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Sheet and cloud cavitation
Generally speaking, partial cavities have two forms of appearance as well in case of internal flows (in a Venturi) as in case of external flows (on a hydrofoil). For small incident angles (hydrofoil – angle of attack; Venturi – divergent and convergent angles) and high free-stream cavitation numbers, the attached cavity appears to be stationary at a fixed location, and the observed cavity length is rather constant. This situation is referred to as sheet cavitation. A typical sheet cavitation forming on the suction side of a hydrofoil or on the divergent wall of a Venturi channel is presented in Figure 2.1. When the cavitation number is decreased or/and the incident angle is increased to a certain extent, the stable sheet cavity cannot be sustained. A large portion of the cavity is shed periodically from the main cavity forming a cloud-like structure in the cavity wake, and as a result the cavity length undergoes significant oscillations. This phenomenon is commonly called cloud cavitation. Figure 2.2 shows two examples of cloud shedding.
Although cavitation is inherently unsteady, sheet cavitation is usually stated to be stable or quasi-stable since the shedding of small vapour-filled vortices is confined in the cavity closure region, whose characteristic length scale is much smaller than the whole cavity length. Sheet cavitation is sometimes described to be an open cavity due to its frothy appearance at the closure as classified by Laberteaux & Ceccio (2001a). In contrast, cloud cavitation results in large fluctuations of cavity volume and thus is stated to be unstable. The violent collapse of the shed cloud in the downstream wake region can emit pressure waves of high amplitude, which is considered as the main source of noise and erosion (Reisman et al. 1998; Dular et al. 2015). Therefore, cloud cavitation is much more destructive than a stable sheet cavity.
Mechanisms for cloud shedding
In a classical point of view, the different behaviors of a partial cavity depend on the existence or absence of re-entrant flow originating from a stagnation point behind the cavity closure.
As for sheet cavitation (open partial cavities), Gopalan & Katz (2000), Callenaere et al. (2001) and Laberteaux & Ceccio (2001a) concluded that no clear re-entrant jet or only the weak reverse flow existed at the trailing edge of the cavity due to weak adverse pressure gradient. Leroux et al. (2004) did not detect a clear sign of a pressure wave traveling from the cavity closure towards the leading edge inside a stable sheet cavity through ten aligned pressure transducers flush-mounted along the suction side of a hydrofoil, and they attributed it to the absence of the re-entrant jet. Barre et al. (2009) measured a clear re-entrant flow in a globally-steady sheet cavitation using a double optical probe technique. However, in their simultaneous numerical simulation, the re-entrant jet was not predicted, and eventually they did not further clarify the role played by the re-entrant jet in stable sheet cavitation. In general, the absence of re-entrant flow was regarded as the main reason for the stable flow regime of sheet cavitation.
The periodic shedding of large cloud was observed firstly by Knapp (1955) and he proposed a re-entrant jet model to explain the transition from stable sheet cavitation to periodic cloud cavitation. This re-entrant jet mechanism is presented schematically in Figure 2.3. As the attached cavity grows to a certain length, a thin re-entrant jet, mainly composed of liquid, forms near the cavity closure region and moves upstream beneath the cavity. When this jet reaches the cavity leading edge, the whole cavity is pinched off forming a rolling cavitation cloud that is then convected downstream by the main flow until it collapses. Meanwhile a new cavity begins to grow again and the entire process is repeated.
Studies on cavitation-turbulence interactions
The cavitation dynamics is also strongly related to the cavitation / turbulence coupling: the effect of cavitation (including formation and collapse of vapour cavities) on turbulence has been investigated numerically and experimentally.
