Recent progress in CFD for naval architecture and ocean engineering*

STERN Frederick, WANG Zhaoyuan, YANG Jianming, SADAT-HOSSEINI Hamid, MOUSAVIRAAD Maysam, BHUSHAN Shanti, DIEZ Matteo, YOON Sung-Hwan, WU Ping-Chen, YEON Seong Mo, DOGAN Timur, KIM Dong-Hwan, VOLPI Silvia, CONGER Michael, MICHAEL Thad, XING Tao, THODAL Robert S., GRENESTEDT Joachim L.

1. IIHR-Hydroscience and Engineering, University of Iowa, Iowa City, IA, USA, E-mail: frederick-stern@uiowa.cn

2. Center for Advanced Vehicular Systems, Mississippi State University, Starkville, MS 39759, USA

3. CNR-INSEAN, Rome, Italy

4. Department of Mechanical Engineering, University of Idaho, Idaho 83844-0902, USA

5. Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, 18015, USA

Recent progress in CFD for naval architecture and ocean engineering*

STERN Frederick1, WANG Zhaoyuan1, YANG Jianming1, SADAT-HOSSEINI Hamid1, MOUSAVIRAAD Maysam1, BHUSHAN Shanti2, DIEZ Matteo3, YOON Sung-Hwan1, WU Ping-Chen1, YEON Seong Mo1, DOGAN Timur1, KIM Dong-Hwan1, VOLPI Silvia1, CONGER Michael1, MICHAEL Thad1, XING Tao4, THODAL Robert S.5, GRENESTEDT Joachim L.5

1. IIHR-Hydroscience and Engineering, University of Iowa, Iowa City, IA, USA, E-mail: frederick-stern@uiowa.cn

2. Center for Advanced Vehicular Systems, Mississippi State University, Starkville, MS 39759, USA

3. CNR-INSEAN, Rome, Italy

4. Department of Mechanical Engineering, University of Idaho, Idaho 83844-0902, USA

5. Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, 18015, USA

(Received January 1, 2015, Revised January 14, 2015)

An overview is provided of CFDShip-Iowa modeling, numerical methods and high performance computing (HPC), including both current V4.5 and V5.5 and next generation V6. Examples for naval architecture highlight capability and needs. High fidelity V6 simulations for ocean engineering and fundamental physics describe increased resolution for analysis of physics of fluids. Uncertainty quantification research is overviewed as the first step towards development stochastic optimization.

CFD, naval architecture, ocean engineering

Introduction

CFD capabilities continue to advance at ever-faster speed and ever-more-impressive accomplishments, as recently reviewed for ship hydrodynamics by Stern et al.[1]. None-the-less CFD is slow in its adaptation by industry since most users are at universities and R&D laboratories[2]. However, slowly-but-surely CFD is transforming engineering design as the build-and-test design spiral approach transforms to the simulation based design (SBD) approach offering innovative outof-the-box 21st century design concepts with improved safety, energy and economy. First generation SBD capability has focused more on functionality than high fidelity and exascale computing requiring significant advancements to achieve the next generation SBD capability for fully resolved, fully coupled, sharp-interface, multi-scale, multi-phase, multi-disciplinary turbulent ship flow including fluid structure interactions and utilizing billions of grid points.

Herein, recent progress in CFD for naval architecture and ocean engineering is overviewed based specifically on CFD Ship-Iowa URANS/DES toolbox, as an example of the current state-of-the-art. The emphasis is on the latest research since Stern et al.[1]. For a more complete list of references with regard to the development and applications of CFD Ship-Iowa URANS/DES toolbox within the field of computational ship hydrodynamics, the readers are referred to Stern et al.[1]. Iowa science and technology paradigm for the development of the SBD capability is described. An overview is provided of CFDShip-Iowa modeling, numerical methods and HPC, including both current V4.5 and V5.5 and next generation V6. Examples for naval architecture highlight capability and needs. High fidelity V6 simulations for ocean engineering and fundamental physics describe increased resolution for analysis of physics of fluids. Uncertainty quantification research is overviewed as the first step towards development stochastic optimization. Recent progress deterministic and stochastic optimization research is not reviewed herein since recently provided by Campana[3].

1. Paradigm for development SBD for ship hydrodynamics

Rapid advancements in simulation technology are revolutionizing engineering practice, as SBD and ultimately virtual reality are replacing current reliance on experimental observations and analytical methods. It is expected that a major shift in how scientific method forms its basis of conceptual truth, a shift from reliance on observations, based on experiments, to reliance on logic, based on simulations supported by experiments. SBD covers a broad range from computerized systems based methods to solutions of physics based initial boundary value problems (IBVP). Present interest is in solutions of physics based IBVP for ship hydrodynamics. SBD for ship hydrodynamics merges traditional fields of resistance and propulsion, seakeeping, maneuvering, open-ocean and littoral environmental effects, and offers new opportunities for future ships to meet challenges of the 21st century. Development SBD involves new paradigm for hydrodynamics research in which CFD, experimental fluid dynamics (EFD), and uncertainty analysis (UA) are conducted simultaneously for benchmark geometries and conditions using an integrated approach along with optimization methods, all of which serve as internal engine guaranteeing simulation fidelity. International collaborations with other research institutions and organizations include participation in ITTC and NATO AVT working groups and naval engineering educational consortium (NEEC), organizing international CFD workshops and current NICOP projects. Those activities are mutual-beneficial and magnifying individual institute capabilities, which has been foundational in the unprecedented achievements of computational ship hydrodynamics.

2. CFDShip-Iowa URANS/DES/LES SBD Toolbox

CFDShip-Iowa is general-purpose CFD simulation software developed at the University of Iowa’s IIHR-Hydroscience and Engineering for support of student thesis and project research as well as transition to Navy laboratories, industry, and other universities. CFDShip-Iowa has been a leading ship hydrodynamics CFD code for over 20 years, which has been verified and validated for many applications in ship flows. The current versions include CFDShip-Iowa V4.5, V6.1, and V6.2, with V5.5 and V6.3 under development.

