Fluid-structure interaction during ship slamming Kevin Maki Dominic J. Piro Donghee Lee Department of Naval Architecture and Marine Engineering University of Michigan Fifth OpenFOAM Workshop June 21-24 2010 Gothenburg, Sweden 1 OF5 2010
Overview Objective: Dynamic structural analysis of high-speed vessel under slamming loads Analysis process that incorporates FEA and CFD methods computational efficiency method that is not tailored to any particular design utilizes contemporary analysis tools (CFD and FEA) handles complex geometry suited to utilize High-Performance Computing (HPC) 2 OF5 2010
Introduction Outline Analysis Process: Hydrodynamic Solver: OpenFOAM Structural Dynamics Solver: ABAQUS Coupling and grid matching RESULTS Impact of a rigid wedge Impact of a wedge-shaped simply-supported plate Impact of a horizontal flat plate on curved free surface Impact of a stiffened panel on the wetdeck of a high-speed catamaran Summary 3 OF5 2010
Simulation Process Overview Grids (Structure/Fluid) Set Association CFD Pressure Transform Load Time Integration w FEM Frequency Modeshape Finite element and fluid solvers operate independently Grid matching utility allows for different grids to be used in each physics domain One-way coupling and modal analysis is robust and efficient CFD analysis is necessary once for each hull design, one set of hydrodynamic pressures can be used for many structural designs Use acoustic elements in FEM model to account for added-mass due to flexure 4 OF5 2010
Fluid Grid Grid Matching Methods 1. Widely used projection method (Mamam and Farhat 1995, Cebral and Löhner 1997, Farhat et al. 1998, etc.) - use structural normal from Gauss point to find fluid associate 2. Proximity-based - use nearest neighbor of Gauss point as fluid associate Structure Grid structural and fluid grids generated by different people fluid grid is much finer than structural grid (typically) 5 OF5 2010
Constant Velocity Impact of a Wedge-Shaped Body Simplified slamming problem Constant vertical velocity Wedge-shaped body Large peak pressure Commonly occurs on wetdeck Large number of results available for comparison - boundary-element method Zhao and Faltinsen (1993) - analytic theories summarized in Korobkin (2003) From Zhao and Faltinsen(1993) 6 OF5 2010
Constant Velocity Impact of a Wedge-Shaped Body Constant velocity impact 15 deg. deadrise angle two-dimensional simulation Grid # cells l/b Super Coarse 12,449 0.01 Coarse 24,691 0.005 Medium 42,917 0.0025 Fine 112,971 0.00125 7 OF5 2010
Constant Velocity Simulation Videos 8 OF5 2010
Free-surface Profile Boundary-element solution from Zhao and Faltinsen (1993), figure 6 present effort 9 OF5 2010
Pressure Profile 40 30 OF super coarse OF coarse OF med OF fine BEM: max pressure coefficient (p-p o )/(1/2! U 2 ) 20 10 0-1 -0.5 0 0.5 1 z/vt Boundary-element solution from Zhao and Faltinsen (1993), figure 6 present effort 10 OF5 2010
Force Time Series 50 BEM time of chine wetting 40 max force: Wagner F 3 /(1/2! U 2 B) 30 20 max force: Logvinovich OF super coarse OF coarse OF med OF fine BEM Zhao and Faltinsen 10 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Boundary-element solution from Zhao and Faltinsen (1993) Wagner and Modified Logvinovich results taken from Korobkin (2004) 11 OF5 2010 Vt/B
Introduction the deadrise angle Simulation of the Method equivalent rigid Rigid-Wedge wedge and L ishydroelastic the length of Wedge the side walls. Horizontal The side Flat Plate walls of thesummary wedge are modelled by simply supported Euler beams. Due to the symmetry, the right side wall can only be considered. Normal deflection of the beam is denoted by w Hydroelastic-Wedge (s, t ), where s Impact is the coordinate along the initially undeformed side walls, s = 0 corresponds to the wedge tip and s = L to the beam end point. The beams are deforming owing to their interaction with the liquid. Figure 1. Scheme of the impact. from T.I. Khabakhpasheva, A.A. Korobkin (2003) We shall determine the liquid flow, the pressure distribution in the liquid region, deflection of the wedge, the stress distribution in the wedge platings and the dimension of the wetted part of the entering wedge. Non-dimensional Un-stiffened variablespanel are usedinbelow. the wet-deck The beam length region L is taken as the length scale and the impact velocity V as the velocity scale of liquid particles. Assuming that the wedge is rigid and the free surface is undeformed Results during thefor: penetration, wet and we obtain dry modal that theanalysis wedge totally wetted at instant T = (L/V ) sin γ and the vertical displacement of the wedge is equal to L sin γ at this time instant. The quantity T is taken as the time scale and Compare the product with: L sin γ as the displacement scale. We denote ɛ = sin γ and consider the coupled problem of elastic wedge interaction with the liquid the case ɛ 1. The pressure scale is ρv 2 ɛ 1, where ρ 1. Khabakhpasheva and Korobkin coupled elastic beam is the liquid density. (simply-supported) and Wagner solution for a 10 deg deadrise Formulation of the Wagner problem The plane and potential wedge flow generated by the wedge penetration is described by the velocity potential ϕ(x, y, t) which satisfies the following equations within the Wagner theory 2. Lu, He, and Wu (2000) coupled Euler beam with fully-nonlinear potential flow, 30 deg deadrise ϕ = 0 (y < 0), (1) ϕ = 0 (y = 0, x > c(t)), (2) 12 OF5 2010
