CFD-Supported Design of Lifeboats

Transcription

1 CFD-Supported Design of Lifeboats Hans Jørgen Mørch*, Milovan Perić**, Jasmin Röper**, Eberhard Schreck** *CFD Marin, Tvedestrand, Norway **CD-adapco, Nürnberg, Germany Summary: Lifeboats are important for the safety of crew on oil platforms and marine vessels. Their design has so far been mostly based on experimental studies. However, the large number of factors which influence the loads on the lifeboat structure and its occupants makes optimization studies by experimental means both time-consuming and expensive. Besides, many effects cannot be studied at laboratory scale due to the inability to match all similarity parameters, and certain conditions cannot be realized in a laboratory. Numerical simulations based on modern computational fluid dynamics (CFD) methods could complement experimental studies if proven to be sufficiently accurate and efficient. The aim of this study is to demonstrate that this indeed is the case: comparisons between experimental data and simulation results performed by the authors so far indicate that the achieved accuracy in numerical simulations is comparable to the accuracy of experiments. It is also shown that a simulation of one drop test can be performed with sufficient accuracy in one day on a single core of a personal computer. Together with a computational method which uses overlapping grids to simplify the handling of lifeboat motion and specification of initial and boundary conditions, parametric studies of lifeboat water entry have thus become practicable. Keywords: Simulation, Lifeboat, Fluid-Body-Interaction, Overlapping Grids 1

2 1 Introduction Lifeboats have to be designed according to the following criteria: they must not be damaged during deployment, which means that the loads on the structure should not exceed certain limits in critical zones; the accelerations experienced by an occupant in any seat must not exceed certain limit over a period longer than allowed by medical safety rules; they must not dive too deep and should re-surface soon after water entry; they must move away from the hazardous area. Design of lifeboats is therefore a difficult task, since the conditions under which they might have to be used can vary greatly. The most important factors which affect the motion of a lifeboat and the loads acting on it are: drop height; initial conditions (inclination of the lifeboat, initial linear and angular velocity); wind speed and direction, wave height, period and direction of propagation; hit point on a wave; orientation of the lifeboat relative to wave; current in water; hull geometry; distribution of mass inside lifeboat. All of these factors can vary in a wide range. For both oil platforms and ships, the service location or route determines the probability that certain conditions might be encountered, which should be considered when weighting the importance of each factor in the final decision. Optimization of lifeboat design by experimental studies is very tedious, time-consuming and costly. Tens of thousands of drop tests have already been performed at various experimental facilities, but this is still not enough to reliably account for all relevant influences, especially for the design of new lifeboats. Measurements on full-size lifeboats under the conditions comparable to the likely deployment conditions (e.g. large height, strong wind, high waves, platform or vessel damage causing unfavourable inclination etc.) are usually not possible. On the other hand, measurements on scaled models under laboratory conditions introduce scaling problems (not all similarity parameters can be matched) and some of the conditions cannot be realized (e.g. the maximum wave height or drop height are limited by the available equipment). Numerical simulations offer several advantages over experimental studies: computations can be performed using real geometry (full-size); there are no limitations with respect to drop height and initial position of the lifeboat; any initial and boundary conditions can be realized; any current, wave pattern and wind condition can be realized; detailed information regarding local flow conditions and relevant phenomena is delivered, thus allowing a deeper insight into the physics of the problem; parametric studies can easily be performed. However, there are also conditions to be fulfilled by the numerical solution method to be useful in the design and optimization of lifeboats: the method must be able to deal with complex geometries, including resolution of small but important details which affect the flow around the lifeboat; the method must allow an easy handling of geometry variation, i.e. an automatic replacement of CAD-data and generation of a new computational mesh; the accuracy of obtained solutions must be sufficient to allow a reliable selection of an optimum design and determination of loads acting on the structure and occupants; the efficiency of simulations must be sufficient to allow a large number of parameters to be varied within an affordable period of time. In the following section the solution method used in this study will be briefly described; more details can be found in cited references. This is followed by the presentation of main findings from an earlier study involving comparisons with experimental data. Thereafter, results from simulations of lifeboat launching into Stokes 5th-order waves at different incidence and relative position are presented, with the aim of determining which wave orientation and hit point lead to highest loads. In the final section, conclusions are drawn and suggestions for future research are made. 2

