Fluid-Structure Interaction of a Surface Effect Ship Bow Seal and a Free Surface Andrew L. Bloxom and Wayne L. Neu

Aerospace and Ocean Engineering Virginia Tech

Blacksburg, VA, 24061-0203 neu@vt.edu, abloxom@vt.edu

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Introduction

Surface Effect Ships (SES) were born into the high speed marine vehicle world as a hybrid of an air-cushion vehicle (ACV) and a catamaran. A typical SES design has a catamaran-type pair of side-hulls with flexible seals which contain a cushion pressure provided by lift fans pumping air into the void between the hulls. Due to the highly flexible nature of these seals and the complex wake interactions inside the hulls, the free surface is in constant interaction with them, causing increased drag, cushion pressure leakage, and additional material fatigue. Taking advantage of the reduced wetted surface area achieved by lifting the hull to minimize frictional drag, SES’s are able to achieve higher speeds with less thrust. At the same time, an increase in directional stability over a typical ACV is provided by the side hulls, as well as improved seakeeping performance. ACV’s are normally limited to favorable sea conditions due to the likelihood of cushion pressure leakage as a result of large motions in higher wave amplitudes [1]. The SES design allows the craft to seal the cushion pressure in along the length of the craft hulls, but still has flexible seals fore and aft to maintain cushion pressure and allow smoother interaction of the craft with waves.

Beginning in the 1960’s, SES work largely followed a design, build, test, iterate paradigm. Much was learned about the nature of these craft through both model tests and full scale prototype testing which advanced the state of the art and provided a craft which was very useful in selected missions/uses. Notable uses include high speed ferries and littoral patrol craft. Due to the nature of the cushion pressure and twin hulls and the inability to visually observe the dynamics inside the hulls during operation, the true nature of the free surface dynamics and their interaction with the seals was never fully understood. An anecdote told by an early SES designer, Bob Wilson, tells of a Navy Captain who nearly lost his life strapped to the inside of a prototype SES in order to get a better look at the free surface dynamics inside the cushion [2]! SES design still has some areas of open research with the potential to improve the performance characteristics. The Office of Naval Research T-Craft tool development program was started in 2007 to address the need for advanced design capabilities to augment the design of an actual SES for the U.S. Navy. The design concept is an SES which can transit the open ocean, then transform into an ACV mode near shore, and deliver a payload over the beach [3]. This program brought together researchers in industry and academia to develop the tools to aid the design and gain understanding of some of the fundamental dynamics of SES. Figure 1 shows Naval Surface Warfare Center Carderock Division (NSWCCD) Model Number 5887, a generic T-Craft SES model with finger type bow seal. This model was tested in the Maneuvering and Seakeeping Basin at NSWCCD to provide basic data for validation of ship motion simulations [4].

Numerical studies of SES craft have focused on the resistance and seakeeping performance of simplified versions of the craft at varying degrees of fidelity. One common approximation had been the simplification of the seals to rigid bodies, or not including seals at all [5]. In some models, empirical or numerical approximations were chosen to represent the seal’s influence on the overall performance of the craft [6]. Another approach that was taken modeled the seal as a simplified hinged flap, which can respond to wave motions while still providing a more accurate prediction of resistance and overall craft motions [7]. Only in the past decade have

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numerical codes and fluid structure interaction research provided the capability to model the complex behavior of an air cushion vehicle seal interacting with the free surface. Some groups focus more on reduced order modeling of craft motions and performance in order to provide timely information to design teams [8]. Using boundary element calculations of the flow around the ship, with models for cushion pressure and seal effect, these simulations are much less computationally intensive than Navier-Stokes simulations which capture the finer details in the flow. However, to capture the interaction of the seals with the craft wake, it becomes necessary to use more advanced CFD methods. The advantage to numerical testing of SES is the wealth of data on these interactions that can be gleaned from the comfort of a computer chair, however the physical experiment is still very relevant in gaining insight and providing validation data to modelers.

Model scale experiments of an SES bow seal system, which served two purposes, have been performed by researchers at the University of Michigan [9]. The main goal was to increase the understanding of seal dynamics through testing of a canonical SES model, and gathering the most useful data that current state of the art sensors and instrumentation can afford. With such data, the secondary goal was to provide numerical modelers with a valuable set of validation runs to which they could compare the emerging results of their latest FSI codes.

