Chemical and Petroleum Engineering, Vol. 49, Nos. 11–12, March, 2014 (Russian Original Nos. 11–12, Nov.–Dec., 2013)

SHAPE AND INTENSITY OF CAVITATION FIELD FOR SUBMERGED CAVITATION NOZZLE

V. V. Anisimov,1 P. P. Ermakov,1 and O. A. Petrov2

Results are presented for acoustic investigation of the shape and intensity of the cavitation field in a submerged nozzle; these results establish the interrelation between the coordinates of a point in space and the intensity of the cavitation field at the point for different velocities of liquid in the narrow section of the nozzle. Keywords: cavitation field, cavitation domain, cavitation intensity, collapse, pick-up.

Cavitation has recently been successfully employed in the chemical, petrochemical, foodstuff, and other branches of industry for intensification of a number of production processes [1–3]. Widespread use of cavitation in industry dictates the need for further scientific research on this phenomenon, for example, in the direction of a reduction in the specific energy capacity of the cavitation process. A known optical method exists for investigation of cavitation in a liquid with the use of visual observation of the cavitation domain (section of the space in which cavitation bubbles are growing or collapsing) [4]. This method makes it possible to acquire information on its shape and dimensions. The shape and dimensions of the cavitation domain are, however, slightly related to the cavitation intensity (maximum rate of collapse of a cavitation bubble, and maximum pressure or temperature within the cavitation bubble). There are also various types of sensors for evaluation of cavitation intensity, which record the phenomena that develop during cavitation. Acoustic vibrations generated during collapse of cavitation bubbles are referred to as such phenomena [3]. Measuring the amplitude of these vibrations, it is possible to evaluate the cavitation intensity (acoustic method). The use of an acoustic-vibration pick-up alone, however, permits evaluation of cavitation intensity only in a certain zone of the cavitation domain, or an integral characteristic of the intensity over the entire cavitation zone, depending on the dimensions of the sensitive zone of the pick-up in relation to the dimensions of the cavitation domain. The need therefore arises for development of a system for displacement of the pick-up, which makes it possible to measure the amplitude of acoustic vibrations at different points in space. By combining these measurements, it is possible to acquire information on the shape and size not of the cavitation domain, but the cavitation field – the portion of the space in which an acoustic field created by pressure waves that develop during collapse of cavitation bubbles exists. The objective of this study is to investigate the shape, dimensions, and intensity of the cavitation field at the outlet from a submerged nozzle. The investigations were conducted on an experimental jet cavitator (Fig. 1). The cavitator functions in the following manner. Liquid is extracted under vacuum from buffer vessel 1 by gear pump 2 from which it is delivered via pressure line 5 to cavitation nozzle 6 under the pressure assigned to valve 3 as mea-

1 2

Ukrainian State Chemical Engineering University, Dnepropetrovsk, Ukraine; e-mail: [email protected]. Belarus State Technological University, Minsk, Belarus; e-mail: [email protected].

Translated from Khimicheskoe i Neftegazovoe Mashinostroenie, No. 12, pp. 11–15, December, 2013.

0009-2355/14/1112-0785 ©2014 Springer Science+Business Media New York

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Fig. 1. General appearance of cavitator: 1) buffer vessel; 2) gear pump; 3) valve; 4) manometer; 5) pressure line; 6) cavitation nozzle; 7) pick-up; 8) plate; 9) motor; 10) distribution unit; 11) discharge line; 12) pressure compensator.

Fig. 2. Sketch of cavitation nozzle: 1) narrow section; 2) transition confusor; 3) inlet section.

sured by manometer 4. In the cavitation nozzle, the liquid is appreciably accelerated, forming cavitation bubbles in the latter. After exiting the nozzle, the cavitation bubbles collapse, and the pressure pulses generated here are recorded by pick-up 7 based on a TsS-5 piezoelectric element, and transferred to a computer in the form of an oscillogram. The intensity of the cavitation field at a given point in space is evaluated with respect to vibration amplitude on the oscillogram. After exiting the nozzle, the liquid is mixed with the liquid that has remained in the buffer vessel, and is again subsequently drawn into the gear pump via a suction tube, i.e., the liquid is repeatedly treated. These acoustic investigations call for a large number of experiments, and acquisition of complete information on the process under investigation. The basic objective of the study is selection of a submersible type of nozzle, a sketch of which is shown in Fig. 2. A mixture of water and 0.7% of lubricating-cooling liquid SOZh-R (technical specifications TU U 24.6-32038150001–2003) was employed as the effective liquid for the acoustic investigations. In terms of its properties, this liquid is closest to water, but does not cause corrosion. Preliminary experiments were conducted to confirm the normality of the distribution of the measured value of the pick-up signal with respect to the χ2 criterion, which indicated that the distribution can be considered normal. Here, the standard deviation was 0.133 V. The shape and intensity of the cavitation field in the submerged nozzle were investigated acoustically; these investigations established the interrelation between the coordinates of a point in space and the intensity of the cavitation field at that point for different velocities v of the liquid in the narrow section of the nozzle. For constant geometric parameters of the cavitation nozzle, the velocity of the liquid is unambiguously related to the Reynolds number Re which will be indicated additionally. 786

Fig. 3. Schematic showing placement of pick-up: 1) cavitation nozzle; 2) system for displacement of pick-up; 3) pick-up.