3 2 Numerical Solution Method The numerical method used here is of finite-volume type. The starting point are the conservation equations in integral form, with appropriate initial and boundary conditions. By means of a number of discrete approximations, one obtains an algebraic equation system solvable on a computer. First, the spatial solution domain is subdivided into a finite number of contiguous control volumes (CVs) which can be of an arbitrary polyhedral shape and are typically made smaller in regions of rapid variation of flow variables. The time interval of interest is also subdivided into time steps of appropriate size (not necessarily constant). The governing equations contain surface and volume integrals, as well as time and space derivatives. These are then approximated for each CV and time level using suitable approximations. The flow is assumed to be governed by the Reynolds-averaged Navier-Stokes equations, in which turbulence effects are included via an eddy-viscosity model (k-ε or k-ω models are typically used). Thus, the continuity equation, momentum equation, and two equations for turbulence properties are solved; in addition, the space-conservation equation must be satisfied because the CVs move and may also change their shape with time. In order to account for the free surface and allow for its arbitrary deformation, including fragmentation, an additional equation is solved for the volume fraction c of the gas phase (which can be treated either as an incompressible fluid or as a compressible ideal gas). Liquid and gas are considered as two immiscible components of a single effective fluid, whose properties are assumed to vary according to the volume fraction of each component. It is beyond the scope of this paper to go into all the details of the numerical solution method, so only a brief description is given here, while details can be found in Muzaferija and Perić (1999) and Ferziger and Perić (2003). The important point is that all integrals are approximated by midpoint rule, i.e. the value of the function to be integrated is first evaluated at the centre of the integration domain (CV face centres for surface integrals, CV centre for volume integrals, time level for time integrals) and then multiplied by the integration range (face area, cell volume, or time step). These approximations are of second-order accuracy, irrespective of the shape of the integration region (arbitrary polygons for surface integrals, arbitrary polyhedra for volume integrals). Since variable values are computed at CV centres, interpolation has to be used to compute values at face centres and linear interpolation is predominantly used. However, first-order upwind interpolation is sometimes blended with linear interpolation for stability reasons. In order to compute diffusive fluxes, gradients are also needed at cell faces, while some source terms in equations for turbulence quantities require gradients at CV centres. These are also computed from linear shape functions. In the equation for volume fraction of the gas phase, convective fluxes require special treatment. The aim is to achieve a sharp resolution of the interface between liquid and gas (preferably within one cell), which requires special interpolation of volume fraction. The method used here represents a blend of upwind, downwind, and central differencing, depending on the local Courant number, the profile of volume fraction, and the orientation of interface relative to cell face; for more details, see Muzaferija and Perić (1999). The scheme is adjusted to guarantee that the volume fraction is always bounded between zero and one, to avoid unphysical solutions. The scheme resolves the interface typically within one cell and effectively prevents mixing of liquid and gas, thus allowing long-time simulations with maintained accuracy. The solution of the Navier-Stokes equations is accomplished using a segregated iterative method, in which the linearised momentum component equations are solved first using prevailing pressure and mass fluxes through cell faces (inner iterations), followed by solving the pressure-correction equation derived from the continuity equation (SIMPLE-algorithm; see Ferziger and Perić, 2003, for more details). Thereafter equations for volume fraction and turbulence quantities are solved; the sequence is repeated (outer iterations) until all non-linear and coupled equations are satisfied within a prescribed tolerance, after which the process advances to the next time level. Typically, 5 to 10 outer iterations per time step are performed. When the motion of a floating body is also computed, the outer iteration loop within each time step is extended to allow for an update of body position. The equations of body motion are first solved to obtain the velocities using a predictor-corrector scheme of second order (equivalent to Crank-Nicolson scheme) and then for displacements and rotations. In the present study, overlapping grid technique has been used: the background grid is adapted to the boundaries of solution domain and to waves, while another grid is attached to the lifeboat and moves with it like a rigid body (the solution domain allows for grid deformation, as might be necessary in the case of multiple bodies approaching each other). Details of the solution method adaptation to overlapping grids can be found in Hadžić (2006). 3

