HYDRODYNAMIC ANALYSIS

TRAININGYUNI ARI WIBOWO

PRINSIP HIDRODINAMIKA

• Menghitung besarnya beban fluida air laut dari gelombang dan/atau arus yang bekerja pada struktur

Prinsip Hidrodinamika

Pemodelan medan aliran

Perhitungan kecepatan

aliran

Perhitungan tekanan yang

timbul

Gaya & Momen aksi

fluida

1

2

3

4

MEDAN ALIRAN

• Source• Uniform

• Sink • Vortex

MEDAN ALIRAN KOMBINASI

Uniform + Source Flow Superposition flow

Medan Aliran Fluida pada Struktur

• Strip Theory 2D• (+) Input mudah• (+) Simpel• (+) Waktu running singkat

• (-) Model kurang detail

• 3D Diffraction Theory (panel method)• (+) Model detail• (+) Lebih akurat

• (-) Input susah• (-) Waktu running lama

PERSAMAAN GERAK

Gaya Inersia

• Gaya inersia Finersia = m 𝑢

• Translasionalmass, added mass & COG

• Rotationalmass, added mass & Radius of Gyration (I = M x R2)

• Added mass arah gerak vessel arah datang gelombang

Gaya Redaman

• Gaya redaman Fredaman = C 𝑢

• Faktor redaman, Cf = C/Cc

• Cc = 2 𝐾(𝑚 +𝑚𝑎)

• Redaman C biasanya ditentukan

Gaya Pengembali

• Gaya pengembali Fpengembali = k 𝑢

• Hydrostatic stiffness gerakan ke arah vertikal

• Heave (33) : x g x WPA

• Heave-pitch (35) : x g x WPA x (LCF – LCB)

• Roll (44) : x g x V x GMT

• Pitch (55) : x g x V x GML

FREKUENSI NATURAL

• Frekuensi natural terjadinya resonansi (dengan frekuensi gelombang)

• 𝜔 =𝐾

𝑚+𝑚𝑎

• 𝜔 = frekuensi natural

• 𝐾 = kekakuan gerakan

• 𝑚 = massa struktur

• 𝑚𝑎 = massa tambah gerakan

GAYA EKSITASI

• Gaya eksitasi gaya gelombang 1st order

• F = 𝐴 cos(𝜔𝑡)

• Gaya eksitasi = gaya tekanan dinamis + gaya percepatan partikel gelombang

RESPONSE AMPLITUDE OPERATOR (RAO)

• RAO karakteristik gerakan• F = gaya eksitasi

• K = kekakuan

• w = frekuensi gelombang

• wn = frekuansi natural

• Cc = redaman kritis

• Periode gelombang 3s – 20s

22

2

0

21

/

nn

zz

Cc

KFz

w

w

w

w

Respon Struktur

• Respon struktur Respon spektra

• Respon spektra = RAO2 x Spektra gelombang

• Puncak RAO pada frekuensi gelombang = Puncak energi gelombang (dalam spektra gelombang) Resonansi (magnifikasi)

• Respon struktur nilai-nilai stokastik :• s = Amplitudo signifikan (2,00 × 𝑚0)

• av = Rata-rata amplitudo (1,25 × 𝑚0)

• max = Amplitudo ekstrim ( 𝜁𝛼 = 𝑚0 × 2 ln602𝑇

2𝜋𝛼

𝑚2

𝑚0)

Fenomena 2nd Order

• Large moored tankers Low frequency resonance associated withslowly varying wave drift force

• Signifikasi pengaruh 2nd order kedalaman + mooring

• Combination of large mass + small spring forces (slack mooring)

• 𝜔 =𝐾

𝑚

small

large

Very small

Associated with

Drift force / low frequency

Resonance

Evidence of 2nd order loads

• Consider the case where

• 𝐹 = 𝐴1 cos 𝜔1𝑡 + 𝐴2 cos 𝜔2𝑡

• 𝐹2 =𝐴12

2+

𝐴22

2

+𝐴12

2cos 2𝜔1𝑡 +

𝐴22

2cos 2𝜔2𝑡

+𝐴1𝐴2cos[(𝜔1-𝜔2)𝑡] + 𝐴1𝐴2cos[(𝜔1+𝜔2)𝑡]

Mean components Rapidly varying components

Slowly varying components

NON-LINEAR wave load effect

• Mean wave drift force determine the equilibrium position of themoored system (together with wind and current). They are importantfor the design of mooring lines

• Slowly varying wave drift force the force have frequencies muchslower than the wave elevation frequency. These can excite resonantmodes in the horizontal position of the moored vessel.

• Rapidly varying wave drift force these force have frequencycomponents which are higher than the wave elevation frequency.

LOADS IMPACT TO THE SYSTEM

LOADS IMPACT TO THE SYSTEM

SUMMARY

• Hydrodynamic analysis needs :• Surface model• Mass (displacement)/draft, COG, RG• Heading of propagated waves

• Mooring analysis needs :• RAO (Response Amplitude Operator)/Transfer Function• Added mass & damping matrix• Mean wave drift force (mean drift force + slowly varying force) QTF (Quadratic

Transfer Function)• Excitation force (Panel force)• Wave spectra (include : Hs & T), Current & Wind load• Mooring layout• Mooring equipment

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