2.1 V4.5 and 5.5 modeling, numerical methods, HPC

CFDShip-Iowa V4.5 is an incompressible URANS/DES solver designed for ship hydrodynamics[4]. The equations are solved in either absolute or relative inertial non-orthogonal curvilinear coordinate system for arbitrary moving but non-deforming control volumes. Turbulence models include blended k-ε/k-ω based isotropic and algebraic stress model (ASM) based anisotropic RANS, and DES approaches with near-wall models or wall functions. A singlephase level-set method is used for free-surface capturing. Captive, semi-captive, and full 6DOF capabilities for multi-objects with parent/child hierarchy are available. The fully discretized propeller or bodyforce propeller model can be employed for propulsion. The water-jet propulsion can be included using actual water-jet with detailed simulation of the duct flow or water-jet model with the reaction forces and moments. Incompressibility is enforced by a strong pressure/velocity coupling, achieved using either PISO or projection algorithms. The fluid flow equations are solved in an earth-fixed inertial reference system, while the rigid body equations are solved in the ship system. Other modeling capabilities include semi-coupled two phase air/water modeling, environmental waves and winds, bubbly flow, and fluid-structure interaction.

Fig.1 Free surface deformation around ship hull for fixed static condition

Numerical methods include finite difference discretization on body-fitted curvilinear grids, with high order upwind schemes for the convection terms and second-order centered for the viscous terms. The temporal terms are discretized using a second-order back-ward difference Euler scheme. Since the solver is designed for high-Reynolds number flows, the transport and re-initialization equations are weakly elliptical and thus pentadiagonal line solvers in an alternate-direction-implicit (ADI) scheme are used. A MPI-based domain decomposition approach is used, where each decomposed block is mapped to one processor. The resulting algebraic equation is solved with the PETSc toolkit using block Jacobi incomplete factorization (ILU) pre-conditioners and bi-conjugate gradients stabilized (BCGSL). All equations of motion are solved in a sequential form and iterated to achieve convergence within each time step.

Extension of CFDShip-Iowa Version 4.5 to Version 5.5 with a fully coupled two-phase flow solver using the volume-of-fluid (VOF) method is in progress. The approach includes implementing the highly accurate geometric VOF interface tracking method developed for V6, developing fully-coupled twophase flow solver, implementing cavitation and mixture models for air/water/vapor three-phase interaction, and developing capabilities for the necessary applications. The numerical methods, HPC, and SBD functional areas are similar to Version 4.5. The VOF method has been implemented into V5.5 to replace the level set method for the interface tracking and incorporated into the single phase flow solver. The current version of the code works with single-phase flow solver, multi-block grids, turbulence, and full 6DOF motions without overset grids. Figure 1 shows free surface deformation around the Numerette Planing Hull for fixed static condition.

2.2 V6.1, 6.2 and 6.3 modeling, numerical methods, HPC

The next-generation high-fidelity SBD tools, CFD Ship-Iowa V6, are already under development for milestone achievement in increased capability focusing on orders of magnitude improvements in accuracy, robustness, and exascale HPC capability.

In Version 6.1, Cartesian grids are used with immersed boundary methods for complicated geometries[5], and the level set based ghost fluid method is used for sharp interface treatment and fully two-phase coupling with the VOF method for interface tracking. Extension to orthogonal curvilinear grids was made in V6.2[6]with enhanced technologies for the interface modeling[7,8]and similar numerical methods and HPC capabilities as V6.1.

A finite-difference method is used to discretize the governing equations on a non-uniform staggered grid, in which the velocity components are defined at the cell face centers. All other variables are defined at the cell centers. Time advancement is based on the semi-implicit four-step fractional step method. The diagonal diffusion terms are advanced with the second-order Crank–Nicholson method and the other terms by the second-order explicit Adams-Bashforth method. The pressure Poisson equation is solved to enforce the continuity equation. The convective terms are discretized using the fifth-order WENO scheme. The other terms are discretized by the second-order central difference scheme. The pressure Poisson equation is solved using a semi-coarsening multi-grid solver from the HYPRE library.

The code is parallelized via a domain decomposition (in three directions) technique using the MPI library. All inter-processor communications for ghost cell information exchange are in non-blocking mode. Parallel I/O using MPI2 have been implemented such that all processors read from and write to one single file simultaneously[9]. In order to speed up the computations and improve the accuracy and efficiency for very large grid simulations (billions of grid points), some enhanced technologies have been implemented such as semi-Lagrangian advection schemes and optimized memory usage. The water/air interface is extracted as PLY polygon file format for post-processing. A multi-block grid capability has been recently incurporated into CFD Ship-Iowa Version 6.2.

Development of the general curvilinear grid solver, V6.3, is in progress, which is built on the success of V6.1 and V6.2 to achieve all functionalities of V4.5 and beyond. CFDShip-Iowa V6.3 is aimed at the highfidelity, high-resolution simulations of fully coupled, multi-scale, multi-phase, turbulent ship flows with fluid-structure interactions utilizing billions of grid points. The approaches include finite volume method, multi-block, body-fitted, general non-orthogonal curvilinear structured grids, overset background Cartesian grids, and highly modularized, developerfriendly code structure written in Modern Fortran (2008) and MPI.

The second-order finite volume method with accurate geometric approximations for non-smooth, non-orthogonal structured grids is used for the discretization. A generic transport equation is solved for momentum components and scalars with central difference and high-order upwind schemes used for facecentered value reconstruction. Exact projection method is implemented for machine-accuracy mass conservation where central difference and high-order upwind schemes for contra-variant volume flux reconstruction at cell face centers. Scalable MPI communication using new MPI-3 features will be implemented and MPI sub-array data type is extensively utilized for scalable MPI communication and I/O in V6.3.

