DAI Xu-gang, WANG Bao-shou

(China Ship Scientific Research Center, Wuxi 214082, China)

Abstract: The air bleeding through holes and good fusing together within certain area on the model surface would change the pressure distribution on the model and vary the hydrodynamic characteristics of model motion. The close-look at air bleeding discovered that the gas jet from hole is mixed with or broken by the water to form large number of bubbles, and under certain condition the bubbles fused downstream. The effects of mass flow rate, model speed and hole diameter on fusion phenomenon were studied experimentally in a special facility also. The dimension analysis was done based on the experiment results and a criterion is suggested to evaluate possibility of fusion.

Key words: air bleed; bubbles fusion; dimension analysis; fusion criterion

0 Introduction

The use of air bleed to generate two-phase flow around underwater vehicles to improve their mechanical properties is a more advanced hydrodynamic technology. Through air bleed holes on the surface of the moving body, exhausting continuously, the gas jet is mixed with or broken by the water to form a large number of bubbles, and to be further fused into a complete cavity, thereby changing the lift and drag force of the body.

Bubbles fusion refers to fusing of discrete bubbly flow generated by air bleed. In the air bleeding, the fusion characteristics of bubbles have an important influence on the mechanical properties of the body. Zhang[1]pointed out that the fusion characteristics of air bubbles are the basis for the improvement of the mechanical properties of the body. Yu’s[2]research shows that the two-phase flow formed by air bleed reduces the surface friction of the body. So it has meaning of both science and engineering.

The bubbles fusing is different from the cavitating somehow. The former is concerned with the change of the flow pattern of the gas-liquid two-phase flow. The latter is focused on depressing region of the flow mostly. Though both involve unsteady and non-linear effect, the fusion mechanism of gas-liquid two-phase flow is more complicated. Zhang[1]treated bleeding gas as continuous jet, its downstream expansions obey slender super-cavity law under independent expansion assumption. Yu[2]got drag reduction of air bleed from the SHPB (Split Hopkinson Pressure Bar) horizontal emission method. Various numerical models were used to study the fusion process of the two bubbles[3-4], but there are few experimental studies on the subject.

In this paper, experiments are carried out to investigate the fusion of air bleed bubbles during vertical navigation of body. The influence of mass flow rate, navigation speed, and hole diameter on the fusion of bubbles is studied. By dimension analysis, a criterion is introduced to evaluate the fusion of air bleed bubbles in model vertical navigation.

1 Experiment facility and its characteristics

The scheme of the facility was drawn in Fig.1. It consisted of a vertical tank (3.5 m high in total), a linear servo motor and its transmission (8 times amplifier), an air pressure vessel and its controller, a vertical moving model with 60 mm in diameter. The model had 40 same holes distributed averagely on the surface at the section 78 mm apart from tip of the model nose.These holes connected with regulatory chamber inside the model which got air supply continuously from the pressure vessel by special tube. The five of six pressure sensors were installed on the surface of the model along a generatrix. Their locations were listed in table 1. The rest one sensor was fit in the chamber.The pressure signals were transferred to data collector and computer by towline. The high speed digital camera was used to record bleeding and fusing process of the moving model.

Fig.1 The facility sketch

Tab.1 The locations of pressure sensors from tip of head nose

The typical performances of the linear servo motor were shown in Fig.2. The motor kept constant speed 400 mm/s within the displacement 150 mm, which corresponded to the vertical displacement 1.2 m with constant speed 3.2 m/s for the model.

The gas controller gave the reading of volume air flow rate under the standard condition,which is easily transferred to the mass flow rate. For example, the 50 L/min were related to 1.02 g/s. The pressure difference between sensors inside the chamber and No.1 on the surface coupling with air supply was shown in Fig.3.

Fig.2 The displacement and speed of servo motor

Fig.3 The flow rate and pressures inside and outside the chamber of model

The bubbly flow generated during the initial acceleration stage was stripped from the surface of the model by a bubble scratch device as soon as the model passed through the position where stage of constant speed started.

2 Experiment conditions

The volume air flow rates were five levels listed in Tab.2. The model vertical speeds were three levels listed in Tab.3.

Tab.2 The air mass and volume flow rate

Tab.3 The motor and model speed

There were two diameters (1 mm and 2 mm) for model holes. Finally, the combinations of four mass flow rates, three model speeds and two hole diameters were constructed to form the experiment conditions, demonstrated in Tab.4 and Tab.5.

Tab.4 The test conditions for small hole

Tab.5 The test conditions for large hole

3 Results and discussion

The all important experimental results were shown in Fig.5 to Fig.11. The black dot on coordinate of displacement means the position of model exit from water.