Fig. 4. Dependencies of magnitude of pick-up signal on coordinates of its position for various liquid velocities v in narrow section of nozzle: 1) 34 m/sec (Re = 6.7·104); 2) 39 m/sec (Re = 7.70·104); 3) 44 m/sec (Re = 8.8·104); 4) 50 m/sec (Re = 9.8·104).

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TABLE 1 Values of coefficients in polynomial Coefficient

Dimension v = 34 m/sec

v = 39 m/sec

v = 44 m/sec

v = 50 m/sec

a1

–0.9901

3.6693

9.5251

5.4415

V/mm

a2

–2.269

8.8621

20.26

12.821

V/mm

a3

–0.0181508

3.3969e–2

0.10202

6.6521e–2

V/mm2

a4

–7.28185e–3

1.5278e–2

4.6825e–2

2.8707e–2

V/mm3

a5

5.0229e–4

–70811e–4

–2.4088e–3

–1.6085e–3

V/mm2

a6

6.89646e–5

–11965e–4

–4.0057e–4

–2.3783e–4

V/mm4

a7

–4.56816e–6

5.1367e–6

1.9793e–5

1.3321e–5

V/mm5

a8

3.02212e–2

–8.5754e–2

–0.25462

–0.14094

V/mm2

a9

–2.90449e–4

6.5696e–4

2.1652e–3

1.14e–3

V/mm3

a10

0.183888

–0.45927

–1.1736

–0.77035

V/mm4

a11

–5.35014e–3

9.4324e–3

2.7543e–2

1.8418e–2

V/mm2

a12

5.01911e–5

–6.7715e–5

–2.2612e–4

–1.517e–4

V/mm3

a13

5.27528e–3

–8.2402e–4

–2.7621e–3

–1.7797e–3

V/mm4

a14

–1.42577e–5

1.7403e–5

6.5239e–6

4.2997e–5

V/mm5

a15

–4.89284e–5

6.5686e–6

2.367e–5

1.4782e–5

V/mm5

a16

1.27512e–7

–1.2754e–7

–5.351e–7

–3.5528e–7

V/mm6

a17

1.29993e–7

–1.4063e–7

–5.5861e–7

–3.5615e–7

V/mm6

a18

–1.14781e–9

1.0424e–9

4.5726e–9

2.9325e–9

V/mm7

a19

0.242919

–0.64125

–1.7372

–1.0798

V/mm2

a20

9.111

–50.997

111.78

66.008

V

Fig. 5. Shape of cavitation field in axial direction (at radial distance of 22 mm from axis of nozzle) for liquid velocity v: 1) 34 m/sec (Re = 6.7·104); 2) 39 m/sec (Re = 7.7·104); 3) 44 m/sec (Re = 8.8·104); 4) 50 m/sec (Re = 9.8·104). 788

To determine the shape and intensity of the cavitation field, pick-up 7 (see Fig. 1) was situated relative to the cavitation nozzle as shown in Fig. 3. A cylindrical coordinate system was introduced with x (axial coordinate) and R (radial coordinate) axes. The origin of reference of the x axis resides at the end of the cavitation nozzle, and the R coordinates are laid-off against the axis of the nozzle. The current position of the pick-up relative to the nozzle is defined as a function of the coordinates ƒ(x, R). A relative coordinate system, where the axial and radial coordinates are referred to the diameter of the narrow section of the cavitation nozzle was employed additionally. In conducting the experiments, the position of the pick-up was varied from 10 to 50 mm along the x axis (spacing of 10 mm), and from 20 to 55 mm along the R axis (spacing of 5 mm). The velocity v of the liquid in the narrow section of the nozzle (see Fig. 2) was varied from 34 m/sec (Re = 3.8·104) to 50 m/sec (Re = 9.8·104). A combination of surfaces describing the intensity and shape of the cavitation field for various liquid velocities was acquired on the basis of these experiments (Fig. 4). The experimentally obtained surfaces within the framework of the domain investigated are mathematically described by the equation: U(R, x) = a1R + a2x + a3Rx2 + a4R2x + a5Rx3 + a6R3x + a7R4x + a8R2 + a9R3 + a10R4 + + a11x2 + a12x3 + a13R2x2 + a14R2x3 + a15R3x2 + a16R3x3 + a17R4x2 + a18R4x3 + a19Rx + a20.