3. Naval architecture

3.1 Resistance and seakeeping, captive and free running maneuvering, free running course keeping, and intact and damaged stability

Resistance and seakeeping predictions are inclu-ded in Gothenburg 2010 (G2010) and upcoming Tokyo 2015 (T2015) workshops. Prediction of resistance is the oldest application of CFD in ship hydrodynamics and its accuracy has been significantly improved since Gothenburg 1980 (G1980), the first CFD workshop held in 1980. In G2010, 89 submissions of resistance prediction are documented, which is the largest number in the workshop series[10]. More than 90% of the simulations were conducted using grids smaller than 10M points. The resistance prediction simulations were carried out for a wide range of applications and conditions. Other than resistance, sinkage and trim, local flow fields such as boundary layer and wake, and wave patterns were also predicted by many simulations. Different geometries including tankers, container ships, and surface combatants were studied at a range of very small to large Froude numbers ()Fr. The simulations showed average error of 3.3%D for resistance for both low and high Fr while sinkage and trim showed less errors for high Fr. The average error for sinkage/trim at low and high Fr was 9.7/ 11%D and 35/55%D, respectively. For seakeeping, several seakeeping test cases were included in G2010 with numerous contributions for each case. CFD computations of seakeeping have been rapidly increasing since Tokyo 2005 CFD workshop (T2005) in which there was only one forward-speed diffraction case with no motions. The applications for seakeeping predictions included a wide range of wave conditions, Froude numbers, and motion conditions. Similar to the resistance test cases, different geometries including tankers, container ships, and surface combatants were studied. Grid sizes ranging from 0.4 M to 71 M points were used with a clear trend toward increasing accuracy with grid size. The CFD predictions are assessed separately for 1storder vs. 2ndorder terms. The mean value of resistance and the amplitude of motions were considered 1storder terms whereas the amplitude of resistance and mean value of motions were considered 2nd order terms. The simulations showed large average error for the second order terms (44%)D while the average error was less than 15%D for the first order terms.

Fig.2 Turning maneuver simulation with water-jet propulsion

Captive and free running maneuvering simulations are included in the SIMMAN 2008 workshop[11]and upcoming SIMMAN 2014. The applications for captive predictions included PMM-type forced motions such as static rudder, static drift, pure sway, pure yaw, and yaw and drift conditions for different geometries. For SIMMAN 2008, 16 submissions were received for the forced motion simulations, comprising different CFD-based methods such as RANS, URANS, and DES. Grid sizes ranging from 2.1 M to 250 M points were used. It was concluded that finer grids were needed especially for the rudder and appendages and in regions of large vortices, as well as more advanced turbulence and propeller models for improvements in the CFD predictions of static and dynamic PMM maneuvers. Overall, the average error for captive maneuvering simulation was 13.6%D. The largest error values were generally observed for pure yaw and static rudder simulations. For linear derivatives, the average error was much larger for yaw moment (40%)D than sway force (15%)D. For nonlinear derivatives, the average error value was about 40%D. Free running maneuvering simulations were reported for limited cases in the SIMMAN 2008 workshop. The maneuvering simulation included standard maneuver test cases such as turning circle and zigzag. The results showed 6%D error for trajectories for turning maneuver prediction while larger errors (13%)D were obtained for zigzag maneuver. The grid sizes were from 0.4 M to 14.9 M points for these simulations. For most SIMMAN 2008 computations, the propulsion was implemented as an axisymmetric body force distributed in the propeller disk. The body force was specified in a non-iterative manner in which the ship wake on the body force was neglected. Recently, Wu et al.[12]used Yamasaki propeller model coupled with the RANS code to give a model that interactively determines propeller-hull interaction without requiring detailed modeling of the propeller geometry. Yamasaki model is based on a potential theory formulation, in which the propeller is represented by bound vortex sheets on the propeller disk and free vortices shed from them downstream of the propeller. Wu et al.[12]showed the Yamasaki propeller model could predict successfully the asymmetric wake field. In addition, the propeller rpm was predicted with less than 0.5%D error for Yamasaki compared to 12%D fornon-iterative axisymmetric body force. Free running simulations are also conducted with more advanced propulsion system such as water-jet. Sadat-Hosseini et al.[13]performed maneuvering simulations for a catamaran and validated the results against the experimental data (See Fig.2). The simulations were conducted either for bare hull with integral force models for water-jet or with actual water-jet with body force impeller defined by pump curves. Turning maneuver simulations showed average error of 9%D-22.6%D for CFD simulations with minimum error for the actual water-jet simulation. Zigzag maneuvers showed larger errors. In addition, the extremely large overshoot angles in zigzag showed the deficiency of water-jet propulsion system for maneuvering. Since CFD is computationally expensive for maneuvering in comparison to system based (SB) methods, some studies have focused on improving the SB mathematical model by using CFD with system identification methods. Araki et al.[14]employed CFD free running outputs to improve a 4DOF mathematical model developed for maneuvering in calm water and following waves. The CFD predictions were first validated against the experimental data from different facilities including IIHR wave basin[15,16]. For calm water, it was shown that the average system based prediction error drops from 16%D to 8%D using the maneuvering coefficients and rudder forces estimated from CFD free running instead of those from captive experiments. For waves, Araki et al.[14]showed that the mathematical model with wave loads estimated from CFD outputs provides better prediction for maneuvering in moderate following and quartering waves, compared to the original mathe-matical model with the wave loads computed from slender body theory. However, the improved mathematical model was too stable in severe waves and unable to predict the instabilities such as periodic motion or broaching. For SIMMAN2014 workshop, Sadat-Hosseini et al.[17]conducted simulations for free running maneuvers of KVLLCC2 in calm water using body-force propeller model and actual propeller (see Fig.3). The grid size was 6.8M-8.4M for different cases. The computational cost was 3-5 times higher for the simulations with the actual propeller. The results for turning maneuver showed =6.6%ED using propeller model and much less error (E=2.2%D) using actual propeller.