4 Under-relaxation of body motion is used in a similar way as when solving the Navier-Stokes equations; it can be interpreted as adding a virtual mass to the system (see Xing-Kaeding, 2005, for a more detailed description). The sequence of updating the flow and then the body motion is repeated until the changes in both flow and body position become negligible. Thus, at the end of each time step, the new body position and the corresponding flow are obtained. The solution method is therefore fully implicit and fully coupled. This allows larger time steps and provides better stability than when explicit schemes are used in which flow and body motion are computed one after another. The flow chart of the solution method is shown in Fig. 1. Fig. 1: Flow chart of the iterative solution method 3 Results From a Validation Study In an earlier study (Mørch et al, 2008), results of simulations using the present method have been compared with data obtained from experiments using 1:4 model. In this case, the lifeboat was launched from a ramp, with an initial inclination of 35 (bow down) and from 36 m height above flat free surface. A single grid, attached to the lifeboat, was used, with about control volumes; since the free surface was flat and fluid velocity was zero everywhere at boundaries, the whole grid could be moved with the lifeboat. Only half of the solution domain was considered, with symmetry conditions and three degrees of freedom (two linear motions and one rotation). Figure 2 shows photographs taken during experiments. One can see from the first two photographs that the lifeboat enters water at a steeper angle than it has when leaving the launching ramp. The following two pictures show that the lifeboat does not dive deep into water but quickly attains a position parallel to the free surface, and that it moves away from the water-entry location. The last two pictures show that the lifeboat lifts off water surface before attaining its final floating position. An average value of vertical acceleration for the rear and front seats in the lifeboat was recorded as a function of time in both experiment and simulation, cf. Fig. 3. During the critical period immediately after water impact, the computed vertical acceleration for both front and rear seat position agree very well with measured values: both the qualitative shape of the diagram and the absolute values are similar. Immediately after water entry, the front experiences strong deceleration. This leads to rotational motion and an increase of downward acceleration of the rear part. The rear part hits water surface about 0.4 s later and experiences about 30% stronger deceleration than the front part. The second peak seen in the experimental diagram at about 5 s stems from the second slamming effect after the lifeboat jumps out of water and re-enters; this is not resolved in the simulation as accurately as the first impact, but the event can be clearly identified. The simulation technique with overlapping meshes shown in the next section accounts better for these effects since the free surface is then well resolved in the whole domain. In addition to the original lifeboat geometry, two modifications have also been included in both experimental and computational analysis. In one case, the geometry of the aft section was modified, while in the other, both bow and aft section were modified. The three hull shapes are shown in Fig. 4. 4

5 Fig. 2: Photographs taken during an experimental study of lifeboat water entry (from Mørch et al, 2008) Fig. 3: Comparison of measured and computed vertical acceleration at front (left) and rear (right) seats in the lifeboat (from Mørch et al, 2008) The comparison of measured and computed accelerations (expressed as CAR-values) for all three forms are presented in Fig. 5, where 5

6 In the above expression, gx, gy and gz denote accelerations in the three directions of the local coordinate system attached to the hull. The results of simulations are both qualitatively and quantitatively reflecting the effects of design changes in the same way as in experiments. For all three forms, the accelerations are higher in the rear than in the front part, but the difference is reducing as more changes are done to the original design. Also, the absolute level of the CAR-values is reducing with each modification. The hull with modified bow and stern leads to reduction of CAR-values at the rear by 20% relative to the original design. The reduction of CAR-values in the front is much lower of the order of 5%. Fig. 4: The original hull (left), modified aft body (middle) and modified aft body and bow (right) The results from this validation study have shown that the main effects of design changes on the behavior of lifeboat during water entry can be reasonably well predicted even on a relatively coarse numerical grid. This conclusion will not hold once the design approaches the optimum; however, current designs are far from optimum and a large number of numerical tests needs to be performed before the design with best average performance under all conditions is found. The problem is that one design may be optimum for one particular test condition, but it may perform badly in another situation. Fig. 5: The effects of hull modifications on CAR-values in the front and rear part of lifeboats (from Mørch et al, 2008) 4 Simulation of Lifeboat Launching into Waves We considered here 5th-order Stokes wave (according to Fenton, 1985) with a period of 13 s and height of 15.8 m in a 33.5 m deep water without current, corresponding to a typical offshore platform location in the North Sea. Under these conditions the wavelength is m and the wave crest is 10.4 m above still water level. The initial distribution of water volume fraction and the initial velocities were determined by the Stokes wave theory. At all later times, velocities and volume fraction at both inlet and outlet boundaries were also determined from that theory, except in the portion of the boundary occupied by air, where zero air speed was specified. Side boundaries were symmetry planes, bottom boundary was a no-slip wall, and at the top boundary, atmospheric pressure was specified. The lifeboat is similar to one type used on offshore platforms. It is 14.8 m long, its mass is 20 t, its center of gravity (COG) is located 8.3 m from bow and 1.15 m from keel and its moment of inertia around lateral axis is kgm2. The boat is dropped from a location where its lowest point is 32 m 6

