1 / 21

by J. N. Newman jnn@mit

Workshop on Very Large Floating Structures for the Future Trondheim -- 28-29 October 2004 Efficient Hydrodynamic Analysis of VLFS. by J. N. Newman jnn@mit.edu. Theoretical formulation and restrictions. Linear (and 2 nd order) potential theory (small amplitude waves and motions)

telyn
Download Presentation

by J. N. Newman jnn@mit

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Workshop on Very Large Floating Structures for the Future Trondheim -- 28-29 October 2004Efficient Hydrodynamic Analysis of VLFS by J. N. Newman jnn@mit.edu

  2. Theoretical formulation and restrictions • Linear (and 2nd order) potential theory (small amplitude waves and motions) • Frequency-domain analysis (can be transformed to time domain if necessary) • No considerations of current, slamming, viscous loads

  3. Computational approach • Boundary Integral Equation Method (BIEM) a.k.a. `Panel Method’ with free-surface Green function (source potential) • General-purpose codes are applicable to a wide variety of structures and applications (different configurations, air-cushions, hydroelastic effects, multiple bodies) • All relevant hydrodynamic parameters can be computed (loads, RAO’s, pressures, drift forces, free-surface elevations, etc.)

  4. Computational tasks and restrictions • Geometric representation of submerged surface • Structural representation (if hydroelastic) • Confirmation of results requires convergence tests • Computing cost (time and memory) increases rapidly with number of unknowns • Short wavelengths aggravate everything!

  5. recent developments • Higher-order panel method with B-spline basis functions for the solution • pFFT Accelerated solver O(N log N) • Exact geometry • CAD coupling

  6. Examples of Applications and Results • Rigid barge 4km x 1km x 5m • Same barge with hydroelasticity • Hinged barges with hydroelasticity • Hinged semi-subs with hydroelasticity • Large arrays of cylinders

  7. Drift forces on 4km x 1km x 5mrigidbargeWave incidence angle 45o -- Water depth = 50m • Red: Surge drift force • Black: Sway drift force • higher-order method (727 unknowns) • Solid lines: Accelerated pFFT • (`precorrected Fast Fourier • Transform’) method with • 43,000 low-order panels • (Order N log N) • Both methods take about • 0.4 hour/period on a 2GHz PC • Dashed lines: Asymptotic • approximation for short • wavelengths

  8. Methodology for hydroelastic analysis • Structural deflections represented by generalized modes • Uniform stiffness ratio EI/(mass*L^2) assumed for simplicity • Extended vector of RAO’s gives the modal response • Cf. `direct’ method where the structural and hydrodynamic analyses are integrated

  9. 4km x 1km x 5m barge, 27*16 generalized modesL/wavelength = 5,10,20 – depth = 20m – Period = 57,28,15 seconds DEFLECTION PRESSURE Head seas 45 degrees Head seas 45 degrees 5 5 10 20 From C.-H. Lee, `Wave interactions with huge floating structure’, BOSS `97

  10. Array of 5 barges, each 300x80x6mjoined by simple hinges (red)

  11. Symmetric/antisymmetric modes for a hinged structure with five elementsModes j=7-11 and j=12-16 are 1st and 2nd Fourier modes j=17-96 are 3rd to 18th Fourier modes (not shown)

  12. Array of five 300x80x6m barges with zero stiffnessRAO of each mode (j=1-96), period 12 seconds

  13. Array of five barges with stiffness SMotion and shear force at the upwave hinge

  14. Array of 5 hinged semi-subs, each 300m long(lower figure shows zoom of one element)

  15. Array of five semi-subs with stiffness SMotion and shear force at the upwave hinge

  16. Array of 100 x 4 = 400 cylindersRadius=11.5m, Draft=20m, Axial spacing=40m

  17. Mean drift forces on Array of 100 x 4 cylinders Wave incidence angle 45o -- Water depth = 50m Based on Higher-order method with exact geometry. NEQN=4200 2.3 hours per Wave period On 2GHz PC

  18. Array of 100 x 25 = 2500 cylindersRadius=11.5m, Draft=20m, Axial spacing=40m

  19. Drift forces on the 100x25 Cylinder Array Wave incidence angle 45o -- Water depth = 50m 240,000 low-order panels were used here (96 on each Cylinder). These computations were performed on a 2.6GHz PC using the accelerated pFFT method. The CPU time averaged about one hour per period. The peak magnitudes are much larger below 8 seconds, where near-trapping occurs between adjacent cylinders.

  20. Conclusions • Contemporary hardware/software can be used to analyze wave effects for many VLFS configurations with length scales of 1-4 km • These capabilities will increase in the future • Short wavelengths, bottom topography, breakwaters, etc, present special challenges • Analytic/asymptotic theories are still required for >>1km length scales, e.g. ice fields, and to validate computations in the short-wavelength regime

  21. Further information: www.wamit.com/Publications Special Thanks: Chang-Ho Lee, WAMIT, Inc.

More Related