Background and Motivation Cavitation has been investigated in a variety of flows: Tip vortices, e.g., Arndt et al. (1991), Arndt and Maines (2000), Hsiao et al. (2003). Lifting and curved surfaces, e.g., Leger and Ceccio (1998), Astolfi et al. (2000), Gopalan and Katz (2000). Free shear layers, e.g., Ooi and Acosta (1983), O Hern (1990), Ran and Katz(1994), Gopalan et al. (1999), Laberteaux and Ceccio (2001). Literature on cavitation for 2D turbulent shear layer flow past an open cavity is non-existent. Previous studies emphasized self-excited (self-sustained) oscillations of shear layer; (e.g., Rockwell and Knisely (1979), Tang and Rockwell (1983), Lin and Rockwell (2001), etc.); Lack of information on the pressure field and the associated occurrence of cavitation. Cavitation: Vaporization of liquid under the effect of depressurization (Brennen, 1995, Arndt, 2002). Knowledge of the pressure distribution is of fundamental importance for understanding the inception and subsequent develpoment of cavitation.
Use of Cavitation Bubbles as Pressure Sensors Cavitation inception index i p i p v U Pressure coefficient of the flow field i 1 2 U Principle of use of cavitation bubbles as pressure sensors If cavitation bubbles are observed in the flow field, then that means the instantaneous local minimum fluctuating pressure reaches the vapor pressure level, i.e., pmin p v. Thus at that instance, the local minimum pressure coefficient has roughly the same magnitude as the cavitation index, more specifically, Cpmin i, since we can always adjust the ambient pressure so that the 2 conditions for cavitation at local area are satisfied, i.e., Cp min ( pmin p ref ) (0.5U ) i. The adjustment of the ambient pressure will not affect the flow structure, thus the magnitude of the cavitation index i represents the maximum possible fluctuation of Cp in the flow field. Representative work of use of cavitation bubbles as pressure sensors Ooi and Acosta (1983), T.J. O Hern (1990), Ran and Katz (1991, 1994) i Measurement of the inception index Carried out using visual observations by keeping the velocity constant and reducing the pressure of the facility until cavitation appears. p Cavitation inception index Mean static pressure at inception Vapor pressure of the liquid Free stream velocity Density of the Liquid Cp p v 2 p p ref 1 2 2 U pressure P min time Lower ambient Pressure ~ P P ref ~ P P ref ~ P i ~ P v
Lock-on Behavior of Cavitation Inception on 2D Cavity Flow Flow Direction Cavity Trailing Edge 10 mm (a) t = 0 s (b) t = 33.3s (c) t = 66.7 s (d) t = 100 s (e) t = 133.3s (f) t = 200 s Free stream speed: 10 m/s Recording speed: 30,000 fps Cavitation inception index: 0.9 (water is saturated with air) Speed of replay = 10 fps 10 mm Top view Flow (g) t = 266.7 s (h) t =400s (i) t = 466.7 s Flow (j) t = 666.7 s (k) t = 800 s (l) t = 933.3 s (m) t = 1133.3 s (n) t = 1266.7s (o) t = 1466.7 s Click to launch the movie Lock-on: Occurs above the step. Flow (p) t = 1566.7 s (q) t = 1833.3 s (r) t = 1933.3 s (s) t = 2200 s (t) t = 2333.3 s (u) t = 2533.3 s The cavitation process appear to be cyclic. Periodic: ~ 320 Hz.
Ensemble Averaged Velocity and Pressure Distributions Ue = 5.0 m/s; Re=167,500 (based on cavity width) u / U e v /U e Pressure Distribution upstream of T.E. Cp Trailing Edge (a) Cavity Wall Trailing Edge (b) Cavity Wall Cp Cprms -0.045 Lowest mean pressure location in entire flow field Trailing Edge (c) Cavity Wall -0.2 Trailing Edge (d) Cavity Wall
i PDF of Pressure Fluctuations around the Trailing Corner Developed Cavitation at = 0.37, Ue = 10m/s, D.O. level Ue = 5.0 m/s; Re=167,500 (based on cavity width) 0.8ppm Cavitation Inception Index ~ -0.7 Cp P v P i P 1 2 U (m/s) Pv U Vapor pressure of water Static pressure upstream of cavity opening P, U Cpmin i Cavity Trailing Edge The spatial pressure measurements are in full-agreement with cavitation indices measurements.