Simulations of this model have been undertaken to aid in the design and understanding of the complex dynamics that occur between the craft and the free surface which can be detrimental to both seakeeping and powering performance. The authors’ attempts to model the bow seal of the craft in a simplified model date back to 2010. These were carried out using the early versions of the co-simulation tool between STARCCM+ v5.06 and Abaqus v6.10, in which only an explicit coupling scheme for the force-displacement transfer was implemented. These simulations experienced an instability with the force on the seal and its displacement when using 2nd order time discretization in the fluid. Now, with the implementation of the implicit algorithm in the co-simulation engine in STAR-CCM+ v7.04 and Abaqus v6.12, stable simulation of the complex dynamics are being solved with larger timesteps and 2nd order discretization.

Physical Model Experiments

University of Michigan Bow Seal Test

The SES bow seal tests mentioned above were carried out in 2008-2009 at the University of Michigan Hydromechanics Laboratory Towing Tank. The geometry of the rig used, shown in Figure 2, was designed to accommodate different seal designs at the bow, and had a lobe stern seal. A number of tests were run in which initial seal immersion, cushion pressure, seal design, and forward speed were varied. The two seal designs selected for testing were a canonical flat plate type seal, and a finger type bow seal design. The finger seal design shown in Figure 1 on the NSWCCD Model Number 5887 is common in production SES, and the single flap design is more a canonical test case. Both were constructed of 3.175 mm thick vulcanized neoprene rubber with a fabric inner layer. The material was tested in a simple bending test to obtain a flexural rigidity, which was used to calculate the Young’s modulus of 16.9 MPa. The density of the material is 1096 kg/m3. The rig was instrumented with interior cushion cameras having

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good visibility of the seal and wake, taut string potentiometers to measure the seal displacement along the centerline plane, load cells to measure the net forces where the seal meets the craft, and blower fans to provide variable cushion pressure.

During a run, the craft was only allowed to move in the forward direction, and was held fixed in all other directions. A typical run began with the pressurization of the cushion, then the rig was accelerated, and data were collected once the desired test speed was attained. One run was selected as the focus of this work, number 1058, with the flat plate type bow seal. The conditions for this run were a velocity of 8 ft/s, cushion pressure at 2.5 inches of H2O, and an initial seal immersion of 9 inches. The flat plate bow seal design was chosen as the test case for this numerical study primarily to remove the complexity of contact modeling and volume cell deletion that would result from the interaction of the finger type seals with each other and the SES sidewalls.

Numerical Modeling with FSI Co-simulation

When modeling such a complex physical problem, one must decide how much detail to capture in simulation. Will the simulation follow the same test procedure as the physical model test? If not, how should the solution be initialized? Does the physical geometry need to be simplified in the simulation? How would such a simplification affect the fidelity of the simulation? These are just some of the difficult issues which must be addressed in setting up the co-simulation. Fluid Domain

The fluid dynamics side of the co-simulation utilizes the three dimensional, 2nd order, implicit unsteady flow solver with a step size of 0.0001 seconds. The Volume of Fluid (VOF) method is used to capture the free surface. The seal displacement calculated by Abaqus is applied to the fluid domain through STAR-CCM+’s mesh morphing scheme. Because of the inherently expensive computational cost of running FSI simulations, every effort was made to reduce unnecessary grid refinement while still capturing the important flow features. Isotropic volume refinement was applied in the interior of the craft where the free surface is dynamically responding to the pressure field produced by the craft and the cushion pressure. Anisotropic grid refinement in the z-direction was applied throughout the entire domain to preserve the free surface. Currently, the total number of volume cells in the domain is 418,165 and the mesh around the craft is shown in Figure 3.

The flat plate type seal is modeled with the top of the seal pinned in place and the seal sides fixed in the y-direction to maintain zero gap at the sidewalls. The fluid boundary contains no gaps between the edge of the seal and the sidewall. The seal is essentially attached to the sidewalls. This assumption leads to the necessity of fixing the seal in the y-direction with an added boundary condition in Abaqus. This is partially justified by the test rig’s inclusion of steel stiffener bars attached across the span of the seal. These were installed to force the seal to move in a more “two dimensional” manner. Other simplifications to the geometry include: all of the internal equipment support structure was removed, air blower inlets were changed to a single large rectangular momentum source for air inlet, the rear seal was made rigid and

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simplified in geometry, the transverse stiffeners on the bow seal were not included, and the constraint wires to hold the seal from deflecting forward were not included.

