Research Activity of LRETC: Structures

Transcription

1 Research Activity of LRETC: Structures Y. Kim, W.I. Lee, M.H. Cho (MAE) and In-Sik Nho (CNU) Seoul National University The Lloyd s Register Educational Trust (LRET) y g ( ) Marine & Offshore Research Workshop February, 2010 at Engineering Auditorium, NUS

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3 Springing WISH-FLEX by Y. Kim (SNU)

4 Hull Hydroelasticity - Springing & Whipping WF response HF response VBM spectrum with springing

5 1 BV Flex 1 BV Flex 0.0L Uz at L Uz at Wave Freq Wave Freq. Vertical velocity RAO at FP and AP (363m ship) PM Spectrum Energy from linear wave is not ignorable any more.

6 Project Summary Objectives: Development of a new computational technique for ship hydroelasticity y problems including slamming-whipping g and springing, using a time-domain hybrid BEM-FEM method Related Projects: (1) WISH-FLEX JIP (2) ONR NICOP Project (3) LRETC Project PI: Y. Kim (SNU NAOE), S.J. Kim (SNU MAE, for WISH-FLEX JIP) Primary Research Works Task 1 Developing a new hybrid BEM-FEM method for ship hydroelasticity Task 2 V&V of the developed method for slamming-whipping and springing

7 WISH-FLEX Kinematics (Displacement/ Velocity) Hydro: WISH (BEM) Dynamics (Pressure/ re/ Nodal Force) WISH- FLEX Structure: Vlasov Beam (FEM)

8 Coupled Equation Md + Cd + Kd = F Structural domain Finite element method Fluid domain Boundary element method Domain decomposition method Hybrid BEM/FEM scheme Coupling takes place via forcing terms of both equation through the interface boundary

9 Hydro: Boundary Element Method Applying Green s 2 nd identity G φd φd G φd + φd ds GdS = GdS φd ds n n n n S S S B F B F - Unknown on body surface: velocity potential - Unknown on free surface: normal velocity S φ φ nn d d, S B φ φ n d d, S F Discretize computational domain using higher order B-spline function φ ( x, t) = φ, ( t) B ( x), ζ ( x, t) = ζ, ( t) B ( x) d i d i φd φd ( x, t) = ( t) Bi ( x) n i n i i d i d i i Y Z X 1 3hx 2 ( ), 3hx hx x h 2 < x < x hx hx hx bx ( ) = ( x + ), < x< 2 hx h h 3 h 2 2 ( x x x x + ), < x < 2h x

10 Structure: Finite Element Method z 7-DOF 1D beam element using cubic polynomial interpolation function y Shear deformation (Timoshenko beam) ( 0,0, zs ) S φ Warping distorsion i effect for thin walled open section (Vlasov Coupling between bending & torsion z assumption) Q 0,0, z ) Coupling between horizontal bending and torsion y e g G ( Q e S S ( 0,0, z S ) Beam offset

11 Eqn. of Motion - Direct & Modal Given FE equation MU + CU + KU = f Direct integration using Newmark-β method 2 1 U = U + Δt δu + ( 1 δ) U, U = U + ΔtU + Δt α U + αu 2 t+ Δt t t+ Δt t t+ Δt t t t t+ Δt 1 δ t t t t 1 t 1 t 1 t +Δ +Δ M+ C+ K 1 2 U = F + M α t α t U U U Δ Δ αδt αδt 2α Modal superposition method δ t δ t t 1 t δ + C + +Δ 1 U U U αδt α 2α MU + KU = = = Kφ ω Mφ K ω M 0 U () t = ΦX () t MΦX + CΦX + KΦX= F T 2 T X + Φ CΦX + Ω X = Φ F, Δ = diag(2 ω ς ) i i

12 Iteration for Coupling - Newton & FP Coupled equations f = p F(U,U, φ ) = 0 for fluid f s = U S(p) = 0 for structure Newton method (Secant method) I D U U F Δp f p U = D ps I ΔU D =, D = U F ps s U p Fixed point iteration k+ 1 k U t+δ t = S ( pt+δ t ) k+ 1 k+ 1 k+ 1 k+ 1 p = F( U, U, φ ) t+δ t t+δ t t+δ t f, t+δt iterate until U U k k+ 1 t +Δ t t +Δ t ε

13 Rigid vs. Flexible (Hammering Test) X Z Y Response of rigid body Response of flexible body

14 Test Model 1: LNG Carrier Length Overall m Length B.P m Breadth Moulded 55.0 m Depth Moulded 27.0 m Draught Scant m Speed 19.5 knot