As for the numerical aspect, Dittakavi et al. (2010) used large eddy simulation (LES) to predict cavitating flows in a Venturi nozzle. By comparison of three cases at different cavitation numbers, they concluded that the vapour formation due to cavitation suppressed turbulent velocity fluctuations and the collapse of vapour structures in the downstream region was a major source of vorticity production, resulting in a substantial increase of turbulent kinetic energy. Xing et al. (2005) observed, in their numerical simulation of vortex cavitation in a submerged jet, that cavitation suppressed jet growth and decreased velocity fluctuations within the vaporous regions of the jet. Gnanaskandan & Mahesh (2016) investigated partial cavitating flows over a wedge and found that the streamwise velocity fluctuations dominated the other two components within the cavity, while all three components of fluctuations were equally significant near the cavity closure and downstream of the cavity, Regarding the experimental aspect, the acquisition of quantitative velocity fields mainly relied on PIV measurements. Gopalan & Katz (2000) and Laberteaux & Ceccio (2001) observed the largest turbulent fluctuations in the region downstream of the cavity which were regarded as the impact of vapour collapse. Iyer & Ceccio (2002) investigated the effect of developed cavitation on the flow downstream of the cavitating shear layer. They found that the collapse of vapour bubbles led the streamwise velocity fluctuations to be increased but the cross-stream fluctuations and the Reynolds shear stress to be decreased. Aeschlimann et al. (2011b) performed velocity measurements in a 2D cavitating shear layer. They observed that a complex combination of the production of vapour bubbles coupled with their collapse added additional velocity fluctuations, mostly in the main flow direction, while the turbulent shear stresses almost remained constant.
A review of measurement techniques for cavitating flows
Detailed flow measurements are essential for the understanding of cavitating flows. Due to the existence of non-transparent liquid/vapour mixtures, visual observation by a fast speed camera (high speed photography) is the most straightforward and widely-used method to capture the temporal evolution of cavitation structures, thereby providing insight into the underlying physics (Foeth et al. 2008a; Aeschlimann et al. 2012). Through post-processing of the high speed video images, it is possible to derive some quantitative data, such as the cloud shedding frequency and the cavity growth rate (Prothin et al. 2016; Jahangir et al. 2018). Synchronized with dynamic pressure measurements, high speed images can also reveal the pressure change associated with the cavity unsteady behaviors (Wang et al. 2017; Wu et al. 2017). On one hand, cavitation visibility helps to obtain its global flow characteristics. On the other hand, cavitation opacity hinders the measurements inside the two-phase region. In order to analyze the internal flow structures of cavitation, other techniques, able to visualize the two-phase morphology as well as measure quantitative data on void fraction and velocity, are required.
Table of contents :
LIST OF SYMBOLS
1. INTRODUCTION