Fig.3 The grid topology and propeller vortices for KVLCC2 free running simulations with fully discretized propeller

Fig.4 5415M maneuvering simulations in calm water

Fig.5 The predicted transom free surface and vortex structures for turning maneuver simulation

Fig.6 Course keeping simulation in irregular oblique waves

Similarly, zigzag simulations showed better prediction using actual propeller. Sadat-Hosseini and Stern[18]performed maneuvering simulations for 5415M test cases of SIMMAN 2014 using twin counter-rotating propellers based on body-force propeller model with total grid size of 6.7M points (see Fig.4). The results showed about =12%ED for turning and zigzag 20/ 20 while larger errors were shown for zigzag 10/10. In addition, Sadat-Hosseini and Stern[18]conducted system-based simulations for 5415M maneuvering in calm water. The maneuvering coefficients were found from system identification using CFD outputs. To estimate the coefficients, parallel processing technique was used in which CFD free running data for several turning and zigzag maneuvers were first combined and then used to estimate one set of maneuvering coefficients. The system based predictions showed an average error of 5.30%D, 12.64%D and 4.67%D for trajectories for turning 35, zigzag 10/10 and 20/20, respectively.

Among free running maneuvering simulations, there are very limited studies on local flow. Recently, Sadat-Hosseini et al.[19]studied DES predictions of the local flow including transom wave field and vortex structures in turning maneuver. Similar study was previously conducted only for straight-ahead condition[20]. The mean and unsteadiness of transom wave field were predicted with 9%D and 11%D error while the trajectories were predicted with 3%D＜. The asymmetry of mean wave field was significantly under predicted due to surprisingly large asymmetry of EFD data. The unsteadiness spectra at few points in the transom wave field showed f-1.5scaling. The resolved turbulence kinetic energy was 86% in the transom region. The simulations showed Karman-like instability at transom, horseshoe vortices at the juncture of strut-hull and strut-shaft, and shear layer instability at the strut-hull intersection. Figure 5 shows the predicted transom wave field and vortex structures. Compared to straight-ahead condition, the Karman-like frequencies were 3% higher while others were 8%-35% lower for turning. In addition, the predicted frequency for Karman-like, horseshoe and shear layer vortex shedding in turning showed 2.4%, 3.7%-7.7% and 8.6% asymmetry, respectively.

There are few simulations conducted to investigate free running course keeping and instability. Stern and Toxopeus[21]and Sadat-Hosseini et al.[22]performed course keeping simulations in calm water, regular and irregular waves for the fully appended 5415M ship hull, in collaboration with NATO AVT 216 session “Evaluation of Prediction Methods for Ship Maneuvering and Control”. The results were validated against the experiments not only for the ship motions but also for the loads on the appendages. The results showed good prediction for the trajectories and loads on the appendages (10%)D＜ even for very complex geometries with dynamic stabilizer and rudders (see Fig.6). Comparing the irregular wave results with the results computed from regular wave simulations at several discrete wavelength conditions showed that theship has similar motion in both regular and irregular waves with same wavelength condition. The course keeping simulations focusing on intact instability are summarized in Stern et al.[1], showing good prediction for different instabilities including parametric roll, broaching and capsize, surf-riding, and periodic motion. For damaged stability, Sadat-Hosseini et al.[23]showed good prediction for both ship motions and water heights inside the compartment for damaged ship in calm water and waves.

Overall, free running simulations have been increasing in past few years and it is expected that the future challenges and method development efforts for modelling, numerical methods and HPC will focus on free running rather than captive simulations. In addition, more research will focus on improving the SB mathematical model by using CFD since CFD is computationally expensive in comparison to SB methods.

Fig.7 Overall vortical structures predicted by CFDShip-Iowa URANS (a2, b2) and DES (a3, b3) predictions on adapted 84M grid for 5415 with bilge keels

3.2 Turbulence

Prediction of turbulent viscous flow for ship hulls is of central importance and focused topic at CFD Workshops since G1980 to most recent G2010. Verification and validation of CFD predictions have been performed for tanker KVLCC2, container KCS and surface combatant 5415 hull forms at straight ahead conditions. In recent workshop extensive local-flow analysis was performed for KVLCC2 (bluff body) and 5415 (slender body) focusing on the effect of turbulence modeling. URANS with anisotropic turbulence model performed better than isotropic model. For KVLCC2, URANS under predicted axial velocity and vortical strength by 10% and over predicted turbulent structures by 35%, when compared with the experimental data. DES predicted unsteady flow with up to 95% resolved turbulence. DES mean flow predictions were quantitatively comparable to that of URANS, but were over predictive for both velocity and vortical and turbulent structures. DES showed grid induced separation inside the boundary layer and modeled stress depletion. The former was resolved by using delayed DES approach, whereas the latter issue was unresolved. For 5415, URANS provided reasonably good agreement with the experimental data, but under predicted the vorticity magnitude and boundary layer bulge, and over predicted turbulent structures at nominal wake plane. In DES, the resolved TKE levels were less than 3%, thus the results were unacceptable. Nonetheless, for the first time it provided plausible description of the overall vortex structures, and helped in understanding the sparse experimental data. Overall firm conclusions were not possible since grid and turbulence modeling errors could not be separated and sparseness of experimental data, especially for turbulence variables and onset and progression of 5415 vortices.

