-rate. The results show clearly a dependency of the cavitation inception

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for each propeller cavitation type on the liquid tension. The water quality is also important as shown in scale effects. The classical theory for scaling vaporous cavitation inception assumes that σ is constant, which implies that when scaling from one flow state to another, not only the characteristics of the flow field and its boundaries remain geometrically and kinematically similar but also cavitation occurs when the local pressure is equal to the liquid vapor pressure. However, the real flows often do not obey this classical theory and departures are often called the “scale effects”. Experimental results clearly show that in most cases, the cavitation inception index can be greater or less than the minimum pressure coefficient. In this article, the model test of pressure fluctuations induced by cavitation propeller is carried out in the large circulation channel. The ship wake is simulated by a ship model with all accessories. The cavitation is observed when the pressure fluctuations on the hull are measured. The effects of air content on cavitation and pressure fluctuations are studied.

In the model test, the geometric similarity, the kinematic similarity and the dynamic similarity are required. (1)The ship model and the propeller model are made according to the geometric similarity. (2)The cavitation number in the model test is the same as that for the full-scale ship: For full-scale ship:

σ n (0.8 R ) s =

pa + ρ s g (hs − 0.4 Ds ) − pvs 0.5ρ s (ns Ds ) 2

(1)

For model ship:

σ n (0.8 R ) m =

p0 − ρ g (hp + 0.4 Dm ) − pvm

(2)

0.5 ρ (nm Dm ) 2

σ n (0.8 R ) s = σ n (0.8 R ) m

(3)

where ρ s is the density of sea water, hs the depth 2. Test facility and test model The model test is carried out in the large circulation channel of the State Key Laboratory of Hydrodynamics. The work section is a rectangle of 2.2 m in width, 2 m in height and 10.5 m in length. The water speed range in the work section is from 1 m/s to 15 m/s, the pressure range at the center of the work section is from 0.005 MPa to 0.4 MPa. According to the dimension of the test section and the installation requirements, a ship hull model with all accessories is manufactured based on geometric similarity. The hull model is 6.76 m in length, and two propellers are both of internal rotation type. The appendages include one bulbous bow, two bilge keels, two fin stabilizers, several shift brackets and one rudder. The ship model is made of fiberglass. The serial number of the ship model is SM0404. The installation of the ship model and the propeller model is shown in Fig.1.

Fig.1 The installation of the ship model and the propeller model

of the full-scale propeller, Ds the diameter of the full-scale propeller, ns the rotational speed of the full-scale propeller,

pvs

pa the atmosphere pressure,

the vapor pressure of sea water, nm

the

rotational speed of the model propeller, pvm the vapor pressure of the test water, p0 the pressure at the center of the test section, h p the height between the propeller model center and the work section center (3)Reynolds number is larger than the critical Reynolds number.

Rn (0.75 R ) =

L0.75 R Va 2 + (0.75πnm Dm ) 2

ν

> 3 ×105 (4)

where Va is the advance velocity of the propeller model, L0.75R the length of 0.75R propeller section, ν the kinematic viscosity coefficient of the water. (4)The thrust coefficient of the model propeller is the same as that of the full-scale propeller. There are 8 pressure transducers installed at the hull stern. The pressured surfaces of the transducers are leveled with the hull surface, and the diameters of the pressured surfaces are 3.7 mm. The transducers are assembled as shown in Fig.2, and the 2# transducer is placed at the center of the propeller disc upside up. In order to observe the propeller cavitation, two watertight CCDs are fixed, respectively, ahead and behind the port propeller. The cavity pattern and be development on the blade surface can

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recorded by the two

CCDs

with

the stroboscope.

as:

K pi =

pi ρ n Dm 2 2

(6)

(2) When there is the cavitation on the blades, the cavitation shape is plotted on the key blade at different angles. (3) Change the relative air content α / α s to 0.50, 0.68 and 0.82, respectively, repeat the procedures of the Steps (1)-(2).

Fig.2 The measurement points on the SM0404

According to the thrust coefficient KTs and the cavitation number σ ns of the full-scale ship at the

3. Results and analysis When the relative air content α / α s is 0.82, 0.68, 0.58 and 0.50, respectively, the pressure fluctuations coefficients at the different measurement points are shown as in Fig.3 - Fig.7.

ship speed Vship of 28.87 kn, the rotational speed nm of the propeller model, the flow velocity Vsm and the pressure at the test section are determined. The operation conditions of the test model and the full-scale ship are shown in Table 1. Table 1 The conditions of the full-scale ship and the test model Full-scale ship

Test model

KTs

0.170

KTm

0.170

σ n (0.8 R ) m

1.25

σ n (0.8 R ) m

1.25

Vship (kn)

28.87

Vsm

6.056

nm (s−1)