Structural Domain

The dynamic implicit time integration procedure was used in Abaqus/Standard with an initial increment size of 0.0001 seconds and time increment sub-cycling enabled. The default Hilbert-Hughes-Taylor solver parameters were used to calculate the displacements using the transient fidelity mode. This is important to this type of problem where the small time scale fluctuations of the seal remain important. The FEA model is built using 9,464 C3D8i elements in a single thin layer with linear elastic material model based on initial calculations for the material characteristics of the vulcanized rubber/fabric seal material. The model is pinned along the upper edge, and fixed in the transverse y-direction to prevent the seal from displacing away from the sidewalls.

Co-simulation

As mentioned above, early versions of the co-simulation tool allowed only staggered explicit coupling between the codes where the force-displacement exchange only occurs once per coupling step. The instability that results from the use of this scheme is a result of the continuous motion of the coupling boundary being represented in a discretized fashion, with a grid flux term included for the surface velocity when using 2nd order time discretization. A small displacement creates an unrealistically large pressure spike, which pushes the seal in the opposite direction, creating a pressure spike on the other side. In this way, the pressure response on the seal cascades out of control, until either the Abaqus solver fails to converge or the morpher can no longer handle the severity of the displacement. In the literature, this is referred to as the artificial added mass effect (AAME) and is a well-known instability for staggered solution FSI problems [10, 11, 12]. Problems involving high fluid velocities, incompressible flow, low stiffness materials, and large displacements are particularly sensitive to the AAME. There are methods for stabilizing the explicit calculation which will be discussed below, but the implicit coupling is the best way to retain 2nd order flow solutions which is beneficial to the free surface capturing.

A staggered implicit coupling algorithm was first implemented in STARCCM+ in version 7.04. This algorithm takes advantage of iterative coupling, where the force-displacement transfer is allowed multiple passes during a step using successive substitution with adaptive under-relaxation until the calculated co-simulation displacement has converged within a given coupling step. Currently, implicit coupling is being utilized with 5 inner iterations per exchange, and 4 exchanges for a total of 20 inner iterations per time step. Except during periods of high acceleration or displacement, this is sufficient to converge the co-simulation displacement and stabilize the simulation of the highly flexible seal response. Similar methods have been shown to be successful for the calculation of FSI problems in application to free surface flow [13].

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Remeshing

Periodic remeshing of the STAR-CCM+ domain is necessary when the seal response exceeds the limits of the mesh morpher or when degradation of grid quality becomes excessive. Maintaining grid quality in the vicinity of the air-water interface is important to the operation of the VOF method’s High Resolution Interface Capturing (HRIC) scheme. The morpher, which is used with default settings, does have the ability to handle large displacements. However, because of the seal’s proximity to the sidewalls and the bow of the craft, the volume cells in that region can become extremely distorted by motion of the seal. Because the HRIC convection scheme takes into account the relative angle between the advancing interface and cell faces, it is important to maintain grid lines which are oriented roughly with the initial grid and calm free surface.

When the volume mesh has reached a point where the quality is no longer acceptable, the co-simulation must be halted, the volume domain boundary extracted, previous surface representations deleted, and the new extracted boundary must be used as the new input surface for volume meshing. To restart the co-simulation, a new Abaqus input file is required which imports the previous state of the seal, and initializes the remeshed volume domain with the Abaqus displacements from the previous step. The remeshing frequency should be higher near the beginning of the co-simulation as the seal makes a large displacement away from the initial geometry. The fluctuations about a “steady” running displacement of the seal will be less significant, and will not require a large number or remeshing operations. The deformation of the grid and the resulting remeshed grid for two instants in time are shown in Figure 4. Here it can be seen that the remeshing is much more critical at the beginning as the cells become highly distorted when the seal displaces away from the initial condition.

Results

Explicit Coupling

Simulations of the bow seal on an SES present a slew of challenges to the FSI modeling framework. The physical problem contains all the prerequisites for experiencing the AAME in simulation. With explicit coupling, many approaches were taken to try to achieve a stable solution. One of the most important aspects lies in the initial conditions where the coupling is to start. The added mass instability is highly apparent when the seal co-simulation is started at a condition where the fluid flow is not in a converged state. For example, a typical initial condition in the fluid domain has full forward speed of the craft initialized on both sides of the immersed seal. Starting a co-simulation at this point with the explicit solver will never be stable. Instead, freezing the co-simulation solver and morpher while running the fluid solution to a point where the force on the seal stabilizes provides an improved initial condition.