7 above still water level; it is initially inclined towards horizontal plane by 35 (bow down; COG is 4.67 m higher). In order to save on computing time, the free fall over the first 17 m was not simulated; instead, we computed the velocity at this location assuming no resistance, which lead to the initial vertical velocity of m/s (effectively, this means that the true initial position and inclination are slightly different from the values stated above). This is considered acceptable since the aim of this study is to analyze various effects under otherwise the same conditions. The boat is thus initially 15 m above still water level (about 4.57 m above wave crest). For the head and following wave (0 and 180 incidence), only three degrees of freedom for lifeboat motion are considered: vertical and horizontal linear motion and rotation about the lateral axis. Since boat geometry is symmetric, only half of the flow domain is considered. For the 135 incidence, all six degrees of freedom and the full geometry have had to be taken into account. The solution domain was one wavelength long and 32 m (half domain) or 64 m wide; it extended 60 m above still water level. In order to allow for an arbitrary motion of the lifeboat without affecting mesh quality and at the same time keeping the same mesh resolution for the wave region, overlapping grids approach was used. The background mesh was Cartesian, with anisotropic cell-wise local refinement in the free surface region (by halving the cell size in one or more directions) to better resolve the wave; the mesh spacing was here about 1 m in wave propagation direction and 0.5 m in vertical direction (about 240 cells per wavelength and 32 cells per wave height). Based on previous studies, this is considered sufficient for an accurate prediction of wave propagation when a second-order discretization in space and time is employed. For 0 and 180 incidence, the mesh around the boat was also predominantly Cartesian with anisotropic cell-wise refinement, but it had two prism layers along boat surface. The surface of this prism layer trimmed the remaining Cartesian mesh, so there were some polyhedral cells with up to 16 cell faces, and the prisms near wall had polygons as their base with between three and eight edges. The whole mesh for half of the geometry consisted of 623,622 cells (420,758 cells attached to boat; the remaining 202,864 cells were in the background mesh). For 135 incidence, the mesh attached to the lifeboat was polyhedral, with about cells; the background mesh was again Cartesian with local refinement and consisted of about cells. Cuts through the two meshes are shown in Fig. 6. As the boat moves, some cells in the background mesh are de-activated while others are re-activated; this process is automatically controlled, with the aim to ensure an overlap region of about three cell layers. Fig. 6: Cuts through the two meshes used in simulations of lifeboat launch into waves. The wave position and propagation direction was varied; for each wave incidence (0, 180 and 135 ), a set of test cases with 9 different initial positions relative to the initial lifeboat position, differing by 20 m, was defined. This gives 9 hit points on a wave, 20 m apart. The hit points are indicated for two wave incidences in Fig. 7. The aim of this variation is to find the worst hit point for each wave direction, for the given drop hight and initial boat orientation. The worst case must be taken as the basis for design, because one cannot choose the hit point in an emergency. In order to evaluate spatial discretization errors, a second, finer mesh around half lifeboat has been created (the background mesh was kept the same as it was considered fine enough for wave propagation computation). The refined mesh had over 1.1 million cells attached to the lifeboat (almost three times more than the coarser mesh). The cells in the vicinity of the boat were cubic with 3.2 cm base size, compared to 5 cm base size of the first mesh. Simulations were performed using both grids for one test case with a following wave and a hit point about 51.5 m downstream of wave crest (this 7

8 turned out to be one of the worst cases). The time step was 1 ms with the coarse and 0.5 ms with the fine grid. Also, fine grid simulation was started with initial conditions taken from coarse grid simulation after lifeboat has traveled 7 m. The differences in computed accelerations at COG were very small, so that there is no need to present the comparison. This indicates that the coarser mesh is adequate enough to analyze the effects of hit point position and wave propagation direction. As will be shown below, the differences between results obtained in different test cases are quite large, so that the difference between solutions obtained on the two meshes is negligible. This is in agreement with the results from validation study, where a good agreement with experiment has been reached by using an even coarser mesh. Fig. 7: The location of nine hit points for the following wave (180 incidence; left) and head wave (0 incidence; right). Fig. 8: Free-surface deformation (left) and pressure distribution on the hull (right) during water entry. Fig. 9: Free-surface deformation during re-surfacing of the lifeboat after water-entry. Figure 8 shows free-surface deformation and pressure distribution on the hull during water entry for one hit point and 180 incidence. High-pressure regions are at the intersection of free surface and kiel, and the steps on hulls sides along which it slides down the ramp during launching. Figure 9 shows free-surface deformation during re-surfacing of the hull after water entry. A large air bubble is 8