15 Simulation Condition Heading Angle : 180 Speed : 10.3m/sec (Fn=0.180) Structural damping : 0.5%, 1%, 2% Regular Simulation : 0.4 rad/sec, resonance wave frequency Irregular Simulation : 0.2 rad/sec~1.0 rad/sec, 1.0 rad/sec~2.0rad/sec Z Z X Y X Y for Low Wave Frequency for High Wave Frequency

16 Low-Frequency Results Pressure Distribution at ω = 0.4 rad/sec Pressure Distribution (N/m2) at t=216 Pressure Distribution (N/m2) at t=216 Structural damping=0.5% Structural damping = 2.0%

17 Resonance Frequency Natural freq. for VBM = rad/sec. (dry state) rad/sec. (wet state) wave freq rad/sec 0.8 6E E+09 Heave RAO VBM RAO 4E+09 3E+09 2E E w(rad/sec) w(rad/sec)

18 High-Frequency Results Disturbed Wave Elevation with ω = 1.48 rad/sec at 211 sec. Wave Elev. Wave Elev Structural damping=0 0.5% Structural damping = 2.0%

19 High-Frequency Results Pressure Distribution at ω = 1.48 rad/sec Pressure Distribution (N/m2) at t=211 Pressure Distribution (N/m2) at t=211 Structural damping=0.5% Structural damping = 2.0%

20 Test Model 2: Containership Closed Closed Closed Lpp=348m Draft=51.61m V=12.7m/sec Hull form of Container Carrier

21 Load RAOs under b=180 o 4.5E+07 /m] Vertical bendin ngmoment[nm 6E+09 4E+09 2E+09 0 Frequency DB-noSPRd Uni-noSPRd nosprd Vertical sh hear force[n/m] 4E+07 Frequency DB-noSPRd 3.5E+07 Uni-noSPRd 3E E+07 2E E+07 1E+07 5E Wave Frequency [rad/sec] -5E Wave Frequency [rad/sec] VBM at 0.5L (b=180 o ) VSF at 0.5L (b=180 o )

22 Test Model 3: LNG Carrier Hull form of LNGC Lpp = 303 m Draft = 11.9 m at full Speed = m/sec Under head sea

23 Sectional Load RAO LNGC 3.5E E+09 m] 3E+09 Time Frequency m] 3E+09 Frequency Time-EB ing moment [Nm/ 2.5E+09 2E E+09 ing moment [Nm/ 2.5E+09 2E E+09 Vertical bend 1E+09 5E+08 0 Vertical bend 1E+09 5E E Wave frequency [rad/sec] -5E Wave frequency [rad/sec] VBM at 0.5L : Rigidid VBM at 0.5L : Flexible

24 Sloshing Analysis of NO96 type LNG container system by W.I. Lee, M.H. Cho (SNU, MAE)

25 Objectives Analysis of heat transfer in LNG cargo tank structure considering the layup of different materials. Analysis of structural dynamic behavior and static strength analysis due to sloshing

26 Thermal analysis Analysis of heat transfer in LNG cargo tank structure composed of layup of different materials and thermal conductivity for the insulation system in cargo tank Analysis of heat transfer through the cargo tank wall FEM modeling of NO96 cargo tank Analysis of heat transfer for the layup of insulation materials Characterization of thermal conductivity (under cryogenic condition) Dynamic analysis Membrane type LNG containment system(no96) has critical issues related to sloshing effect. - Sloshing : dynamic load acting over a tank structure as a result of the motion of a fluid with free surface confined inside the tank - Membrane type containment t system has no internal structural t members. Weakness to sloshing effect + Complexity of 3D modeling Accurate prediction to dynamic behavior of the containment system.

27 Thermal conductivity of composite material under cryogenic condition Thermal conductivity analysis of cryogenic insulation materials It is critical problem how to reduce the amount of heat flowing into a structure from the environment. Important tparameter of heat transfer: thermal conductivity, it thermal diffusivity i it Thermal diffusivity thermal conductivity α = k k ρ c p Thermal conductivity

28 Thermal conductivity-test it t t method Standardized guarded hot plate technique (e.g. ISO 8302, ASTM C 177 or DIN EN 12667), the system features unrivalled performance over an unmatched temperature range. K Qd = A ( T T ) 2 1 ΔT Q= k2a Δ X Among the component of CCS, most heats are blocked in the part of perlite and polyurethan component. Under the cryogenic condition, knowing the thermal conductivity is most important one. 27/7