NATO AVT-183: Reliable Prediction of Separated Flow Onset and Progression for Air and Sea Vehicles research effort for the sea facet focused on procurement of detailed experimental data using PIV techniques, and evaluation and validation of CFD predictions using different codes by NATO members[24-26]. The study focused on three ship hulls: KVLCC2 atstatic drift β=30o, 5415 with bilge keels at straight ahead and β=20o, and Delft Catamaran at static drift conditions. Note that for 5415 cases, EFD data were procured for both planar sections and volumes surrounding the primary vortices. This allowed evaluation of Q- criteria along the vortex, which enabled validation for the vortex core predictions for the first time. Validation of 5415 case has been largely completed, and discussed below. CFDShip-Iowa simulations for the 5415 cases were performed using anisotropic URANS and DES models using finest adaptive grids to date, to reduce grid errors. In both the cases, URANS results do not improve when the grid is refined beyond 50M points. The best URANS predictions showed excessive decay of the vortices as shown in Fig.7, and resulted in large errors for the progression of the vortices as shown in Fig.8(a), when compared with experimental data. Considering that the results did improve with grid refinement, the large errors in URANS predictions were attributed to modeling errors. DES predictions for the straight-ahead case showed very low resolved turbulence levels, similar to G2010. For the static drift case, DES predictions improved with grid resolution. On the finest 84M grid, the resolved turbulence levels were 95%＞, and the flow predictions compared better with experimental data than those obtained using URANS. However, as shown in Fig.8(b), they predicted stronger vortex strength at onset and weaker vortex strength downstream. Note that the large errors could be partly due to grid resolution issues. CFD submissions using other codes were mostly using URANS, and one submission for the straight ahead case was using DES. The URANS results from other codes were very similar to that of CFDShip-Iowa for the static drift case. However for the straight ahead case, solvers predicted different decay rate of the vortices for similar size grids. The differences could be due to differences in numerical methods, grid topologies or turbulence model implementation, which needs to be investigated. The DES submission for the straight-ahead case, showed significantly high vortex strengths than experiments, similar to CFDShip-Iowa prediction, affirming the limitations of DES models.

Fig.8 Variation ofpeakQ (LEFT) and TKE (RIGHT) at primary vortex cores predicted by best CFDShip-Iowa simulations are compared with EFD data. (a) URANS predictions on 84M grid for sonar dome vortex (SDV) and fore body keel vortex (FBKV) cores is compared for straight ahead case. (b) DES predictions on 84M grid for sonar dome tip vortex (SDTV) and bilge keel tip vortex (BKTV)

Vortex onset and separation in the straight ahead case was identified due to open-type cross flow separation. The vortex separates from the surface due to the presence of adverse axial pressure gradient along converging streamline, and is identified from the peak of div (τw). The vortex separation pattern for the static drift case included both open-, closed- and openclosed type separations. The separation pattern and topology were consistent with those available in the literature. The closed-type separation satisfied the topo-logical rules expected for a close-separation formed over an isolated body or body intersecting a wall or free-surface.

Overall, turbulence modeling is a roadblock for improved prediction of viscous flow for ship hulls, as URANS is too dissipative and DES has limitations for both slender and bluff bodies. For the slender body at straight ahead condition, DES fails to trigger resolved turbulence. For slender bodies at static drift and bluff bodies at both straight ahead and static drift conditions, DES predicts sufficient resolved turbulence levels and the predictions are better than that of URANS, but shows large comparison errors for the progression of the vortices probably due to modeled stress issue. LES are ideal for accurate CFD predictions, as they have less dependence on modeling, however, they are prohibitively expensive due to grid resolution requirements in the boundary layer. Hybrid RANS/LES models provide a reasonable alternative, wherein URANS is used in the boundary layer and LES in the wake. However, more advance hybrid RANS/LES models should be investigated to address the DES modeling issues. The research should particularly focus on investigation of: turbulence trigger models to enable transition from RANS to LES for slender body simulations, blended RANS-LES models with explicit LES modeling that are more rigorously validated than the LES mode of single parameter models, such as DES, and physics based RANS-LES blending rather than grid based blending to address modeled stress depletion issues.

3.3 Ship-ship interaction

CFD computations of ship-ship interaction have been reported in the recent International Conference on Ship Maneuvering in Shallow and Confined Water. Mousaviraad et al.[27]used CFDShip-Iowa to study Hope and Bobo in replenishment condition in calm water and waves, and in overtaking maneuver in waves. The average error against EFD was 21%D for calm water, and 10%D for replenishment in waves. The sheltering effect was significant for oblique waves, with 105% difference between mid-mid and mid-bow configuration. The separation distance effect was more important for head waves than oblique waves, being 43% and 23% respectively. During the overtaking, the interaction effect decreases motions and increases sway forces, roll and yaw moments, being more significant for the smaller vessel. Sadat-Hosseini et al.[28]and Wu et al.[12]investigated the interaction between two different tankers Aframax and KVLCC2 using CFDShip-Iowa. The ships were free to heave and pitch advancing in shallow water with same speed and fixed separation distance. Both ships were appended with rudder and operating propellers, which were modelled by axisymmetric body force propeller model with same RPM as experiments.

Fig.9 WAM-V CFDShip-Iowa regular head wave results in most probable conditions of SS3 (Fr=0.52(10 kt))

Overall, the simulations showed large errors for predicted forces, moments and motions compared with the experimental data. Later, it was found the longitudinal positions of the two ships in the experiments were notreported correctly. Therefore, the simulations were repeated with the revised conditions but the errors were still large and thus more studies should be conducted to evaluate the experimental setup. In addition, the accuracy of the axisymmetric body-force propeller model for propulsion in shallow water should be investigated.

Fig.10 WAM-V hydrodynamic modeling for CFD simulations in regular head waves compared with EFD sea trials in random seas

Fig.11 WAM-V 2-post testing (a) and 6-post suspension simulation (b) using CFD results as inputs. Comparison of payload accelerations is shown (c) for 6-post simulation (white) and 2-post test data (grey)

3.4 Advanced hull forms and fluid-structure interaction: ACV/SES, WAM-V, planing hulls

CFD studies of advanced hull forms impose significant challenges due to complex and multi-disciplinary modeling requirements, very high speeds introducing different physics than conventional ships, and difficulties in validation studies due to limitations in model testing and limited measurements in sea trials. Modeling requirements are different for specific hulls, e.g., fluid-structure interactions (FSIs) including multi-body dynamics (MBD) for suspension systems and finite element (FE) modeling for flexible hulls.

ACV/SES capabilities are implemented in CFDShip-Iowa including cushion models, seal models, air-flow over the above water seals and superstructure, decoupled cushion cavity flow, waterjet propulsion with side forces and yaw moments induced by nozzle rotations and reverse buckets, and air-fan propulsion model. Validation simulations are carried out for a combined SES/ACV ship (T-Craft) for captive tests in deep and shallow water. Free-running simulations of T-Craft in turning and zigzag maneuvers in deep and shallow water and in calm water and waves are also carried out. Recent analyses showed that the resistance and moment due to cushion pressure distribution inside the cavity is significant for seakeeping cases while not considered in the initial simulations. The improved results will be published for captive validation studies and free-running demonstration simulations.