9 created in the wake, as can also be seen in photographs from experiments in Fig. 2. This bubble collapses afterwards and creates a lot of spray as the lifeboat jumps completely out of water. This is also visible in experiment, e.g. in the fifth photograph in Fig. 2, where one can see the mirror image of the complete hull. Afterwards, the hull slams again onto free surface, which creates another but rather mild peak in pressures and accelerations, which can be seen in Fig. 3. Fig. 10: Variation of vertical (left) and angular (right) acceleration at COG for the 180 (top), 0 (middle) and 135 (bottom) wave incidence and different hit points on wave. Of major interest here are variations in accelerations and pressures for different wave incidence and hit points on wave. Maximum vertical acceleration is obtained when the wave crest is initially 40 to 60 m behind lifeboat drop location, cf. Fig. 10. At the centre of mass, deceleration that amounts to about 13-fold gravity acceleration is obtained under those conditions; as shown in Fig. 3, substantially higher values can be expected at rear seats, where deceleration is preceded by acceleration. Although the distance from drop position (32 m above still water level) to free surface is largest when the boat falls into wave trough (the boat velocity is then the largest), this is not where the highest loads occur. Due to water motion, the hit point about 40 m downstream of wave crest seems to be the worst. The following wave (180 incidence) causes the highest accelerations. Peak pressures on hull are obtained when the wave crest is initially 20 to 40 m behind lifeboat drop location, cf. Fig. 11. The pressure is averaged over several control volume faces, covering an area of about 0.5 m in diameter. Peak impact pressure is probably locally substantially higher, but it acts on a 9

10 small area which is not resolved by the computational grid. However, for practical purposes, average pressure over a larger area is much more relevant than peak pressure at a point which lasts only a very short time. Even with this averaging, the time during which the pressure exceeds half of the maximum value is very short of the order of 25 ms, cf. Fig. 11. The highest pressures are obtained for following waves (180 incidence), so that this condition is the worst for both structural loads and accelerations on occupants. Fig. 11: Variation of pressure at the same sensor in kiel region for 180 (left) and 0 (right) incidence and different hit points. With a systematic variation of initial wave position, one obtains a reliable estimate of the worst hit point for given drop height and orientation relative to wave propagation direction. One can connect the maxima from simulations for all hit points to obtain an envelope spanning the whole range. The maximum vertical accelerations vary by a factor of 2.5 and maximum pressures by a factor of 5 between different hit points. 5 Conclusions In this study, it was found that dropping a lifeboat into a Stokes 5th-order wave with 13 s period and 15.8 m wave height at 180 incidence, the largest loads on both the structure and the occupants of the lifeboat occur. However, the situation may be different for waves of different wavelength and for different drop conditions. More studies are necessary to determine the most critical scenario for the given lifeboat and likely operation conditions. As far as the determination of maximum loads is concerned, it is sufficient to compute the flow and lifeboat motion during only about one second after the hull hits free surface. The simulation of the first 2 seconds of water-entry on a mesh with about cells and a time step of 1 ms (2000 time steps with 8 outer iterations per time step) took about a day on a single core of a quad-core PC-processor. This means that, on a cluster with 32 quad-core processors, one could perform about 100 simulations per day. This makes simulation an excellent design tool and allows the reduction of necessary experimental tests to a minimum. Future studies will look at the effects of wind and wave breaking. 6 References J.D. Fenton: A fifth-order Stokes theory for steady waves, Journal of Waterway, Port & Coastal Engineering, Vol. 111, pp (1985). J.H. Ferziger, M. Perić: Computational Methods for Fluid Dynamics, Springer, Berlin, 3rd ed., H. Hadžić: Development and application of a finite volume method for the computation of flows around moving bodies on unstructured, overlapping grids, PhD thesis, TU Hamburg-Harburg, H.J. Mørch, S. Enger, M. Perić, E. Schreck: Simulation of lifeboat launching under storm conditions, Proc. 6th Int. Conf. on CFD in Oil & Gas, Metalurgical and Process Industries, SINTEF/NTNU, Trondheim, Norway, June 10-12, S. Muzaferija, M. Perić: Computation of free surface flows using interface-tracking and interfacecapturing methods, in Nonlinear Water Wave Interaction, WIT Press, Southampton, Y. Xing-Kaeding: Unified approach to ship seakeeping and maneuvering by a RANSE Method, PhD thesis, TU Hamburg-Harburg,