Developed Cavitation at = 0.37, Ue = 10m/s, D.O. level 0.8ppm Recording speed: 8,000 fps; Replay speed: 10 fps; Top View 38 mm Click to launch the movie Trailing-Edge Flow Shedding vortices away upstream Trailing edge cavitation appears Shedding vortices approach T.E. Trailing edge cavitation disappears
Developed Cavitation at = 0.37, Ue = 10m/s, D.O. level 0.8ppm Recording speed: 8,000 fps; Replay speed: 5 fps Click to launch the movie Recording speed: 30,000 fps; Replay speed: 10 fps Click to launch the movie
Developed Cavitation at = 0.37, Ue = 10m/s, D.O. level 0.8ppm 38 mm (p) t = 0 s (q) t = 500s (r) t = 750 s (p) t = 1250 s (q) t = 1500s (r) t = 2000 s (p) t = 2250 s (q) t = 2750s (r) t = 3000 s (p) t = 3250 s (q) t = 3750s (r) t = 4000 s (p) t = 4250 s (q) t = 4500s (r) t = 5000 s Flow Shedding vortices away upstream (p) t = 5250 s (q) t = 5500s (r) t = 5750 s Trailing edge cavitation appears Shedding vortices approach T.E. Trailing edge cavitation disappears Recording speed: 8,000 fps; Replay speed: 10 fps Click to launch the movie
Low Vorticity Shedding Vortex Location and Pressure above T.E: Sample Pictures P (pascal) L U Shedding vortex near T.E. Cavity Trailing Edge Cavity Trailing Edge High pressure above T.E. High Vorticity L U P (pascal) Shedding away upstream Cavity Trailing Edge Cavity Trailing Edge Low pressure above T.E. Ue = 5m/s
Conditional Sampling L U Cp PDF of V Threshold: V<0 Threshold: V<0 217 samples L U Cp Threshold: V>0 Threshold: V>0 753 samples
Vortex Shedding Frequency from Pressure Spectrum 0.006 0.006 0.005 0.005 0.004 0.004 0.003 0.003 0.002 0.002 0.001 0.001 Flow Direction P, U Cavity Wall 0 1 10 100 1000 10000 Frequency (Hz) Ue=5m/s Trailing Edge fw U e Location of Pressure Transducer fl 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 fl 1 0.5 n Ue 4 0 1 10 100 1000 10000 Frequency (Hz) Ue=10m/s Ue=5m/s Theory Ue=10m/s fl c 1 n U U 4 e c Take 0. 5 e U e (Martin et al, 1975; Blake, 1986 L=38.1 mm 0 0 1 2 3 4 n Frequency of shedding vortices impinging on the trailing corner based on high-speed movie: ~320Hz. Cycle: ~3ms. Shedding vortex convection speed: 5~6m/s. In agreement with Blake (1986).
Cavitation Inception High-Speed Movie Free stream speed: 10 m/s Recording speed: 30,000 fps Replay speed: 10 fps Dissolved Oxygen Level: 8.0 ppm Cavitation inception index: 0.91 Dissolved Oxygen Level: 1.4 ppm Cavitation inception index: 0.52 Click to launch the movie Click to launch the movie 10 mm 10 mm
Forward Protruding of Cavitation in Degassed Water Flow Direction Side view 4 mm (a) t= 0.0 ms (c) t= 1.0 ms (b) t= 0.5 ms (d) t= 1.5 ms Free stream speed: 10 m/s Image recording speed: 2,000 fps Cavitation inception index: 0.53 Dissolved oxygen concentration: 1.7 ppm (e) t= 2.0 ms Cavity Trailing Edge (f) t= 2.5 ms
A Rare Cavitation Event Captured in the Shear Layer Side view Flow Direction (a) t= 0.0 ms (c) t= 1.0 ms 4 mm (b) t= 0.5 ms (d) t= 1.5 ms Free stream speed: 10 m/s Image recording speed: 2,000 fps Cavitation inception index: 0.53 Dissolved oxygen concentration: 1.7 ppm Cavity Trailing Edge The pressure minima in the shear layer are sufficiently low to initiate cavitation once a nucleus is available, though very rare statistically.
Measured Cavitation Inception Index Definition of cavitation inception index: P v P U i P 1 2 P U Vapor pressure of water v Static pressure measured upstream of cavity opening Free stream velocity measured upstream of cavity opening Density of water i Measured cavitation inception indices at different dissolved oxygen concentrations Flow Direction P, U Trailing Edge U (m/s) Cavity Wall L=38.1 mm H=30.0 mm Cavitation inception index is velocity dependent. Note: the dissolved air content has a substantial impact on the cavitation inception index.
PDF of Pressure Fluctuation and Measured Cavitation Inception Indices Cavitation index: 0.53, D.O.: 1.7ppm Cp rms Cavitation Inception Indices Ue=10m/s Re=335,000(based on cavity width) Re = 340 U (m/s)
Conclusions The onset of cavitation always occurs on top of the cavity trailing edge. The cavitation inception process appears to be cyclic, with frequency that matches theoretical predictions of vortex shedding frequencies. The mean spatial pressure distribution and PDFs of pressure fluctuations explains why the onset of cavitation is always locked on the cavity trailing edge. Flow induced by interaction of shear layer vortex structures with the downstream corner generates a cyclic pressure field, and consequently, a cyclic cavitation process, even at very low cavitation indices. Pressure velocity and pressure-rate of strain correlations have been measured. Analysis of trends is in progress.