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Journal ArticleDOI

Visualisation and les simulation of cavitation cloud formation and collapse in an axisymmetric geometry

01 Jan 2015-International Journal of Multiphase Flow (Elsevier)-Vol. 68, Iss: 68, pp 14-26

Abstract: Visualisation and Large Eddy Simulations (LES) of cavitation inside the apparatus previously developed by Franc (2011) for surface erosion acceleration tests and material response monitoring are presented. The experimental flow configuration is a steady-state closed loop flow circuit where pressurised water, flowing through a cylindrical feed nozzle, is forced to turn 90° and then, move radially between two flat plates towards the exit of the device. High speed images show that cavitation is forming at the round exit of the feed nozzle. The cavitation cloud then grows in the radial direction until it reaches a maximum distance where it collapses. Due to the complexity of the flow field, direct observation of the flow structures was not possible, however vortex shedding is inferred from relevant simulations performed for the same conditions. Despite the axisymmetric geometry utilized, instantaneous pictures of cavitation indicate variations in the circumferential direction. Image post-processing has been used to characterize in more detail the phenomenon. In particular, the mean cavitation appearance and the cavity length have been estimated, showing good correlation with the erosion zone. This also coincides with the locations of the maximum values of the standard deviation of cavitation presence. The dominant frequency of the ‘large-scale’ cavitation clouds has been estimated through FFT. Cloud collapse frequencies vary almost linearly between 200 and 2000 Hz as function of the cavitation number and the downstream pressure. It seems that the increase of the Reynolds number leads to a reduction of the collapse frequency; it is believed that this effect is due to the agglomeration of vortex cavities, which causes a decrease of the apparent frequency. The results presented here can be utilized for validation of relevant cavitation erosion models which are currently under development.
Topics: Cavitation (58%), Vortex shedding (53%), Reynolds number (51%), Vortex (51%)

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City, University of London Institutional Repository
Citation: Gavaises, M., Villa, F., Koukouvinis, P., Marengo, M. and Franc, J-P. (2015).
Visualisation and les simulation of cavitation cloud formation and collapse in an
axisymmetric geometry. International Journal of Multiphase Flow, 68, pp. 14-26. doi:
10.1016/j.ijmultiphaseflow.2014.09.008
This is the accepted version of the paper.
This version of the publication may differ from the final published
version.
Permanent repository link: https://openaccess.city.ac.uk/id/eprint/13566/
Link to published version: http://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.09.008
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1
VISUALISATION AND LES SIMULATION OF CAVITATION CLOUD FORMATION AND
1
COLLAPSE IN AN AXISYMMETRIC GEOMETRY
2
3
Manolis Gavaises, Fabio Villa and Phoevos Koukouvinis
4
School of Engineering and Mathematical Sciences, City University London, Northampton Square,
5
EC1V 0HB, London, UK
6
7
Marco Marengo
8
Department of Mechanical Engineering, University of Brighton, UK
9
10
Jean-Pierre Franc
11