(1)

The numerical values of the coefficients before the terms of the polynomial are presented in Table 1. It is apparent from the plots obtained (see Fig. 4) that the relationship is extremal in nature in the direction of the axial coordinate x, and predominately monotonic in nature in the direction of the radial coordinate R over the entire range of these parameters investigated. As the velocity v of the liquid increases, the intensity of the cavitation decreases monotonically on the whole; however, the shape of the cavitation field is gradually changing. Among other things, displacement of the field along axial coordinate x occurs in the direction away from the nozzle, and expansion of the field takes place in the radial direction. The dynamics of the shift in the axial direction is shown in Fig. 5. The intensity extremum of the cavitation field is displaced linearly in the axial direction as the velocity of the liquid increases: (2) xmax(v) = a1v + a0, where xmax is the position of the extremum with respect to the axial coordinate in mm, and a1 and a0 are empirical coefficients (a1 = 0.85 mm·sec/m and a0 = –12 mm). Formula (2) is valid in the velocity region investigated from 34 to 50 m/sec. The monotonic character of the cavitation field (see Fig. 4) in the direction of radial coordinate R is explained by the distance between the zone in which the amplitude of the acoustic vibrations is measured and the region of collapse of the cavitation bubbles. The extremal character of the cavitation field in the direction of axial coordinate x is explained by the fact that a cavitation bubble ejected from the nozzle will travel a certain distance before the onset of its collapse. The distance from the nozzle at which the majority of bubbles will collapse corresponds to the maximum intensity of the cavitation field, and gradually shifts in the axial direction with increasing velocity of the liquid (see Figs. 4 and 5). For the velocity range investigated, a “dead” zone with a length of approximately 10–12 mm exists along the x axis in which the intensity of the cavitation field is comparatively low, and the number of bubbles that collapse in this zone is low, while the acoustic waves that developed during their collapse have a low amplitude. The majority of bubbles collapse at a distance of 20–40 mm from the nozzle, and the number of collapses drops-off slowly when this distance is increased. Results of the acoustic investigations of the cavitation field and those of the optical investigations of the cavitation domain at the outlet from the submerged nozzle are compared on the same scale (Fig. 6, the cavitation field at the outlet from the nozzle in the right portion, and a plot of the cavitation intensity in the left portion). The scale of the axes on the plot cor789

Fig. 6. Comparison of shapes of cavitation field and cavitation domain.

responds to the scale of the photograph: the axial coordinate has absolute correspondence, and the radial coordinate is shifted toward the axis of the nozzle for convenience of perception. The cavitation domain assumes a drop-like shape (the white horizontal streaks on the photo are ghost images of the walls of the vessel and are not related to the cavitation domain), wherein its axial dimension is considerably greater than that its radial dimension. The cavitation field takes on a complex shape, and comparable dimensions. The difference in the shapes of the cavitation domain and cavitation field is explained in the following manner. The cavitation bubbles will grow in the nozzle, and at the moment of their ejection from the nozzle, will have their largest, or closest to largest radius, depending on the geometric parameters of the nozzle. The value of the maximum radius of an individual cavitation bubble will depend on in what region of the flow its growth had occurred. The collapse of the cavitation bubble begins after its discharge from the nozzle. Bubbles of small radius will collapse earlier, and bubbles of large radius later. In zone 1 (see Fig. 6), only single bubbles collapse; the intensity of the cavitation field in this zone will therefore be low, despite the presence here of the cavitation domain. In this stage, the cavitation domain is filled with predominantly cavitation bubbles that are only beginning to diminish in size, i.e., collapse. As an example, collapse of the majority of cavitation bubbles occurs in the median section (zone 2) of the cavitation domain; this explains the high intensity of the cavitation field in this domain. The intensity of the cavitation field will drop-off gradually with increasing axial distance from the nozzle (zone 3), suggesting a smaller number of collapsing bubbles in this region, and their collapse becomes all the less vigorous. The cavitation domain is still clearly expressed in this interval, but is gradually slowly washed away, and filled predominantly with bubbles that have collapsed with subsidence, and also fragments of bubbles that had previously collapsed. Conclusions. The shape and dimensional characteristics investigated for the cavitation field make it possible to formulate a more precise representation of processes that take place during cavitation in a submerged nozzle. The information obtained on the dimensions of the cavitation field permits rational design of combined cavitators based on a submerged nozzle and an additional cavitator to accelerate the resultant cavitation intensity [5].

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REFERENCES 1. 2. 3. 4. 5.

I. Piersol, Cavitation [Russian translation], Mir, Moscow (1975). V. V. Rozhdestvenskii, Cavitation [in Russian], Sudostroenie, Leningrad (1977). E. A. Smorodov, R. N. Galiakhmetov, and M. A. Ilgamov, Physics and Chemistry of Cavitation [in Russian], Nauka, Moscow (2008). L. d’Agostino and M. V. Salvetti, Fluid Dynamics of Cavitation and Cavitating Turbopumps, Springer, Wien, New York (2007). O. A. Petrov and P. E. Vaitekhovich, “Investigation and simulation of hydrodynamic cavitators,” Khim. Prom. Segodnya, No. 12, pp. 52–56 (2003).

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