29 Experimental result Experiment on thermal conductivity measurement according to temperature. Measurement of thermal conductivity of perlite Material : CR 615 water repellent perlite Condition : thickness difference within 5mm tapping test: tapping rate 2400 times per minute, tapping frequency 40 Hz without shocking test, transportation test Thermal Con nductivity (W/m mk) thermal conductivity distribution perlite p plywood temperature ( o C)

30 Thermal analysis in static state ; Thermal conductivity effect of perlite Comparison between constant value of thermal conductivity and variable value of it Constant value of thermal conductivity NO 96 insulation box 1 5 A 2 4 B 3 33 C 4 2 D 5 500mm 4 500mm 3 450mm 2 350mm o C] temperature [ o In case of 0.04 W /mk perlite constant thermal conductivity, the transient thermal analysis of box is done during the 20,000 second. temperature history (plywood part) C] temperature [ o temperature history (perlite) EE 1 300mm time [s] time [s] 2 A 3 B 4 C 5 D E

31 Comparison between constant value of thermal conductivity and variable value of it Variable value of thermal conductivity it ( applying experimental result) NO 96 insulation box 1 5 A 2 4 B 3 33 C 5 500mm 4 500mm 3 450mm 0 In case of perlite variable thermal conductivity, the transient thermal analysis of box is done during the 20,000 second. temperature history temperature history D EE 2 350mm 1 temperature [ o C] 300mm time [s] temperature [ o C] A B C D E time [s] 30/7

32 Comparison between constant value of thermal conductivity and variable value of it Material Thermal conductivity Material Thermal conductivity Invar sheet Plywood Perlite 0.13 (constant) 0.04 (constant) Temperature drop during Point 20,000s ( K) K K K K K A B C D K K K K Invar sheet Plywood Perlite 0.06~0.12 (variable with temperature) 0.01~0.03 (variable with temperature) Temperature drop during Point 20,000s ( K) K K K K K A K B 68.2K C D K K E K E 8.34 K

33 Remarks Global analysis Thermal conductivity of perlite and plywood was obtained by GHP method. Transient temperature drops of insulation box was conducted applying constant value of thermal conductivity and variable value of it. Thermal analysis is done considering conduction as well as convection of fheat. Initial lboundary condition for temperature t is set tto be 110K for LNG contacting area, and the temperature of the rest is set to be 230K. Convection heat transfer which occurs between LNG and air is assumed to be free convection. We assumed that LNG is kept at 110K in liquefied state and the rest is air.

34 Dynamic Structural Analysis Unit cell Modeling C H Homogenization method [ K] [ χ ] = [ Q] 1 = [ C ] [ C ] [ B ][ ] dv C C vol( V ) χ Vy y y Homogenized oge ed Modulus Full model 에적용 Material Property Homogenized Modulus Dynamic Analysis N x N N x N ( ) + y ( ) = ( ) [ M ]{ y t } [ K ]{ y t } { F t } Condensation method ( ) ( ) ( ) R R [ M ]{ y p t } + [ K ]{ y p t } = { Fp t } n x n n x n [Multi-Level System Condensation]

35 Local problem Homogenization method Basic concept X 2 X = X ( x, y) x = X y = X / ε ε = l / L L Macroscopic level Asymptotic expansion of displacement field u X u x y u x y 0 1 ( ) = (, ) + ε (, )... X 1 y 2 l Microscopic level y 1 Xu : C : υ X dvx = b υ dvx t υ ds ε + ε X Virtual work V V S O (1 / ε ) + O (1 / ε ) + O (1) = 0 2 Arranged in order of ε ε ε 0 2

36 Multi-Level System Condensation Full System MeTis(Graph Partitioning) S1 I S3 1,1 I 2,1 I 2,2 S2 S4 Final Reduced System U i 1 I K S K i Si Ij, i = 0 I Craig-Bampton Transformation Hierarchy to each sub-domain System Condensation TLCS & Iterated IRS 35/27

37 Dynamic analysis of LNG containment system (NO96) Transient time response (Commercial package)

38 Eigenvalue analysis #. Nodes 7,192 #. Elem. 7,168 #. Level 4 #. Sub-structures 16 #. Interface nodes 843 #. DOFs 41,358 PDOFs 1,230 % Reduction 2.97% #. Modes 200

39 Slamming Local Behaviors of Bow Structure under Slamming Loads by In-Sik Nho (CNU)

40 Local structural responses under slamming impacts Slamming impact: Serious global transient vibration of hull girder called whipping Local plastic deformation and buckling of bow bottom plating and flare panels Accomplishment of the study: Water impact response of a bow bottom panel 2-D wedge slamming analysis by hydro-code LS-DYNA Pressure time history (Nahm et al, 2007)

