Experimental Study on the Two Sensitivities of Sloshing Impact Pressures

MHLMarine Hydrodynamics Lab.

Yangjun Ahn*, Sang-Yeob Kim, Yongwhan Kim

Seoul National University

International Research Exchange Meeting on Ship and Ocean Engineering

December 21 – 22, 2012Osaka, Japan

State of the Arts: Gas-liquid Density Ratio• Identifying dimensionless numbers

Abramson et al. (1974), Bass et al. (1980) Viscosity and surface tension do not need to be included.

• Suggestion of Froude number and its Limits Bass et al. (1980), Faltinsen and Timokha (2009) Ullage pressure should be Froude scaled, but Froude number cannot cover local phenomenon.

• Suggestion of various scaling properties Cavitation # : Faltinsen and Timokha (2009), Braeunig et al. (2010) Euler # : Lugni et al. (2010), Mach # : Bass et al. (1080), Dias et al. (2007) Local phenomenon, compressibility, and phase changes require proper scaling method, rather

than Froude scaling.• Phase change and gas-liquid density ratio (ρgas / ρliquid )

Bass et al. (1980), Maillard and Brosset (2009), Yung (2009, 2010), Braeunig et al. (2009, 2010)

Ambient air cannot be representative to the natural gas.

• Problems Limited test conditions, and results. Gas-liquid density ratio (ρgas / ρliquid) needs to be checked.

Research Backgrounds

• Bernoulli Equation (Yung et al., 2009)

• How Many oscillations for each case?• How much affect the asymmetric phenomenon?

0.0040gas NG

liquid LNG

Actual LNG cargo

ambient airρgas = 1.2 kg/m3

waterρliquid = 1000.0 kg/m3

0.0012gas air

liquid water

Most sloshing experiments

0.0012 0.0040gas heavy

liquid water

mixed gasρgas = 4.0 kg/m3

waterρliquid = 1000.0 kg/m3

Present study

22

2 21 2

' ' 1 ' 1 1 1 1' ' ' ,' 2 ' 2 ' '

gl l GG Fr W

uu z zt Fr t k ke

where 1 G

L

Test 1: Gas-liquid Density Ratio

Test 2: Time Window

Condition Test 2 : Time window & Asymmetric motion

Excitation Motion Harmonic, regular with 2D model

Filling level 95%H, 70%H, 50%H, 25%H, and 15%H

Excitation frequency 0.7ω0 - 1.3ω0

Simulation time 1,000 periods

Test Condition

Condition Test 1: Impact pressure measurement

Excitation Motion Harmonic, regular with 2D model

Filling level 95%H, 70%H, 25%H, and 15%H

Excitation frequency 0.7ω0 - 1.4ω0

Density ratio (ρgas / ρliquid) 0.0012 - 0.0039

Simulation time 200 periods

Test 1: Gas-liquid Density Ratio

Test 2: Time Window

%H = % filling of the model tank height

SNU Sloshing Experimental Facility

Storage

Coupler

DAQ board

High-speed camera

Pressure sensor

Motion platform& controller

Model tank

Motion platformMotion controller

Coupler

Data acquisition system

Monitoring system

Pressure sensors

Video recorder

Data storage server

• Components of the mixture

• Problems of Application Density level test method for the Non-flammable gas High green house potency Dissolved mixed gas in water

• Solutions The inverse estimate by using oxygen level tester Confirmation of dissolved gas density

Products Density (kg/m3) Ratio (%)

Sulphur hexafluoride (SF6) 6.162 56.9

Nitrogen (N2) 1.146 43.1

Mixture 3.999 100.0

Application of Mixed Gas (1)

• Airtight model tank Liquid type silicon Rubber ring Bubble test

• Mixed gas injection Valves open Mixed gas injection Check the pressure

• Mixture concentration check Oxygen tester Check the portion of gas Injection up to the target density

• Dissolution Forced excitation motion under the violent condition Check the portion of gas Iteration

Application of Mixed Gas (2)

Model Tank

Geometry of model tank10

946

5

5

10118

Panel 1

Unit = mmTank roof

Panel 2

Configuration of sensors

118.0

67.0 (hʹ = 0.10)

201.0 (hʹ = 0.30)

10

Both sides on the tank roof One side on the side wall

Side wall670

Pressure sensor

KISTLER 211B5 (Φ = 5.54 mm)

Data Analysis• Peak Sampling

Sample peak pressure signals from the experimental data Sampled peaks are used to produce statistical results

• Peak Over Threshold Method Widely-used sampling method Threshold pressure Sampling time window

Test 1 Results (1) : ρgas / ρliquid• Filling : 95%H• Locations : Tank roof• Results

• The average of 1/10 largest peak pressure decreases as the density ratio increases. • Decrease level depends on the excitation frequency.