3.1 Characteristic of bubbles fusion

The physical connotation of bubbles fusion should be understood based on the observation firstly. The gas jet from the hole cannot keep undisturbed downstream until meets adjacent one and combines together to cover and form an equal pressure area. In fact the gas jet would be mixed with or broken by the water soon to form large number of bubbles and under certain condition, they are fusing together to form a cavity of equal pressure covering some sections or area of the body.

In Fig.4, the instance image of the experiment video could be seen, the left one possessed a round cavity, the right one did not at all. The pressure of bubbles is almost the same as that of jet near the hole before being broken. The pressure of cavity by bubbles fusing together therefore should be equal to that of bubbles roughly at least. The corresponding pressures measured were shown in Fig.5 where conditions 1a, 6b were listed in Tab.6. The location of sensor No.1 was nearest one to hole, all curves had tendency to approach to that of No.1. It meant the cavity was expanding during body vertical motion, reached the location of sensor No.5 after displacement about 2 100 mm in Fig.5(a). It also meant pressure of the cavity covering the five sensors keeping pace decreased as the body lifting to water surface in Fig.5(a). All it had not be seen in Fig.5(b).

Tab.6 The test conditions for comparison

Fig.4 Comparison of experiment image on different bubbles fusion types

Fig.5 Comparison of pressures on different bubbles fusion types

3.2 Influence of mass flow rate

The mass flow rate is the primary factor determining the speed and momentum of the gas outflow, thereby further affecting the fusion process.

Fig.6 Comparison of pressures under different mass flow rates

The pressure characteristics of the model surface with small hole under three mass flow rates and a model speed 4.0 m/s were shown in Fig.6. It can be seen that under the condition of 0.5 g/s, the pressure difference among five sensors did not decrease, indicating that the bubbles did not merge together in Fig.6(a).

The pre-separated pressures of the sensors No.1, No.2 and No.3 were becoming almost the same by approaching from pressures of No.2 and No.3 to pressure of No.1 after the displacement 2 000 mm during the continuously air bleeding process, but not including sensors No.4 and No.5 in Fig.6(b) for 1.0 g/s.

The cavity covered sensors No.1, No.2 and No.3 as early as the body displacement was about 1 900 mm, the cavity expanded to sensor No.4 at displacement 2 000 mm and to sensor No.5 at displacement 2 200 mm in Fig.6(c) at 1.5 g/s.

The pressure characteristics of the model surface with large hole under three mass flow rates and a model speed 4.0 m/s were shown in Fig.7.

From the Fig.7(a), it can be seen that under the condition 1.0 g/s, the first three of five pressures had a short-term closeness at the displacement of 1 700 mm to 1 900 mm, and then stratifying. It could be judged that the fusing temporal cavity was not stable in Fig.7(a). The first three section pressures had apparently merged, and the fourth-section did not completely enter the cavity in Fig.7(b) for 1.5 g/s.

Fig.7 Comparison of pressures under different mass flow rates

When the mass flow rate reaches 2.0 g/s in Fig.7 (c), the first three cross-sections had fused together already, the cavity expanded and covered all five sections after displacement 2 200 mm and a complete fusion had taken place.

The statistics of the fusion situations under different conditions were shown in Tab.7.

Tab.7 The bubbles fusion types of different mass flow rates on model speed 4.0 m/s

As the mass flow rate reached to certain degree, the bubbles fusing started near holes downstream to form a cavity of equal pressure, and the cavity expanded further downstream,became longer while mass flow rate kept increasing.

3.3 Influence of model speed

The model vertical motion in gravity filed restricts the behavior of the bubbles, the only space they can stay is around the model surface. The fusing between bubbles needs time which is determined by both buoyance of bubbles and water velocity. From Fig.4 and the previous analysis, it can be seen that the bubbles fusion is closely related to the tail closure of the bubbly flow, which therefore is greatly affected by Fr number. The speed of the model directly affects Fr, further affecting the bubbles fusion process. The pressure characteristics of the same mass flow rate at different model speeds under the same hole diameter were compared. The pressure characteristics for small hole, mass flow rate 1.0 g/s, and model speed 3.6 m/s, 4.0 m/s and 5.0 m/s were shown in Fig.8.

Fig.8 Comparison of pressures on different model speeds

From the Fig.8, it demonstrated that in the case of 3.6 m/s, the fusion was obvious (a), in the case of medium speed 4.0 m/s, partial fusion (b), in the case of high speed 5.0m/s, no fusion occurred (c).