The wave adaptive modular vessel (WAM-V) is an ultra-light flexible catamaran that conforms to the surface of the water through a collective suspension and is modularly designed enabling a wide variety of applications. The springs, shock absorbers, and ball joints articulate the vessel such that the hulls can move semi-independently and along with the inflateble pontoons adapt to the water surface/waves to mitigate structural stresses and reduce drag. WAM-V capabilities are implemented in CFDShip-Iowa including: LS_IBM (level-set immersed boundary) method for treatment of the gap between pontoon and hinged pod, a two-body dynamics model for hinged pod motions, and a jet force model moving with hinged pod for free-running simulations. Captive calm water verification and validation studies are carried out with average error of 5.7%D[29]. Validation against fullscale sea trial data and coupling with MBD modelingare carried out in collaboration with Prof. Mehdi Ahmadian of Virginia Technology University. Freerunning validation studies are carried out against sea trial data in calm water and seas[30]. For simulations in waves, statistical analysis of the sea trial data in waves is conducted to provide an estimate of the dominant encounter frequency. CFD regular head waves simulations (Fig.9) are carried out at the dominant encounter frequency and with a wave height over wavelength of H/λ=1/64, the typical value for sea state 3. The results are compared with sea trial data in Fig.10 and show that although the EFD data have large peaks, their standard deviation (SD) values converge to values very close to CFD. The CFD regular head wave results are then used by Virginia Technology University as inputs to run a 2-post shaker rig testing and a SIMULINK virtual shaker rig modeling and the results for the payload suspension motions are shown in Fig.11 with very good agreement. MBD modeling for the suspended payload is carried out for a 2DOF cylinder drop as a first step to WAM-V suspended payload modeling. The SIMULINK MBD code is coupled with CFDShip-Iowa in 1-way weak coupling and 2-way strong coupling approaches and the results are shown in Fig.12. The 2-Way coupling results show significant improvement over 1-Way results: for the un-sprung mass displacement the initial slope after the pontoon hits the water free surface is more accurately predicted, the double hump at the first peak is predicted, and the frequency of occurrence is maintained correctly through the displacement curve, for the sprung mass displacement, 2-Way results follow the EFD displacement curves both in magnitude and frequency, especially for the first second, while after 1 s the sprung mass displacement is slightly over-predicted. Overall the results are validated with acceptable agreement. Future work will couple the CFDShip-Iowa and the MBD model for WAM-V, and perform validation studies against measurements of the motions/accelerations of the suspended payload during the full-scale sea trials.

Fig.12 CFD-MBD 2DOF 1-Way and 2-Way coupling results for cylinder drop compared with EFD data for pontoon ((a), (b)) and sprung mass ((c), (d)) motions

Fig.13 Underwater surface photo from EFD for USNA planing model at Fr=1.83 (a) and comparison with CFDShip-Iowa predictions

Fig.14 USNA planing hull regular wave simulations using CFDShip-Iowa and NFA compared with experiments

Fig.15 Irregular wave slamming pressures for USNA planing hull: (a) EFD slamming events aligned by peak pressure, (b) CFDShip-Iowa validation showing expected value (EV) and +/– standard deviation (SD) bars for re-entering and emerging pressures and duration

Fig.16 CFD-FEA simulation results for FSI studies showing force and displacement distribution for the bay 4, port panel on the full-scale Numerette planing vessel in regular head waves corresponding to sea state 3 most probable wave condition at =0.7Fr

Planing hull capabilities including hydrodynamic performance and structural loads and slamming are mplemented and validated for calm water, regular waves, and irregular waves for the Fridsma geomery[31,32]. CFD and EFD studies are carried out to validate the hydrodynamic forces, moments, hull pressues, accelerations, motions, and the multiphase freesurface flow field generated by the USNA planing craft at high-speed (Fr=1.8-2.1) in calm water and egular and irregular waves[33]. The work is conducted by collaborations with Carolyn Judge of United States Naval Academy (USNA). CFDShip-Iowa simulations or calm and regular waves were carried out blind, beore EFD data was available. Calm water spray root at Fr=1.83 is compared in Fig.13 with underwater sur-face photo from EFD indicating very close agreement. CFDShip-Iowa V5.5 simulations with volume of fluid free surface solver showed negligible effects on resistance and motions, while the extension of the jet spray flow was resolved better than V4.5 level-set solver. Regular wave results for USNA experiments (run 43 and 44) and CFD simulations using CFDShip-Iowa V4.5 and NFA solvers are compared in Fig.14 for motions and slamming pressure. The phase of the heave and pitch is well predicted, while the amplitude of the numerical simulations is greater than measured experimentally. Pitch motions at twice the lowest frequency are not evident in simulations performed using either CFDShip-Iowa or NFA. Single point pressure measurements show good agreement for slam duration while the re-entering pressure amplitudes are underpredicted for both codes. A smaller time step may be needed to capture the peak pressure. The emerging peak pressures are missed in NFA simulations while captured in CFDShip with close agreement. Irregular waves simulations are validated with good agreement in terms of expected values and standard deviations of motions, accelerations, and slamming pressures. Slamming statistical studies are carried out for both experimental data and simulation results and validation results are shown in Fig.15 for slamming pressure. Extreme slamming events are studies both for EFD and CFD by examining the standard score for re-entering pressure (zP=(P-EVP)/SDP). For EFD, 4 slam events with zP＞2 and 6 events with 1＜zP＜2 are detected. These events are found to correlate with ship motions, namely the vertical velocity of the ship bow at the time of impact. CFD studies are carried out to provide further insight by correlating the extreme slam events with relative bow/wave motions as well as history of previous zero crossing waves. The CFD extreme events are grouped in 3 categories: zP＞1.5 (3 events), 1＜zP＜1.5 (4 events), and 0＜ zP＜1 (14 events). For each slam event, wavelength over ship length (/)Lλ and wave height over wave-length (/)Hλ values for the immediate wave, as well as averaged values for the last 2, 3, 4, and 5 waves are calculated. In group 1, slam pressures correlate 100% with smaller /Lλ and larger /Hλ for the last 3 waves. For groups 2 and 3, strongest correlations are for larger /Hλ averaged over the last 2 and 3 waves, respectively. Considering all the slams in all 3 groups, strongest correlation is found for smaller /Lλ from the last 3 waves and larger /Hλ from the last 2 waves. Type-2 slams characterized by containing only one pressure peak (re-entering pressure) with smaller peak values and shorter duration are identified both in EFD and CFD.