LEGI, Grenoble University, BP 53, 38041 Grenoble Cedex 9, France
12
13
14
ABSTRACT
15
Visualization and Large Eddy Simulations (LES) of cavitation inside the apparatus previously
16
developed by [1] for surface erosion acceleration tests and material response monitoring are
17
presented. The experimental flow configuration is a steady-state closed loop flow circuit where
18
pressurised water, flowing through a cylindrical feed nozzle, is forced to turn 90 degrees and then,
19
move radially between two flat plates towards the exit of the device. High speed images show that
20
cavitation is forming at the round exit of the feed nozzle. The cavitation cloud then grows in the radial
21
direction until it reaches a maximum distance where it collapses. Due to the complexity of the flow
22
field, direct observation of the flow structures was not possible, however vortex shedding is inferred
23
from relevant simulations performed for the same conditions. Despite the axisymmetric geometry
24
utilized, instantaneous pictures of cavitation indicate variations in the circumferential direction. Image
25
post-processing has been used to characterize in more detail the phenomenon. In particular, the mean
26
cavitation appearance and the cavity length have been estimated, showing good correlation with the
27
erosion zone. This also coincides with the locations of the maximum values of the standard deviation
28
of cavitation presence. The dominant frequency of the ‘large-scale cavitation clouds has been
29
estimated through FFT. Cloud collapse frequencies vary almost linearly between 200 to 2000Hz as
30
function of the cavitation number and the downstream pressure. It seems that the increase of the
31
Reynolds number leads to a reduction of the collapse frequency; it is believed that this effect is due to
32
the agglomeration of vortex cavities, which causes a decrease of the apparent frequency. The results
33
presented here can be utilized for validation of relevant cavitation erosion models which are currently
34
under development.
35
36
Keywords: cavitation, erosion, collapse, LES
37
38
1. INTRODUCTION
39
40
Understanding and controlling cavitation has been a major challenge in engineering for many years.
41
Cavitation erosion is generally believed to be the result of violent collapses of the flowing cavitation
42
micro-bubbles within very short time scales [2]; it often leads to vibration and damage of mechanical
43
components, for example, marine propellers and rudders, bearings, fuel injectors, pumps and turbines.
44
Studying the sheet/cloud cavitation is important to understand the causes of cavitation erosion, and to
45
predict accurately its aggressiveness in terms of erosion risks, or even more, damage rate. In [3] a
46
review of the physical mechanisms for cavitation erosion loads is given. These mechanisms are
47
evaluated with observations on the detailed dynamics of the flow over a cavitating hydrofoil and with
48
observations that are available from ships where cavitation has led to erosion damage on the rudder or
49
the propeller. Many recent studies (selectively [1, 4-14]) have examined the time dependent
50
progression of cavitation erosion for different materials. Due to the aforementioned detrimental
51
effects of cavitation on hydraulic equipment, most of experimental research has focused over the
52
years on methods with which cavitation damage could be quantified and linked to measurable
53