Since initial conditions alone could not stabilize the transient solution, additional techniques suggested in [14] were utilized. Grid flux under-relaxation, material damping in Abaqus, artificial compressibility in the fluid, reduced time steps, pressure ramping, pressure clipping and use of 1st order time discretization in the fluid are the primary means by which to stabilize

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the solution. Of those, the grid flux under-relaxation and 1st order time discretization were utilized more heavily in these efforts. Grid flux under-relaxation effective in some problems where a steady state is being sought out, however in the case of an problem with a free surface, neglecting the grid flux terms can impact the convection of volume fraction through the morphing grid. This result makes under-relaxing the grid flux terms undesirable. Figure 5 presents a comparison of the drag force on the seal during the initial stage of an explicit and implicit co-simulation with the 2nd order time discretization and a time step of 0.0001 seconds. Note the signature reversing of the forces with the motion of the seal which is indicative of the artificial added mass effect.

Implicit Coupling

The implementation of the implicit coupling algorithm with iterative force-displacement exchange has eliminated the necessity to apply stabilizing techniques. Co-simulations of the FSI of the bow seal and free surface are now realizable with good initial conditions and proper selection of the solver parameters. These include the number of inner iterations, the number of inner iterations per exchange, the individual time steps for each code, and the coupling step. In this case, 20-30 total inner iterations per time step are used with 5 inner iterations per exchange, resulting in 4-6 total exchanges. The fluid time step and coupling step are 0.0001 seconds, and the structural time step is 0.0001 seconds with sub-cycling enabled.

The first step is acquiring a good initial condition to start the co-simulation. The authors’ best practice has been to freeze the co-simulation and morpher solvers, then calculate the fluid solution for 1-3 seconds until the initial constant velocities have been relaxed and the force on the seal reaches a stable value. At this point the solution fields are kept and used as the new initial condition, with the simulation history up to that point deleted. Using this method has not required the use of any of the stabilization techniques like pressure ramping or grid flux under-relaxation. In Figure 5, the implicit coupling solution stabilizes nicely as compared to the explicit calculation.

Figure 6 shows the displacement of the seal after 0.27 seconds of co-simulation and the resulting free surface profile. The seal has bulged outward in the middle due to the cushion pressure acting on the inner face, and the bottom of the seal is deflecting inward because of the hydrodynamic loads. By allowing the solution to run with the co-simulation frozen, the aft side of the seal becomes un-wetted due to forward speed and the flow separation at the tip. This is an advantage when dealing with the added mass effect, since the seal does not have to interact with water on the aft side, experiencing physical added mass effects. Ideally, the start of the co-simulations should mimic the experimental test runs with a stationary craft, then adding cushion pressure, and ramping up the craft velocity to the test condition. However, since the seal eventually becomes un-wetted on the aft side there should be no issue with this approach.

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Conclusion

The simulation of a flexible bow seal on a SES has been produced using the co-simulation tool for coupling STAR-CCM+ and Abaqus. A thin flexible flap hangs between the sidewalls of the craft which together contain the cushion pressure which is provided by a momentum source model representing the blower fans. The seal is acted on by both the interior cushion pressure on the inner surface, and the hydrodynamic loads on the wetted side as the craft moves at forward speed.

Early work, using the explicit coupling scheme, was unable to successfully model the displacement of the bow seal due to the instability inherent in this problem. Current work, using the newly-available implicit coupling scheme, is simulating the bow seal interacting with the free surface at full forward speed. Future work must be completed to better characterize the highly flexible rubberized fabric materials in the FEA model, create a Java macro routine for remeshing the fluid domain based on cell quality metrics, and include more of the physical features of the experiment which are not currently being modeled, such as the transverse stiffener bars on the seal.

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Figures

Figure 1: NSWCCD Model Number 5887, generic T-Craft SES model with finger type bowl seal

(top). A view of the underside of the craft showing the bow seal, transverse mid-cushion seal,

and stern seal (bottom). [4]

Figure 2 - The full geometry of the University of Michigan bow seal test platform. The flat plate

bow seal on the left side in light purple, the calm free surface is shown in light blue. [9]

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Figure 3 – The initial volume mesh of the model has 418,165 cells. Volume source refinement was applied for resolving the free surface, as well as additional refinement near the bow seal to ensure the fluid boundary will be able to morph along with the Abaqus displacement.

Figure 4 – The mesh must be periodically remeshed to preserve the solution quality and ensure the VOF method has a quality grid to capture the free surface. Left hand figures are prior to remeshing, right hand figures are after remeshing.

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Figure 5 – A comparison of the drag force time histories on the seal for both the implicit and explicit coupling algorithms for ∆t = 0.0001 s and 2nd order time discretization in the fluid.

Figure 6 - A contoured isosurface highlights the free surface elevation surrounding the craft and the co-simulation nodal displacement is shown on the diagonal seal at the bow on the right side of the figure.

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