Fig.17 Average, min and max of EFD (experimental fluid dynamics) strain with its expected value (EV) and standard deviation (STD) at peak compared with CFD/FE predicted strain for sea state 3 most probable wave condition and =2.9Fr

FSI studies[34]are carried out for the Numerette planing hull (slamming load test facility at Lehigh University) to provide a better understanding of slamming using benchmark full-scale validation EFD data. The studies are conducted in collaboration with Dr. Joachim Grenestedt of Lehigh University. Initially rigid body CFD simulations are conducted for both bare hull and appended hull with sterndrive unit and body-force propeller model excluding the superstructure. The predicted motions and loads are used for one way coupling with FE model for composite bottom panels to evaluate displacement, strain, and stress. CFDShip-Iowa is used for CFD simulations and the commercial FE code ANSYS is used as structural solver. Studies are carried out in calm water (Fr=0.7) and different regular head waves conditions at =Fr 0.7, 2.24 and 2.9. CFD/FE results show good prediction for displacement, strain, and stress distribution for both starboard and bottom panels. Figure 16 shows the panel force and displacement for a regular head wave simulation with Sea-State 3 most probable wave conditions at =0.7Fr. Figure 17 shows EFD and CFD-FE strain for a regular head wave simulation with sea state 3 most probable wave condition at Fr=2.9. Two-way coupling will be implemented by first using modal analysis with added mass modeling, and then fully coupled CFD-FEA. FSI V&V studiesare also planned for slamming loads on Athena semiplaning hull.

Fig.18 Vortical structures with -Qcriterion (left) and energy spectra of the streamwise velocity in the shear layer (right)

4. Ocean engineering

Simulations of 3-D unsteady separation (vortex shedding) around offshore structures and wave run-up induced by ocean waves are still challenging for ocean engineering applications. Recently, the capabilities of state-of-the-art CFD codes for vortex shedding and wave run-up are investigated in ITTC ocean engineering workshop held in Nantes, France October 17-18, 2013. The capabilities of CFDShip-Iowa V4.5 and V6.2 for these applications are reported in Yeon et al.[35]and Yoon et al.[36]. The studies focused on the flow around single/multiple cylinder(s), a typical geometry for both applications.

4.1 Single- and two-phase vortex shedding

In Koo et al.[37]the two-phase turbulent flow past an interface-piercing circular cylinder was studied using large-eddy simulation with a Lagrangian dynamic subgrid-scale model. It was shown that the airwater interface makes the separation point more delayed for all regimes of Re and the air-water interface structures are remarkably changed with different Froude numbers. However, the deep flow did not display the correct single-phase flow behavior due to the deficient grid resolution and non-conservative convection scheme, among other issues, employed with CFDShip-Iowa V6.2. Yeon et al.[35]conducted a detailed study of the single-phase vortex shedding around acircular cylinder for ITTC ocean engineering workshop test cases. The simulations are conducted using CFDShip-Iowa V6.2, covering sub- to super-critical Re. A careful verification and validation study were carried out. The effects of aspect ratio/span length, conservative vs. non-conservative convection schemes, and grid resolution were investigated. The mean velocity, mean pressure, Reynolds stresses, and TKE distribution were obtained and discussed. The snapshot POD method was employed to analyze flow structures in the boundary layer, shear layer and wake. Figure 18 shows coherent flow structures visualized with isosurface of Q criterion colored by the non-dimensional eddy viscosity. The wake width and amplitude of the shedding is large for the sub-critical Reynolds number ()Re and become smaller as Re increases. Energy spectra of the streamwise velocity in the shear layers are also shown in Fig.18. At lower wavenumbers the energy spectra give scaling exponents close to the Kolmogorov slope, which verifies that the largeeddy simulations properly modeled the turbulence and preserved the correct energy decay behavior, although the ranges of wavenumbers with the -5/3 spectral slope become narrower as Re increases. On the other hand, for larger wave numbers, the rates of energy decay are faster than Kolmogorov’s decay law and the scaling slopes become much steeper. A main cause of this rapid decay is the numerical dissipation from the upwind convection schemes used in the simulations. The Kolmogorov wavenumbers estimated from the local velocity fluctuations are smaller than the grid cut-off wavenumbers. This indicates the grid resolution is adequate in the shear layers, where the turbulence intensity is usually lower than that in the wake. Figure 19 shows comparisons for CD,θLS/ θTS, and -Cpb. The drag crisis is well predicted, although more cases in the critical and post-critical regime are desirable. The LESis close to the most reliable data for sub-, critical and super-critical Re. The angle of separation is close to the experiments for sub- and critical Re, but substantially under predicted for super-critical Re. The base suction pressure shows good agreement with the experiments for sub- and super-critical Re, but is under predicted for critical Re. The largest difference is for critical Re, where the drag drops sharply with small changes in Re resulting in large changes inDC between facilities and likely simulations. The grid resolution, convection scheme, and the effect of upstream disturbance ubiquitous in experiments, but missing in the simulations, are most likely responsible for the under-predicted separation angle for the critical Re.