2
material properties. In [15], systematic cavitation erosion tests have been performed on a water
54
hydraulic system; results from this study have been reported in the past and have been widely used for
55
benchmarking relevant computational fluid dynamics and cavitation erosion models. Briefly, it was
56
shown that cavitation erosion during the incubation period was occurring via pitting. Cavitation
57
damage was not correlated with the elastic limit determined from conventional tensile tests and it is
58
conjectured that other parameters such as the strain rate might play a significant role. However, the
59
flow details associated with the erosion tests have not been recorded.
60
61
At the same time, many studies have been reported on flow visualisation in cavitating flows in a
62
number of devices. A review on numerical and experimental investigation of sheet/cloud cavitation
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was carried out by[16]. Sheet/cloud cavitation could influence the dynamic flow pattern. In [17] a
64
numerical and experimental investigation of sheet/cloud cavitation on a hydrofoil at a fixed angle of
65
attack is reported. The results show that, for the unsteady sheet/cloud cavitating case, the formation,
66
breakup, shedding, and collapse of the sheet/cloud cavities increase the turbulent intensity, and are
67
important mechanisms for vorticity production and modification. Another important feature of the
68
problem is the lift oscillations due to the highly periodic nature of the sheet/cloud cavitation. In [18] it
69
was found that the dynamic characteristics of the cavitation vary considerably with various
70
combinations of angle of attack and cavitation number, σ. At higher angles of attack, two types of
71
flow unsteadiness are observed. At low σ, there is a low frequency shedding of cloud cavitation
72
observed at a Strouhal number of about 0.15. This non-dimensional number is relatively insensitive to
73
changes in σ. As σ is raised, the sheet frequency varies almost linearly with cavitation number.
74
75
A recent study by [19] was focused on the simultaneous observation of cavitation structures and
76
erosion, in order to find a pattern linking the evolution of cavities with the erosion development. The
77
studies were conducted in a cavitating Venturi nozzle section, where part of the nozzle was covered
78
by a thin aluminium foil; this enabled the rapid accumulation of erosion pits and allowed the
79
observation of the erosion development, since the rest nozzle walls were transparent. From the
80
observations, it was concluded that, while the exact volume and distance of the vapour cavity does not
81
play a significant role to erosion damage, extensive erosion was caused by the collapse of uneven and
82
asymmetrical vapour cavities. The authors hypothesize that erosion might be caused by two
83
mechanisms (or a combination of both): a) the shock wave generated by the cloud collapse is
84
triggering the collapse of microbubbles in the vicinity of the wall area b) the irregular shape of the
85
cavitation cloud causes asymmetrical, non-spherical shock waves that have a distinct orientation.
86
87
Along these directions, a number of computational studies on cavitation have been reported over the
88
years. Direct numerical simulation of the whole process is computationally very demanding but
89
provides a good insight into the relevant mechanisms and physics. One notable example of a DNS
90
study of the collective bubble collapse is the recent work of[20], where the authors employed massive
91
parallelism to simulate a cluster of 15,000 bubbles collapsing near a wall, utilizing a grid with size of
92
13 trillion cells. Of course the resources required to run such a simulation are prohibitive for industrial
93
application; for the specific application the authors utilized a supercomputer consisting of 1.6 million
94
cores, which obviously is impractical to use in everyday engineering computations.
95
96
Another approach to simulate the effects of erosion is by including the exact behaviour of the fluid,
97
using a complicated equation of state that reproduces the phase diagram of the liquid/vapour phases.
98
This approach has been followed in[21], who employed a density based solver with shock capturing
99
schemes to simulate the cavitation in the same geometry described in the current paper. Erosion is
100
predicted in the form of shock waves, which originate from the collapse of vapour structures. The
101
simulation methodology, though, had the limitation of small time steps, due to the inclusion of
102
compressibility effects for both liquid and vapour phases.
103
104
Considering the above, it becomes obvious that, even if there are state of the art methodologies
105
capable of potentially accurate representation of the behaviour of cavitation structures, their
106