Beam Modal Analysis Mode Shapes Frequencies: 25 mm plate 4000 wet dry frequency (Hz) 2000 0 1 2 3 4 mode number Hydroelasticity parameter (Faltinsen): R F = tan β EI V ρ loading period wl 3 structural period R F < 2 : hydroelastic effects are relevant 13 OF5 2010
Hydroelastic Wedge Results: Comparison Korobkin deflection / L sinβ deflection / L sinβ deflection / L sinβ 0.30 0.20 0.10 0.00-0.10-0.20 0.04 0.02 0.00-0.02 0.01 0.00 dry wet Korobkin t = 9 mm 0.0 0.5 1.0 1.5 t = 18 mm 0.0 0.5 1.0 1.5 t = 25 mm 10 deg. deadrise angle fully-dry approximation yields poor results, especially in the case of thin plate fully-wet has poor time accuracy, but decent prediction of total deflection theory of Korobkin shows the time of chine-wetting is delayed due to flexure of beam -0.01 0.0 0.5 1.0 1.5 2Vt / B tanβ 14 OF5 2010
Hydroelastic Wedge Results: Comparison Lu, He, and Wu W (1e -5 m) 60 40 20 t = 5 mm wet Lu, He, and Wu W (1e -5 m) 0 0 0.05 0.1 0.15 0.2 0.25 15 t = 8 mm 10 5 0 0 0.05 0.1 0.15 0.2 0.25 5 t = 11 mm 4 30 deg. deadrise angle slight over-prediction of maximum deflection CFD solution solves for chines-wet and chines-dry regimes, and extends to 3-d complex geometry impact velocity is relatively small such that hydroelastic effects are minimal: R F > 2.5 W (1e -5 m) 3 2 1 0 0 0.05 0.1 0.15 0.2 0.25 Time (sec) 15 OF5 2010
Hydroelastic Wedge Results: Summary max deflection: present/korobkin 2.5 2.0 1.5 1.0 0.5 dry wet max deflection: present/lu 1.5 1.0 0.5 wet 0.0 0 1 2 3 R F Fully-wet assumption tends to overpredict deflection by 10% 0.0 0 2 4 6 8 10 12 R F properly accounts for hydroelastic influence on structural response R F = tan β EI V ρ loading period wl 3 structural period 16 OF5 2010
tally. This is partly due to the very short time duration sufficiently fast. of an impact associated with an expected very high pres- The tests were carried out for five different drop sure, and partly due to the requirement of high accuracy speeds, with impact speed ranging from 2.2 m/s to 6.2 m/ of the models produced and the waves generated. Com- s (corresponding to drop heights from 0.20m to 2.0m). pared with conventional model testing, a much higher Five different regular waves conditions were used for sampling frequency of the digital recording of the differ- each drop speed. The curvature radius of the wave crest / - Relative vertical Accelerometer~!., displacement transducer Horizontal Flat Plate Impact Stiff / / f 9 / ' A 1' ~ Transducer Boundary plate..... 9 ~ \ S G4 ~ SG2 SG1 spring!.~ 200,'q'- 100 -' T \.,, 200,j Strain,.-~ gauges I 8 Plate I r/////.-.-.-.-.-.-..y..h.-.-, Steel e / 100 ~ o~,, P l a t e II ~J~]...~...~...~,~ Aluminium Pressure Cells Measuring Section Dummy Section / Free drop of test rig onto plane-progressive waves Measurement of flexural displacement, strain Varied wave steepness and drop height R = 1/k 2 a V radius of curvature velocity i i o L. r" P2 450,~[10Ok," 450 "7' j J b,.~i - - - Wave gauge tape Faltinsen, Kvålsvold and Aarsnes (1997) Korobkin and Khabakhpasheva (2006) Fig. 2. Details of the steel and aluminum plates used in the drop tests. The length dimensions are in millimeters from Faltinsen, Kvålsvold and Aarsnes (1997) 17 OF5 2010
Numerical Simulation: Rigid Body Motion rigid body velocity (m/s) -2.2-2.4-2.6-2.8-3.0 experiment UofM -3.2-0.005 0.000 0.005 0.010 0.015 0.020 0.025 time (s) mixed implicit/explicit equation of motion solver 18 OF5 2010
Numerical Simulation:Time Series of Elastic Response 0.010 deflection (m) velocity (m/s) µstrain 0.005 0.000-0.005-0.010 5.0 2.5 0.0-2.5-5.0 2000 1000 0 experiment Faltinsen UofM Korobkin 0.00 0.01 0.02 0.00 0.01 0.02 steel plate R = 2.5 m V = 2.5 m/s Faltinsen, Kvålsvold and Aarsnes (1997) Korobkin and Khabakhpasheva (2006) -1000-2000 0.00 0.01 0.02 time (s) 19 OF5 2010
Summary One-way coupled hydroelastic analysis that utilizes: - CFD for rigid body motions and surface forces - FEA for modal analysis of wet condition - Grid matching for data transfer between physics domains - Modal equation of motion solver for dynamic response in time domain Comparison with theory, numerical, experimental data for elastic wedge and horizontal-plate impact Benefits: 1. Complete procedure allows for fluids and structures experts to operate independently 2. One hydrodynamic solution for many structural designs 3. General implementation to couple with many different programs 20 OF5 2010
Questions Thank you for your attention! 21 OF5 2010