The pressure characteristics for small hole, mass flow rate 1.5 g/s, and model speeds 3.6 m/s, 4.0 m/s, and 5.0 m/s were shown in Fig.9.

Fig.9 Comparison of pressures on different model speeds

From the Fig.9, it can be seen that in the case of 3.6 m/s, complete fusion happened (a),in the case of 4.0 m/s, the fusion situation was still good (b); at high speed 5.0 m/s, no fusion occurred (c).

The statistics of bubbles fusion situations for small hole under corresponding conditions were shown in Tab.8.

Tab.8 The bubbles fusion types of different model speeds for small hole

Based on Tab.8, it can be seen that within the test speed range, the higher the model speed was, the more difficultly the bubbles were able to fuse, and the decreasing speed facilitates the evolution of bubble flow from the unfused state to the fused state.

Fig.10 Comparison of pressures on different hole diameters

3.4 Influence of hole diameter

The effects of different hole diameters on bubbles fusion were compared under the same speed and mass flow rate. The pressure characteristics of small hole and large hole under speed 3.6 m/s, mass flow rate 1.0 g/s are shown in Fig.10.

At the low speed 3.6 m/s, mass flow rate 1.0 g/s, the bubbles from small hole are completely fused, and that from large hole did not fuse at all.

Fig.11 Comparison of pressures on different hole diameters

The pressure characteristics of small hole and large hole under speed 5.0 m/s, mass flow rate 2.0 g/s were shown in Fig.11. The bubbles from small hole did not fuse, and that from large hole fused. The statistics of bubbles fusion situations for all comparative test conditions were shown in Tab.9.

Tab.9 The bubbles fusion types of different test conditions

It can be seen from Tab.9 that under the condition of low speed and small mass flow rate, the fusion performance of small holes is better than that of large hole; in the case of high speed and large mass flow rate, large hole performs better than small hole. This may be due to that all factors in Tab.9 determine the speed of gas jet from holes, the differences of flow speed between gas and water, the strength of shear flows, the bubble size, the density of bubbles, the coverage on model surface, the pressure of bubbles, the fusing times of adjacent bubbles, and so on. As a result, the effect of holes diameter on bubbles fusion is not unilateral.

3.5 Fusion criterion

Therefore, the gas content rate is the function of these physical quantities and can be expressed in the dimensionless way.

The function g in Eq.(2) is unknown yet. Maybe we could build the function g based on physical meaning and effect law of test in simplest way.

Tab.10 The Rh values of different test conditions

As it can be seen from Tab.10, no matter for large hole or small one, as the model speed decreases and the mass flow rate increases, the corresponding dimensionless parameters Rh also increase, that means there are more gas bubbles around and the bubbles have more chance to meet and more time together, therefore are more prone to fusion.

Comparing the Rh values of large hole and small hole, it can be found that under highspeed conditions (5.0 m/s), for large hole, the Rh values increase obviously from 0.43 to 0.86 by mass flow rate 1.0 g/s to 2.4 g/s, but for small hole the Rh values only increased from 0.59 to 0.73, with a smaller increment. This is due to the fact that when the mass flow rate increases, the pressure in the chamber for small hole increases significantly than that for large hole and so does ΔPg, It causes higher pressure of bubbles, which leads to more difficultly equalize the pressures on the model certain surface to that on nearest section of the holes. That is the negative impact on contrary to the above mentioned positive impact due to increasing bubbles of increasing mass flow rate. Besides the bubble size is strongly determined by hole diameter,for given mass flow rate, the smaller the hole is, the larger the number of bubbles is, the more easily and densely the bubbles cover around whole cylinder surface. Therefore, it can be expected that under high mass flow rate condition, the Rh value of large hole is larger than small hole; while under small mass flow rate, the Rh value of small hole is larger than large hole, and this agrees well with the test results.

Fig.12 Bubbles fusion criterion on all test conditions

4 Summary

In this paper, the bubbles fusion characteristics of air bleeding and the effects of mass flow rate, model speed, and hole diameter on the fusion characteristics are studied. The results show that within the range of the experiment, as the mass flow rate increases and the model speed decreases, the bubbles are more prone to fusion; the effect of holes diameter on bubbles fusion is not unilateral. In the case of low model speed and low mass flow rate, the fusion performance of small hole is better than that of large hole; in the case of high model speed and large mass flow rate, large hole performs better than small hole. Based on the dimension analysis, the dimensionless number Rh that dominates the bubbles fusion is suggested, and the fusion criterion Rh=0.7 as a boundary to judge fused or not is established under single-row hole conditions based on the experimental results. The fusing phenomenon is very important and interested, is needed to study further.