29.06 Fig.4 The 2nd pressure fluctuations coefficients

The relative air content α / α s of the water in the large channel is adjusted to 0.58. When the air content is stabilized, the following measurement operations are carried out: (1) Calibrate the sensitivity of the transducers, and measure the pressure fluctuations on the hull stern at different conditions. With Fast Fourier Transform (FFT) of the pressure time-domain signal p , the blade frequency amplitudes pi and the phase-angles φi of the pressure fluctuations can be obtained. ∞

p = p0 + ∑ pi cos(iωt + φi )

Fig.3 The 1st pressure fluctuations coefficients

(5)

i =1

The non-dimensional amplitudes are calculated

Fig.5 The 3rd pressure fluctuations coefficients

From the above results, it is shown that the air content has a great effect on the pressure fluctuations. The pressure fluctuation amplitudes increase with the decrease of the air content except the 2nd order amplitudes. For example, the 1st order amplitude at α / α s = 0.5 is 14.4% larger than that at

α / α s = 0.82 on the measurement point 6#.

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Fig.6 The 4th pressure fluctuations coefficients

Fig.7 The 5th pressure fluctuations coefficients

Fig.8 The cavity shape on the key blade

When the relative air content α / α s is 0.58, the cavitation range on the key blade from 0o to 40o is shown in Fig.8. In the test, there are a large number of gas bubbles floating up in the water because of the low pressure in the channel, which affect the observation of the bubble cavitation and the tip vortex cavitation to some extent. But the sheet cavitation can be observed clearly because it is relatively stable and its range is relatively large. So the range of the sheet

cavitation in Fig.3 is more accurate than those of the bubble cavitation and the tip vortex cavitation. When the relative air content α / α s is adjusted to other values, the sheet cavitation range on the blade changes little. Unfortunately, the results of the cavitation observation indicate that the sheet cavitation ranges change too diminutively to be observed clearly. And it is also difficult to observe clearly the effects of the air content on the bubble cavitation and the tip vortex cavitation in our model test because of the instability of the bubble cavitation and the tip vortex cavitation and the large number of gas bubbles in the water. But from the results of the pressure fluctuations, it is shown that the air content has a great effect on the pressure fluctuations induced by the cavitating propeller. So the air content must have important effects on cavitaiton, especially on the bubble cavitation and the tip vortex cavitation. This can be explained as follows. The cavitation nuclei are the defects of the viscous fluid, which causes a decrease of tensile force. So the cavitation nuclei concentration in the water has significant influences on the water tensile force. The cavitation nuclei concentration decreases with the decrease of the air content, therefore, the water tensile force becomes bigger, which results in the instability of the bubble cavitation and tip vortex cavitation and the increase of pressure fluctuations. The water tensile force comes from the fluid viscosity characterized by Reynolds number. In the 23ITTC, both the gas pressure and the bubble tension terms become less important when the velocities increase. So the tensile effects are also related to Reynolds number. With the increase of Reynolds number, the tensile effects decrease. Because the Reynolds number in the real case is much larger than that in the model test, the tensile forces are not similar in the real case and in the model test, that is to say, the tensile effects in the model test are larger than those in the full-scale case, which is called the scale effects. To lower the scale effects, some measures must be taken to reduce the tensile effects in the model test. Based on the analysis above, there are two methods to reduce the tensile effects in the model test: increasing the nuclei content and increasing Reynolds number. So the experiments should be run at high Reynolds number with high nuclei content in order to minimize the scale effects. The high Reynolds number is often realized by increasing the flow velocity and the propeller rotation speed, and the high nuclei content is often obtained by increasing the dissolved air conten. 4. Conclusions The effects of air content on propeller cavitation and pressure fluctuations are studied in this article.

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The cavitation is observed when the pressure fluctuations on the hull are measured. The air content is changed at the same working condition. When adjusting the air content, the sheet cavitation range does not change very distinctly, but the pressure fluctuations see obvious differences. The pressure fluctuation amplitudes increase with the decrease of air content except the second order amplitude. The results indicate that the air content has great effects on the pressure fluctuations induced by the cavitating propeller. So it must have important effects on the bubble cavitation and tip vortex cavitation. The reason is that the cavitation nuclei concentration decreases with the decrease of the air content. The cavitation nuclei concentration in the water has a significant influence on the tensile force of the water, and in its turn, on propeller cavitation characteristics. When the air content decreases, the water tensile forces become bigger, which would result in the instability of the cavity and the increase of the pressure fluctuations. Because Reynolds number in the full-scale case is much larger than that in the model test, the effects of the tensile force in the model test are larger than that in the full-scale case, which is called the scale effects. To minimize the scale effects, the experiments should be run at high Reynolds number with high nuclei content. The high Reynolds number is often realized by increasing the flow velocity and the propeller rotation speed, and the high nuclei content is often obtained by increasing the dissolved air content.

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