3
application in everyday problems is limited, due to vast amount of computational resources they
107
require. Thus, in practice, a significant effort is put to derive semi-empirical models to describe the
108
cavitation erosion, which is inherently related to the micro scale effects. Typically, the large-scale
109
problem can be addressed by e.g. multi-phase RANS/LES solvers while the micro-scale problem can
110
be addressed by either a numerical model [22, 23], or by a semi-empirical erosion model or damage
111
functions [24-26]; along these lines, validation against experimental erosion data is of significant
112
importance. Here it should be highlighted that various researchers [24, 27, 28] have found that
113
traditional URANS models suffer from a deficiency in predicting the shedding frequency of cavitating
114
flows; the proposed methodologies to treat this deficiency is either to modify the turbulent viscosity
115
formulation of the traditional URANS models, or employ hybrid RANS/LES or pure LES
116
methodologies.
117
118
The present contribution aims to provide more insight to the details of the cavitation sheet/cloud
119
developing in a purpose build device that has been previously used for extensive cavitation erosion
120
measurements[15]. In this paper the same apparatus is used to visualise the cavitating flow in an effort
121
to correlate the observed cavitation erosion locations with the location of cavitation development. The
122
next section of the paper gives a short description of the experimental apparatus used, followed by a
123
brief description of the computational model; then the presentation of the obtained results follows
124
while the most important conclusions are summarised at the end.
125
126
2. EXPERIMENTAL SETUP
127
128
As already mentioned, the experiments were conducted in a cavitation flow loop described in detail
129
in[15]. The test section is axisymmetric and made of a straight feed nozzle with 16mm diameter. The
130
flow is accelerated by two converging nozzles with cross-section ratios of 2.86:1 and 2.12:1 and
131
lengths 178 and 80mm respectively. As illustrated in Fig. 1, the flow is deflected by the sample to be
132
eroded which is set at a distance of 2.5mm from the nozzle exit. It then moves radially within the
133
2.5mm gap formed between the sample and the nozzle exit orifice. The radius of curvature of the feed
134
nozzle exit was 1mm. The working fluid was tap water kept at fixed temperature of 25
o
C. Cavitation
135
erosion data are only available for a cavitation number of 0.9, showing three distinct and clearly
136
separated cavitation erosion sites: two at the upper surface and one of the lower surface. On the upper
137
surface, cavitation erosion is observed just at the turning location of the flow where cavitation is
138
generated and then a few mm further downstream. A cavitation erosion free zone between them
139
exists. On the lower surface, erosion has been observed only at the closure region of the cavity in the
140
form of a circular ring whose mean radius is around 25mm[15].
141
142
The test section is placed in a closed circuit comprised by different equipment: centrifugal pump, heat
143
exchanger, test section, electromagnetic flowmeter. The centrifugal pump of 80kW is driven by a
144
variable speed motor. It can provide a pressure of 40bars and a maximum flow of 11l/s. The flow
145
through the system is measured using an electromagnetic flow meter. A heat exchanger allows
146
maintaining the water temperature constant. The maximum operating pressure of the circuit is 40bars,
147
which corresponds to a mean velocity of 65m/s at the turn located at the nozzle exit, calculated at the
148
peripheral surface of the cylinder with height 2.5mm and radius 8mm. The pressurization of the
149
system is supported by means of a balloon located downstream the test section. A pressure control
150
device is used to finely control this downstream pressure (P
down
) in the installation. Various pressure
151
and temperature sensors are used to determine precisely the test conditions. Here it is important to
152
mention the definition of the cavitation number σ, used in the present paper:
153
downup
down
downup
vdown
PP
P
PP
PP
=
σ
154
where P
down
and P
up
are the static pressures upstream and downstream the test section and P
v
is the
155
vapour pressure of the liquid at the temperature of the experiment.
156
157

