·
(1)
Guoyu Wang Shuliang
Cao Zhigang Zuo
Lingjia Zhao
Department of Thermal Engineering, Tsinghua University, Beijing 100084, China
Tel: 86-10-62782187 Fax: 86-10-62785699
E-mail:
wanggy@te.tsinghua.edu.cn
Abstract:
avitating vortex behaviors in the separated flow region behind the needle of a
hollow-jet are investigated by both numerical and experimental methods. The
moment aspects of the cavitating vortices in different cavitation conditions are
observed by high-speed photographs. Unsteady viscous flows around the valve are
simulated numerically by using an implicit SMAC scheme. It is found that the
generations of cavitating vortices is related to the vortex motion in shear
layer flow region of the separated flow. With a vortex formating, the pressure
in the region decreases. In cavitation conditions, there are some cavitation
bubbles occurred in the vortex formation area. A vortex forms a cavitating
vortex by containing some bubbles. Typical cavitating vortices appear as
circular bubble chains around the valve needle. However, in different cavitation
conditions, the cavitating vortices in the separated flow region exhibit
different aspects, namely, bubble chains, bubble cloud, and supercavitation,
since the bubble number contained in a vortex is increased with the decreasing
of the cavitation number. In splitter area, the typical cavitating vortices
exhibit bubble masses which imping to the surfaces of splitters and collapse on
it.
Keywords: separated flow, Implicit SMAC scheme, high-speed photographs, cavitating vortex
Cavitation occurred in flow systems, for example, in impeller pumps, water turbines, valves and so on, is vortex cavitation in most cases (Kato, 1998) . Vortex cavitation is usually generated in separated flows. Both vortex formation and shedding in this area controls the cavitation inception and development. Compared with other kinds of cavitation, vortex cavitation is harmful, because it can induced violent vibration and serious damage (Wang, 1999). Due to the complex of a vortex cavitation, to the author’s knowledge, it is far for us to understand this phenomenon.
The vortex cavitation is a phenomenon where small cavitation bubbles are contained in large-scale vortex motion (Yamauchi et al. 1991), which related to the pressure and viscous flow patterns (Ceccio et al. 1991). In vortex cavitating flows, there are two kinds of cavities, that is, cavitation bubbles and cavitating vortices. Because cavitating vortices contain a lot of individual bubbles, the collapses of them are the main reason for the generations of violent vibration and serious damage (Wang et al., 1997,1999) . The study of cavitating vortex behaviors is a way for us to find methods to suppress the cavitation.
It has been found that the cavitation occurred around a hollow-jet valve is a kind of vortex cavitation (Wang et al., 1997). In order to give some information about vortex cavitation further, in this paper, the unsteady flows around the valve were analyzed by a numerical simulation method, and the cavitation-aspects were observed in different cavitation numbers and valve openings by using high-speed photographs. Based on the numerical and experimental results, the factors, which affect vortex structures and cavitation aspects, were discussed.
The experiment was conducted in an open-type cavitation tunnel. To keep the cavitation nuclei during the experiment as uniform as possible, the test water was sampled from clean tap water stored in a big volume-storage-tank for long time, so as to be sufficiently saturated by air. The air content rate was 1.08 uniformly.
Figure 1 is the schematic of the experimental facilities. The test section of the experiment is a hollow-jet model valve. The whole wall of the valve was made of a transparent acrylic resin to observe the cavitation aspect. Two methods were employed to observe the cavitation appearances In one of them, a high-speed camera and an xenon flash lamp with an exposure time of 1μs were used to photograph the aspects around the needle and between the splitters, respectively. In anther method, a laser beam sheet (LBS) was formed behind the valve needle. Cavitating flow aspects on LBS were observed, by using a high-speed camera with a photograph speed of 500 frames/s.
The cavitation number σwas defined as follows: σ=2(P2-Pv)/ρV2, where P2 is the downstream pressure of the model valve, Pv is the saturated vapor pressure, V is the mean flow velocity at needle seal in valve section, and ρis the density of water. In this paper, β, the percentage of the valve stroke, is used to express the opening of the valve.
A finite-difference method was employed to simulate numerically the unsteady incompressible viscous flows around the valve. The fundamental equations of unsteady incompressible viscous flows can be written in conservative form in general curvilinear coordinates as (Shin et al., 1993):
·
(1)
(2)
Where u, p,
UI and ZI are velocity, static pressure, contravariant
velocity components and contravariant vorticity components, respectively. In the
present computation, the two equations were
solved by an implicit SMAC scheme, in which the initial value problem is
calculated using a third upstream difference and the boundary value problem of
an elliptic equation of pressure increment is calculated by Tschebycheff SLOR
method. In this scheme, the continuity equation is sufficiently satisfied and
the occurrence of spurious error in the pressure field is suppressed completely
in the same manner to the original SMAC scheme.
Figure 2 shows a flow pattern behind valve needle. Figure 2(a) is a photograph of an instantaneous flow pattern obtained by a high-speed camera with LBS. Figure 2(b) shows flow stream traces which were obtained by the unsteady computation mentioned above. Both the observation and computation results suggested that, when water pasted the valve needle, the flow separated from the needle alone so-called separating streamlines. The flow between these streamlines constituted a wake; it was called separation vortex region. A high-speed jet flow was formed. This fast-moving main flow was called the main flow region. A zone of high shear developed between the fast-moving main flow water and the slow-moving wake water, which was called the shear flow region. As shown in Fig.3, which give two photographs of instantaneous flow patterns in the cavitating area of the valve. Cavitation was only observed in the shear layer flow region as a series of circumferential strings. These strings were occurred periodically, especially in the cavitation inception and sub-cavitation stages.
