A preliminary study of natural supercavitation in SAFL water tunnel

Siyao Shao, Ashish Karn, Roger Arndt, Jiarong Hong

Catalogues• Objectives and model descriptions

Project objectives (Slide 3 ) Model types and water tunnel description (Slide 4) Nomenclatures and acronym list (Slide 5)

• Experiments with Backward Facing Model (BFM) Experimental conditions (Slide 6) Sample images (Slide 7) Cavity’s evolution under vacuuming (Slide 8) Choking phenomena (Slide 9) Supercavity’s closure type (Slide 10-11) A comparison across different cavitator diameters (Slide 12-15)

• Experiments with Forward Facing Model (FFM) Experimental conditions (Slide 16) Sample images (Slide 17) Choking phenomena (Slide 18)

• A comparison across ventilated and natural supercavitation Dimension and shape (Slide 19-21)

• Future directions (Slide 22)

Project objectives

• Measurement of the minimum cavitation number with different models;• Obtaining of natural supercavity’s geometry digital images;• Observation of supercavity’s evolution under choking;• Effects of blockage on the natural supercavities; • A comparison across ventilated and natural supercavities’ geometries;• A preliminary study of natural supercavities’ closure.

Model types and water tunnel description

SAFL high-speed water tunnel

Test section geometry:L: 1.2m, W×H: 190mm×190mm

Maximum velocity attainable:Vinf=20m/s.

Forward facing model Backward facing model

Nomenclature and acronym list• Nomenclature • Acronym list

Cavitation number:

Froude number:

Blockage ratio:

D: test section diameterdc: cavitator diameterP(Po): test section pressurePv: vaporous pressure (natural supercavitation)Pc: cavity pressure (ventilated supercavitation)V: flow speed

FFM: Forward facing modelBFM: Backward facing modelTV: Twin vortexQV: Quad vortexRJ: Re-entrant jetFC: Foamy cavity

Pressure difference:or

Experimental conditions with BFM

SAFL

Test section 190x190D (mm) 214.4dc (mm) 20.0 30.0 40.0

D/dc 10.72 7.15 5.36

Velocity range, V (m/s) 9.1-11.4 8.4-10.8 7.5-10.5

Fr range 20.6-25.6 15.5-20.0 11.9-16.8

Lowest stable operation pressure, P (kPa) 15

σmin, theory 0.1996 0.3174 0.4556σv, attainable 0.2490 0.3535 0.5050

*: maximum operational velocity was set as 12.0m/s for the stable operating and safety concern, excluded cases operated under unstable conditions (P<15kPa);**: referred from Ellison 2011’s work;***: measured and calculated from a linear regression method, in the experiment operation, this value could bounce around this measured value.

Sample images

dc=20mm

dc=30mm

dc=40mm

σv=0.25

σv=0.35

σv=0.50

K-H Instability has strong effect on 20mm’s experiment (high flow speed)

Cavity’s evolution under vacuuming

• Vacuuming leads to the development of natural supercavity;• Rapid transition from foamy cavity to supercavity;• Reference case: 40mm cavitator, BFM.

Pres

sure

redu

ctio

n

Dense bubbly flow

Bubbly flow with spiraling bubble jets

Foamy cavity

Supercavity

ChokingOnce choking cavitation number is attained, further vacuuming does not influence it. Instead, there is a velocity drop to satisfy the same choking cavitation number*.

* the Pressure difference-dynamic pressure line provides the method of the measurement of choking/minimum cavitation number (the slope of this regression line corresponding to the choking cavitation number).

Pressure

reducti

on after

choking (th

e

slope o

f the l

inear

regres

sion lin

e is th

e

minimum/ch

oking cavita

tion nu

mber,

σ choking=0.50

50)

Cavity closures’ evolution: before choking (similar V)Stage 1: Dense bubbly flow

Stage 2: Bubble jet

Stage 3 (1): Foamy cavity & bubble jet

Stage 3 (2): Re-entrant jet & bubble jet

Stage 3 (3): Vortices (Quad vortex)

Stage 3 (4): Vortices (Twin vortex)

Stage 4: Twin vortex

σv=1.2607, P=43.9kPa,V=8.1m/s

σv=0.9116, P=32.5kPa,V=8.1m/s

σv=0.5173, P=19.4kPa,V=8.0m/s

σv=0.5327, P=19.0kPa,V=7.8m/s

σv=0.5070, P=18.5kPa,V=7.9m/s

σv=0.5067, P=18.6kPaV=7.9m/s

σv=0.4979, P=17.6kPaV=7.7m/s

*: velocity descending is due to blockage effect;**: 40mm cavitator, BFM

A evolution of natural supercavity closure (Under choking)TV

TV

TV

QV

QV

RJ & Torodial bubbles

RJ & Torodial bubbles

σv=0.4979, V=7.7m/s

σv=0.5041, V=8.4m/s

σv=0.4976, V=8.7m/s

σv=0.5029, V=9.3m/s

σv=0.5004, V=9.6m/s

σv=0.5047, V=10.1m/s

σv=0.4990, V=10.4m/s*: 40mm cavitator, BFM and minimum cavitation number measured is 0.5050