Citations
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Abstract: This paper mainly summarizes the recent progresses for the cavitation study in the hydraulic machinery including turbo-pumps, hydro turbines, etc.. Especially, the newly developed numerical methods for simulating cavitating turbulent flows and the achievements with regard to the complicated flow features revealed by using advanced optical techniques as well as cavitation simulation are introduced so as to make a better understanding of the cavitating flow mechanism for hydraulic machinery. Since cavitation instabilities are also vital issue and rather harmful for the operation safety of hydro machines, we present the 1-D analysis method, which is identified to be very useful for engineering applications regarding the cavitating flows in inducers, turbine draft tubes, etc. Though both cavitation and hydraulic machinery are extensively discussed in literatures, one should be aware that a few problems still remains and are open for solution, such as the comprehensive understanding of cavitating turbulent flows especially inside hydro turbines, the unneglectable discrepancies between the numerical and experimental data, etc.. To further promote the study of cavitation in hydraulic machinery, some advanced topics such as a Density-Based solver suitable for highly compressible cavitating turbulent flows, a virtual cavitation tunnel, etc. are addressed for the future works.

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Abstract: Sheet/cloud cavitation is an important topic that is a very common type of cavitation in turbo-machinery and marine propeller. Up to now we still have limited understanding of the cavitation shedding dynamics and cloud cavity formation and development. The present study used experimental and numerical studies to gain a better understanding of the complex physics involved in this problem. A series of experimental observations around hydrofoils are carried out in the cavitation tunnel of the China Ship Scientific Research Center (CSSRC) to illustrate the spatial–temporal evolution of the cloud cavity in detail. The results demonstrate that U-type flow structures are common in cloud cavities and can be divided into three stages and the closure line in a sheet cavity often has a convex–concave profile. Reentrant flows occur in the convex region with the jet direction normal to the contour edge so the shedding is mainly caused by the converging reentrant flows. Further analysis demonstrated that there was a striking difference with the cavity growth suppressed substantially in the twisted hydrofoil case if compared with straight hydrofoil and the effect of side entrant jets might make the cavity more uniform across the span. Numerical simulations were used to simulate the formation and development of the cloud cavity. The results show that the strong adverse pressure gradient in the stagnation region at the downstream end of the attached cavity forces the re-entrant flows into the vapor structure with a radially-diverging re-entrant jet and a pair of side-entrant jets, which causes the cavity shedding. Further analyzes of the local flow fields show that the interactions between the circulating flow and the shedding vapor cloud may be the main reason for the formation of the U-type cloud cavity structures.

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References
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Christopher E. Brennen1Institutions (1)
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Abstract: In flows around three-dimensional surface obstacles in laminar or turbulent streamsthere are a number of points where the shear stress or where two or more component,s of the mean velocity are zero. In the first part of this paper we summarize and extend the kinematical theory for the flow near these points, particularly by emphasizing the topological classification of these points as nodes or saddles. We show that the zero-shear-stress points on the surface and on the obstacle must be such that the sum of the nodes ΣN and the sum of the saddles Σs satisfy \[ \Sigma_N -\Sigma_S = 0. \] If the obstacle has a hole through it, such as a passageway under a building, \[ \Sigma_N -\Sigma_S =-2. \] If the surface is a junction between two pipes, \[ \Sigma_N -\Sigma_S =-1. \] We also consider, in two-dimensional plane sections of the flow, the points where the components of the mean velocity parallel to the planes are zero, both in the flow and near surfaces cutting the sections. The latter points are half-nodes N′ or half-saddles S′. We find that \[ (\Sigma_N +{\textstyle\frac{1}{2}}\Sigma_{N^{\prime}}-(\Sigma_{S^{\prime}}+{\textstyle\frac{1}{2}}\Sigma_{S^{\prime}}) = 1-n, \] where n is the connectivity of the section of the flow considered.In the second part new flow-visualization studies of laminar and turbulent flows around cuboids and axisymmetric humps (i.e. model hills) are reported. A new method of obtaining a high resolution of the surface shear-stress lines was used. These studies show how enumerating the nodes and saddle points acts as a check on the inferred flow pattern.Two specific conclusions drawn from these studies are that: for all the flows we observed, there are no closed surfaces of mean streamlines around the separated flows behind three-dimensional surface obstacles, which con-tradicts most of the previous suggestions for such flows (e.g. Halitsky 1968);the separation streamline on the centre-line of a three-dimensional bluff obstacle does not, in general, reattach to the surface.

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Abstract: Unsteady cavitation in a Venturi-type section was simulated by two-dimensional computations of viscous, compressible, and turbulent cavitating flows. The numerical model used an implicit finite volume scheme (based on the SIMPLE algorithm) to solve Reynolds-averaged Navier-Stokes equations, associated with a barotropic vapor/liquid state law that strongly links the density variations to the pressure evolution. To simulate turbulence effects on cavitating flows, four different models were implemented (standard $k-\varepsilon$ RNG; modified $k-\varepsilon$ RNG; $k-\omega$ with and without compressibility effects), and numerical results obtained were compared to experimental ones. The standard models $k-\varepsilon$ RNG and $k-\omega$ without compressibility effects lead to a poor description of the self-oscillation behavior of the cavitating flow. To improve numerical simulations by taking into account the influence of the compressibility of the two-phase medium on turbulence, two other models were implemented in the numerical code: a modified $k-\varepsilon$ model and the $k-\omega$ model including compressibility effects. Results obtained concerning void ratio, velocity fields, and cavitation unsteady behavior were found in good agreement with experimental ones. The role of the compressibility effects on turbulent two-phase flow modeling was analyzed, and it seemed to be of primary importance in numerical simulations.

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