41 Characteristics of water impact pressure time history Water impact pressure measured by on-board and model test Extremely high peak pressure with very short duration time High dependency on test scheme, sensors size and sensitivity of measuring equipments Results of FE based FSI analysis Calculated peak pressure values are very sensitive to analysis method and shapes and size of grid and Inclusion of high frequency numerical noise Influence on structural responses Peak values of pressure are extremely sensitive and have very short duration time. So, the influences of peak value itself on structural responses is restrictive Difficult to apply it directly to structural design

42 Water impact response of a bow bottom panel Study on the modeling of water impact pressure time history Dynamic structural analysis for various pressure time history Rational structural safety assessment of bow bottom panels under slamming impact Consideration of the effects of essential parameters of water impact pressure on the dynamic structural responses Availability of peak values of pressure Effects of duration time Transient vibration analysis of bow bottom panel Idealized water impact pressure time history Consideration of structural responses under varying parameters with unit magnitude of impulse I = P(t)dt = 1( Pa sec)

43 Idealization of water impact time history Effects of the shape of water impact time history and structural responses Idealized simple rectangular and triangular impulses Variation of peak pressure value(p) and duration time (T1) to maintain same Impulse value Duration time (T1) Determined by relative length with the lowest natural frequency of Panel (T) 7 cases of T/32 ~2T Idealized rectangular and triangular impulses

44 Numerical calculation Transient responses of a bow bottom panel in time domain MSC/NASTRAN and Newmark-ββ algorithm Added mass effects at water contacting surface Natural frequency analysis Dynamic analysis under various shapes of pressure time histories with unit impulse Target panel Bow bottom panel of 8,600TEU container ship 3-bay panel Model & Center panel Model

45 Time histories of displacement (rectangular impulse) Duration time = T/32 Duration time = T/8 Duration time = T/4 Duration time = T/2 Duration time = T Duration time = 2T

46 Time histories of displacement (triangular impulse) Duration time = T/32 Duration time = T/8 Duration time = T/4 Duration time = T/2 Duration time = T Duration time = 2T

47 Max. Displacement vs. Duration Time Duration Time T1 (sec.) Max. Displacement Rectangular (x10-8 m) Triangle (x10-8 m) T/ T/ T/ T/ T/ T T

48 Considerations for transient response analysis The maximum displacements tend to be increased gradually as the duration times shrink from 2T to T/8. Finally duration time becomes shorter than T/8, however, the responses converge to a fixed level for both rectangular and triangular impulse. The duration time of real slamming impact pressure (order of 0.01 sec.) is much longer than the lowest natural vibration period of bow bottom panel structures. The magnitude of impulse or peak pressure value can not be the unique parameter for the modeling of water impact pressure time history, So, it is necessary to consider the natural vibration periods of structures to derive the rational transient dynamic responses.

49 Numerical Analysis of 2-D wedge slamming Objectives To examine the applicability of ALE based hydro-code LS-DYNA to hydrodynamic impact pressure estimation Analysis model The 2-D wedge with a deadrise angle is falling down to the free surface of water with constant velocity 1.83m/sec Simulation of the slamming test performed by Yang et al.(2007). Modeling range and schematic view of pressure calculation points

50 Finite element model Numbers of finite element mesh Min. grid size No. of FE mesh 0.5 mm 350, mm 90,000 20mm ,000 Minimum grid size = 2.0mm Minimum grid size = 1.0mm Minimum grid size = 0.5mm

51 Results of Analysis t = 0.01 sec t = 0.03 sec t = 0.05 sec Shapes of free-surface during the bottom slamming minimum mesh size = 2.0mm minimum mesh size = 1.0mm minimum mesh size = 0.5mm Pressure time history

52 Considerations for 2-D wedge slamming analysis The simulation of water impact phenomena using LS-DYNA code can provide considerably good results compared with experiments. So, it could be a potential alternative means to replace the expensive experiments. The calculated pressures tend to increase gradually with fine grid division. Especially, the peak pressure highly depends on the size of mesh. From the considerations of previous chapter, however, the peak value itself would be not a critical parameter and the reasoning of numerical analysis could be recognized because the errors of impulse magnitude seem to be not so large. It means that for estimation of the peak pressure in fluid impact problem it is still difficult to determine the calculation parameters including mesh size without known reference solutions.