Comparison of obtained choking cavitation numbers with Brennen’s simulations

 

Cavity geometry analysis

• Only supercavity data (under choking condition) presented;• Unlike Brennen’s choking definition (infinite cavity geometry), choking in the

experiment corresponding to the flow velocity start to drop continuously to fit the ‘choking lines’ of each cavitator size;

• rc/(L/2) shows a better agreement with Brennen’s result compared to ventilated cases;

• rc/(L/2) only reflects the front part (before maximum diameter) of the cavity’s geometry.

The change in supercavity shape after choking

For all the blockage ratios considered, supercavity size (before maximum diameter) does not change with Fr, once choking cavitation number has been attained.

• Experiments were operated under choking condition• With flow velocities’ (test section pressure) increasing, a evolution of cavity

closure occurred from TV to (QV) to RJ*.

* A similar trend was observed in the ventilated supercavitation experiment (Ashish 2015) (with the increasing of ΔP, a evolution of cavity closure occurred from TV to RJ).

σv,choking=0.5050, 40mm BFM

σv,choking=0.3535, 30mm BFM

σv,choking=0.2490, 20mm BFM

Experimental conditions with FFM

SAFL

Test section 190x190D (mm) 214.4dc (mm) 30.0 40.0

D/dc 7.15 5.36

Velocity range, V (m/s)* 8.7-10.7 7.7-10.7

Fr range 15.9-19.7 12.3-17.1

Lowest stable operation pressure, P (kPa) 15

σmin, theory** 0.3174 0.4556

σv, attainable*** 0.3205 0.4594

*: maximum operational velocity was set as 12.0m/s for the stable operating and safety concern, excluded cases operated under unstable conditions (P<15kPa);**: referred from Ellison 2011’s work;***: measured and calculated from a linear regression method, in the experiment operation, this value could bounce around this measured value.

Sample images*,**

dc=40mm, σv=0.47

dc=30mm, σv=0.31

*: smoother cavity surface observed compared to BFM experiments. (no wake signature etc.);**: no clear supercavity observed with 20mm cavitator.

100mm

100mm

ChokingOnce choking cavitation number is attained, further vacuuming does not influence it. Instead, there is a velocity drop to satisfy the same choking cavitation number* ， **,***.

*： the theoretical analysis of choking cavitation number was provide by Ellison 2010 (MS thesis);**: the Pressure difference-dynamic pressure line provides the method of the measurement of choking/minimum cavitation number;***: lower choking cavitation number measured compared to the BFM experiments.

Pressure

reducti

on afte

r choking (th

e

slope o

f the l

inear re

gressi

on line i

s the

minimum/ch

oking cavita

tion n

umber)

A comparison of cavity geometry of natural supercavity to ventilated supercavity

• Only supercavity (under choking) data presented;• Both FFM and BFM shows a good agreement with Brennen’s result;• A better agreement of the cavity geometry to the Brennen’s result was

observed compared to ventilated supercavity (negligible Fr effect).

Comparison of natural and ventilated supercavitiesBFM 30mm cavitator

The cavity size and shape can be different between natural and ventilated cases even at same cavitation numbers (actual cavitation number for natural case could be lower than 0.43 according to geometry data, and a temperature drop may exists across the cavity

surface, this may leads to the cavitation number’s discrepancy).

Natural SupercavityV = 9.0m/s,

rc/(L/2)=0.15

rc/(L/2)=0.09

Ventilated SupercavityV = 4.0m/s

σc=0.40

σv=0.40

Comparison of natural and ventilated supercavitiesBFM 30mm cavitator

The cavity size and shape can be similar between natural and ventilated cases even at different cavitation numbers (A water vapor pressure drop may occurs across the surface of

natural supercavity).

Natural SupercavityV = 8.4m/s,

rc/(L/2)=0.06, Dmax=71.06mm

rc/(L/2)=0.06Dmax=77.94mm

Ventilated SupercavityV = 7.0m/s

σc=0.35

σv=0.32

Future directions of natural supercavitation study in SAFL

• Test different models to study the structure influence on the natural supercavity (choking cavitation number, cavity geometry, evolution of natural supercavity);

• Develop a stable FFM for the natural supercavitation experiments;• Develop a new shape factor which could reflect the cavity’s dimension

properly;• A detailed study into the temperature drop across the surface of natural

supercavity to make a correction of cavitation number.