Excitation amplitude = 0.042 l Excitation amplitude = 0.016 l

l = Tank length in x-direction

Test 1 Results (2) : ρgas / ρliquid• Filling : 70%H• Locations : Tank roof• Results

• The average of 1/10 largest peak pressure decreases as the density ratio increase. • Variation of the density ratio does not affect under the particular frequency.

Excitation amplitude = 0.042 l Excitation amplitude = 0.016 l

• Jump phenomenon The density ratio does not critically affect magnitudes

of pressures around the particular excitation frequencies.

Sloshing flows shows irregular movements.

• Movies Filling : 70%H ω/ω0 : 1.20

Test 1 Results (3) : ρgas / ρliquid

ρgas/ ρliquid = 0.00199 ρgas/ ρliquid = 0.00392 ρgas/ ρliquid = 0.00396

A B C

AB

C

• Filling : 25%H & 15%H• Locations : Side wall• Results

• The average of 1/10 largest peak pressure decreases as the density ratio increases. • Decrease level depends on the excitation frequency.

Test 1 Results (4) : ρgas / ρliquid

Filling level = 15%HExcitation amplitude= 0.1l

Filling level = 25%HExcitation amplitude= 0.1l

Filling Level(% of tank height)

Excitation Amplitude(% of tank length)

Excitation Frequency(ω/ω0)

95 1.5, 4.2, 10.0 0.7 – 1.3

70 1.5, 4.2, 10.0 0.7 – 1.3

50 1.5, 4.2, 10.0 0.7 – 1.3

25 10.0 0.7 – 1.3

15 10.0 0.7 – 1.3

• Test matrix

• Time history

Filling Level(% of tank height)

Excitation Amplitude(% of tank length)

Excitation Frequency(ω/ω0)

95 1.5, 4.2, 10.0 0.7 – 1.3

70 1.5, 4.2, 10.0 0.7 – 1.3

50 1.5, 4.2, 10.0 0.7 – 1.3

25 10.0 0.7 – 1.3

15 10.0 0.7 – 1.3

Test 2 Condition : Sensitivity of Duration

ω 0 : excitation frequencyω0 : Frequency of the fundamental mode of sloshing

200 oscillations200-1

500 oscillations500-1

500 oscillations500-2

200 oscillations200-2

200 oscillations200-3

200 oscillations200-4

200 oscillations200-5

1000 oscillations1000

Test 2 Movies : Sensitivity of Duration• 70%H filling & 0.015L amplitude

ω/ω0 = 0.95 ω/ω0 = 1.00

ω/ω0 = 1.35 ω/ω0 = 1.50

Test 2 Results (1) : Sensitivity of Duration• 70%H filling & 0.015L amplitude

1000 oscillations ( ) 500 oscillations ( )200 oscillations ( )

Average of 1/10 largest peaks

Impact occurs once every 3 times

No impact once or twiceevery 10 times

Impact occurs once every 3 times

Average of 10 largest peaks

Test 2 Results (2) : Probability of Exceedance• 70%H filling & 0.015L amplitude• ω/ω0 = 1.03

1000 oscillations ( ) 500 oscillations ( )200 oscillations ( )

Weibull fitting GEVD fitting

X

Test 2 Results (3) : Probability of Exceedance• 70%H filling & 0.015L amplitude• ω/ω0 = 0.95

1000 oscillations ( ) 500 oscillations ( )200 oscillations ( )

Weibull fitting GEVD fitting

X

Concluding Remarks

• Test 1: Gas-liquid density ratio Sloshing pressure generally decreases as the density ratio (ρgas/ρliquid) increases, but

not always, not linearly. The density ratio locally affects the sloshing pressure. The resonance frequency of each condition does not change. The jump phenomena were observed in certain rages of frequency, and the density

ratio does not affect under the jump phenomena condition.

• Test 2: Time window Duration of 200 oscillation is not enough for 2D regular sloshing experiment, and at

least duration of 500 oscillation is recommended. The average of 1/10 largest peak pressure is rather assembled than the average of 10

largest. It is not clear that which method of statistics of extremes is the most reliable:

Weibull, Pareto, or GEVD. The result depends on the test condition.

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