In the shear flow region, due to a large gradient of velocity, a train of eddies extended far behind the valve needle. These eddies were generated on the needle seal of the valve. Figure 4 shows instantaneous velocity vector distributions and pressure contours on the needle seal, which describes a vortex formation and shedding process. When t=0, there was a vortex on the seal of the needle. With the evolution of time, the vortex shed from the seal. It moved downstreamly with the change of the structure. When t=0.6, the vortex had shed from the seal completely, and a new vortex began to be formed. When t=1.2, a flow pattern, which was similar to that when t=0, appeared. It was indicated that the vortices were generated periodically in the shear flow region. Computational results shown the shedding periods of the vortices decreased with decreasing cavitation numbers.
The pressure distributions around the needle seal also changed periodically with a vortex formation and shedding. As shown in Fig. 4, the lowest pressure occurred when a vortex was formed. With the evolution of a vortex shedding process, the pressure became higher and higher until it was shed completely, and then with the formation of a new vortex, the pressure became lower gradually. It can be clear that the pressure around a vortex decreased in the generation process of the vortex. In cavitation conditions, due to the decreasing of pressure around a vortex, cavitation bubbles were generated in the low-pressure area, and some of them must be entrained by the vortex forming a cavitating vortex. The bubble strings observed above were some cavitating vortices around the needle.
The cavitating vortices were some vortices, which were generated on the needle seal, contained some cavitation bubbles. The aspects of cavitating vortices were not only decided by vortex structures, but also the number of cavitation bubbles contained in the vortex cores.
In the area around the needle, a cavitating vortex appeared as a bubble mass along a circumference which was just behind the valve needle in inception cavitation stage. Figure 5 shows cavitating vortex aspects around the needle in different cavitation numbers. Due to the changing of cavitation states, cavitating vortices appeared as various aspects. The numbers of cavitation bubble contained in a cavitating vortex increased, with decreasing cavitation number, and the bubble mass extended to form a bubble circular chain.
Cavitating vortices moved with the motion of flow downstream. Figure 6 shows four photographs of typical cavitating vortices between splitters. In the splitter area, due to the effects of splitters, a cavitating vortex was broke up into some bubble masses. A bubble mass was different from cavitation bubble cloud, because in a bubble mass cavitation bubbles contracted with each other very closely. They moved with the vortex motion as an individual cavity. In splitter area, there was a impinging motion of cavitating vortices toward the splitter surface, as shown in the figure, the bubble mass contracted with or moved toward the splitter surface. Most of the cavitating vortices collapsed on the splitter surfaces.
Cavitating aspects between splitters appeared differently with the changes of cavitation states. Figure 7 shows the instantaneous cavitation aspects between splitters in different cavitation numbers. With decreasing cavitation numbers, cavitating vortices contained more and more bubbles. As shown in the figure, when σ=0.56, not only the vortex core but also the whole vortex full with the cavitation bubbles. In this situation, cavitating vortex became cavitation cloud, which was shedding cavitating flow. In cavitation cloud, bubbles did not contracted with each other, but distributed as clould. These bubbles strongly effected the vortex structure until to the super cavitation stage. In this stage, shedding cavitating flows transferred to continuous cavitation bubble flows.
Following conclusions can be drawn from the present experimental and numerical study on cavitating vortices in flows around a hollow-jet valve:
(1) The generations of cavitating vortices related to the vortex motion in shear layer flow region. With a vortex formation, the pressure around it decreased. In cavitation conditions, there were some cavitation bubbles occurred in the vortex formation area. The vortex core forming a cavitating vortex contained some of the bubbles.
(2) Typical cavitating vortices appeared as circular bubble chains around the valve needle. In splitter area, the typical cavitating vortices as bubble masses impinged to the surfaces of splitters and collapsed on it.
References
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[2] Kato H. Complex Structure of Sheet Cloud Cavitation. Proc. Third Int. Conf. on Pumps and Fans, Beijing, China: Tsinghua University Press, 1998: 1-12.
[3] Shin, B.R., Ikohagi, T., and Daiguji, H., An Implicit SMAC Scheme for Two-Dimensional Incompressible Navier-Stokes Equations, JSME Int. J., Series B, 1993, 36 (4): 598-606.
[4] Wang G, Shintani M, Ikohagi T, et al. A Study on the Generation of a Vortex Cavitation around a Hollow-Jet Valve. Proc. 9th Symposium on Cavitation, Akiu, Japan: 1997. 11-14.
[5] Wang G, Shin B R, Ikohagi T, et al. Cavitation Characteristics around a Hollow-Jet Valve (Observation by High-Speed Photographs and Monitoring by Vibration). Trans. Japanese Turbomachinery Society, 1998, 26: 361-368.
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[7] Yamauchi H, Tanaka M and Kato H. A Numerical Study on Mechanism of Vortex Generation Downstream of a Sheet Cavity on a Two-Dimensional Hydrofoil. Cavitation and Multiphase Flow Forum. ASME, FED, 1991, 109: 27-34.
Fig.
1 Schematic diagram of experimental facilities
Fig. 2 Flow pattern behind valve needle
Velocity
vectors Pressure contours
Fig. 3 Instantaneous
flow patterns
Fig. 4 Vortex
formation and shedding
Fig. 5 Cavitation aspects around needle
Fig. 6 Typical cavitating vortices between splitters
Fig. 7 Instantaneous cavitation aspects between splitters