1.1. INTRODUCTION TO CAVITATION PHENOMENON
1.2. OUTLINE OF THE THESIS
2. PHYSICAL BACKGROUND AND MEASUREMENT TECHNIQUES
2.1. SHEET AND CLOUD CAVITATION
2.2. MECHANISMS FOR CLOUD SHEDDING
2.3. STUDIES ON CAVITATION-TURBULENCE INTERACTIONS
2.4. A REVIEW OF MEASUREMENT TECHNIQUES FOR CAVITATING FLOWS
2.4.1. Local measurements by intrusive probes
2.4.2. Particle Image Velocimetry (PIV)
2.4.3. X-ray densitometry based on absorption contrast
2.4.4. X-ray velocimetry based on phase contrast
3. FAST X-RAY IMAGING TECHNIQUE AND QUANTITATIVE DATA EXTRACTION BASED ON IMAGE POST-PROCESSING
3.1. HYDRAULIC TEST RIG
3.2. X-RAY IMAGING MECHANISMS
3.3. X-RAY IMAGING TECHNIQUE
3.4. DATA EXTRACTION BASED ON IMAGE PROCESSING
3.4.1. Separation of the two phases
3.4.2. Void fraction measurement
3.4.3. Particle image velocimetry
3.5. COMPARISON BETWEEN CONVENTIONAL LASER PIV AND X-RAY PIV
3.6. PROCEDURES OF WAVELET-DECOMPOSITION-BASED IMAGE PROCESSING METHOD
3.7. IMPROVEMENT OF VOID FRACTION MEASUREMENT ACCURACY
3.8. CHAPTER SUMMARY
4. STRUCTURE AND DYNAMICS OF DEVELOPED SHEET CAVITATION
4.1. GLOBAL BEHAVIOR OF SHEET CAVITATION BASED ON HIGH SPEED PHOTOGRAPHY
4.2. MEAN VOID FRACTION AND VELOCITY FIELDS BASED ON X-RAY IMAGING MEASUREMENTS
4.3. PROBABILITY OF THE RE-ENTRANT FLOW: DISCUSSION
4.4. SPECTRAL ANALYSIS OF VOID FRACTION VARIATION
4.5. SUMMARY OF TWO-PHASE FLOW STRUCTURES INSIDE SHEET CAVITY
4.6. TURBULENT VELOCITY FLUCTUATIONS INSIDE SHEET CAVITY
4.7. VALIDATION OF THE REBOUD EMPIRICAL CORRECTION
4.8. CHAPTER SUMMARY
5. COMPARISON OF SHEET CAVITY STRUCTURES AND DYNAMICS AT DIFFERENT STAGES
5.1. EXPERIMENTAL MEAN VOID FRACTION
5.2. EXPERIMENTAL RESULTS OF MEAN VELOCITY DISTRIBUTIONS
5.3. ANALYSIS OF CAVITY INSTABILITY
5.4. FREQUENCY ANALYSIS OF VOID FRACTION VARIATION
5.5. EFFECT OF CAVITATION ON TURBULENT VELOCITY FLUCTUATIONS
5.6. CHAPTER SUMMARY
6. TOWARDS THE TRIAL OF INVESTIGATING CLOUD CAVITATION
6.1. MULTI-FUNCTIONAL VENTURI-TYPE TEST SECTION
6.2. MEASUREMENTS
6.2.1. Pressure measurements
6.2.2. PIV-LIF measurements
6.3. EFFECT OF THE SIDE GAP ON CAVITATION REGIME
6.4. MEASUREMENT RESULTS IN THE NEW TEST SECTION
6.4.1. Pressure loss versus cavitation number
6.4.2. Cavity length versus cavitation number
6.4.3. Velocity and pressure fluctuations
6.5. CHAPTER SUMMARY
7. CLOUD CAVITATION SHEDDING MECHANISMS AND GEOMETRY SCALE EFFECT ON VENTURI CAVITATING FLOW
7.1. EXPERIMENTAL SET-UP
7.2. RESULTS
7.2.1. The transitional cavitation
7.2.2. Re-entrant jet induced cloud cavitation
7.2.3. Condensation shock induced cloud cavitation
7.2.4. Pressure wave induced cloud shedding
7.3. DISCUSSION
7.3.1. Origin
7.3.2. Pressure rise and propagation velocity
7.3.3. Cloud shedding processes
7.4. SCALE EFFECT ON VENTURI CAVITATING FLOW
7.4.1 Problem background
7.4.2 Explanations to the observed scale effect
7.5. CHAPTER SUMMARY
8. OVERALL SUMMARY AND PERSPECTIVES
8.1. THE APPLICATION OF X-RAY IMAGING TECHNIQUE TO CAVITATING FLOWS
8.2. INTERNAL TWO-PHASE FLOW STRUCTURES AND DYNAMICS OF QUASI-STABLE SHEET CAVITATION
8.3. EFFECT OF CAVITATION ON TURBULENCE
8.4. CAVITATING FLOWS IN A VENTURI-TYPE TEST SECTION WITH SIDE GAPS
8.5. THREE MECHANISMS TO INITIATE CLOUD CAVITATION
8.6. GEOMETRY SCALE EFFECT ON THE VENTURI CAVITATING FLOW
8.7. PERSPECTIVES
REFERENCES
