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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
THANK YOU