Fig.19 Drag coefficient, RMS lift coefficient, separation angle, and base pressure vs. Re

4.2 Wave run-up

Fig.20 EFD and CFD comparison of mean wave field for single cylinder cases

Fig.21 Mean and 1stharmonic amplitude of the wave field cases

CFD simulations of wave run-up around single/ multiple truncated vertical cylinder(s) for ITTC ocean engineering workshop tests cases were conducted by Yoon et al.[36]. The simulations were conducted in regular head waves for various wave conditions including /=4.7Dλ and /=21.9Dλ with 1/30, 1/16 and 1/10. Sensitivity studies are conducted for the effects of grid distribution, domain size and turbulence model. Validation studies focused on averaged wave height at crest/trough and 0th, 1stand 2ndharmonics for wave elevation and horizontal force. CFD predictions were assessed separately for 1stand 2ndorder variables. The averaged wave height at crest/trough and the 1stharmonics were considered as the 1storder variables, whereas the 0thand 2ndharmonics were considered as the 2ndorder variables. In addition, the wave field pattern around cylinder(s), vortex shedding, and interaction among cylinders were analyzed. The grid sensitivity for the 1stand 2ndorder variables was 3.17% and 77.74%, respectively, both less than the facility bias estimated from the provided experimental data from two facilities. Nonetheless, the 2ndorder variable sensitivity was large indicting the need for finer grids to resolve 2ndorder terms. The domain size sensitivity was also very small, 1.14% and 2.34% for 1stand 2ndorder variables. The turbulence model sensitivity was conducted using URANS and DES and the sensitivity for 1stand 2ndorder variables was 1.64% and 6.55%, respectively, suggesting that the URANS turbulence model is sufficient for the validation studies. The validation studies showed 10%D error for wave crest/ trough, 7%D error for the 1stharmonic of wave elevation, and 70%D error for the 2ndorder variables including the 0thand 2ndharmonics of wave elevation. The horizontal forces also showed 9%D error for the 1stharmonic amplitude while larger errors are predicted for the mean and 2ndharmonics. The detailed study of the wave field showed that the mean wave field elevations are similar to the free surface elevations for a cylinder in a steady flow due to the large wave induced current (up to 15% of the orbital velocity for the steepest wave). The results showed larger effects of the wave steepness on the wave mean and 2ndamplitude than on the 1stharmonic amplitude. The wave steepness effect was also more prominent for λ/D =4.7 than λ/D =21.9. The studies were also conducted on the total wave field to evaluate the diffracted wave pattern. The nonlinearities in the incident wave caused difficulties extracting the diffraction wave from the total wave field. However, the total wave field could show the diffraction wave at upstream which was more dominant for /=4.7Dλ and steeper waves. Figures 20 and 21 show the wave field for single and four cylinder cases. The studies on vortex structures showed more vortex shedding for longer wave conditions as its longer wave period provides enough time to develop vortices around the cylinder. For both wavelength conditions, the vortex shedding is more at instants the wave crest is located near the cylinder as the flow field velocity is larger. Lastly, the comparison of four and single cylinder cases shows that the interaction of cylinders increases wave trough for 4%-10% while the wave crest increases about 9%-25%. The largest interaction effect is found for the shoulder side of the cylinders.

Fig.22 Flow charts of three different strong coupling schemes in one time step for fluid-structure

5. Fundamental physics

5.1 IBM for idealized and practical geometries

Immersed boundary methods are simple and efficient approaches for many problems with complex geometries and moving boundaries, thanks to the relaxation of the requirement of generating boundary-fitting grids in numerical simulations. CFDShip-Iowa V6.1 is a Cartesian grid solver utilizing a direct forcing immersed boundary method. The research focus is on efficient strong coupling schemes for FSIs and the extension to wave-body interaction problems in naval architecture and ocean engineering. In Yang and Stern[38]an efficient strong coupling scheme for 6DOF motion prediction was developed. The predictor-corrector loop in each time step includes the adjustments of the structure displacements and velocities, but the fluid flow solver was excluded. Then in Yang andStern[39]an efficient and robust immersed boundary setup procedure was developed for further accelerating the strongly coupled simulations of FSIs. This approach can be a viable choice for particulate flows as shown in Yang and Stern[40]. Currently a non-iterative strong coupled scheme has been developed. Figure 22 shows the flow charts of three different strong coupling schemes in one time step for FSI problems. Compared with the scheme in Yang et al.[41]with a complete iterative loop including multiple Poisson solves and the scheme in Yang and Stern[38]with one Poisson solve but multiple local reconstruction steps, the present scheme utilizes an intermediate step with a non-inertial reference frame (NIRF) attached to a solid body and no iterative loop is involved. The improved efficiency and reduced algorithm complexity is evident. The next step of development will be combination of this new scheme with an efficient two-phase flow solver for ultra-scale simulations of 6DOF motions in naval architecture and ocean engineering. It should be pointed out that the development of wall models in immersed boundary methods is necessary if high Reynolds number flows are the target application and a reasonable approximation of the turbulent boundary layers is required.

Fig.23 Stokes wave breaking

Fig.24 (a) Cavitating NACA66 hydrofoil with a 6oangle of attack, 2-D solution showing cavity growth and shedding. (b) Close up views of a sharp interface simulation of a cavitating NACA66 hydrofoil with a 6° angle of attack showing bubble growth, merging, and advection shortly after inception at the leading edge

5.2 Bubble, droplet, and spray in breaking waves

Air entrainment, bubbles, droplets, jets, and spray in breaking waves are of great importance to ship hydrodynamics. Previous experimental and computational studies are mainly focused on the global structures of the wave breaking. With the development of the CFD technology, detailed studies of the small scale structures, such as water droplets and air bubbles, in the two-phase region become possible. In the study by Wang et al.[42], wave breakings around a wedgeshaped bow and over a submerged bump are simulated using very large grids (1.0×109-2.2×109grid points). This study is the first attempt to directly simulate the unsteady and energetic wave breaking flows to the scale of micrometers. In Wang et al.[43], even large grids (up to 11.8×109) are used in order to resolve the bubbles/droplets in breaking Stokes waves at the scale of several micrometers. Figure 23(a) shows the wave profile at time =t1.76 when the splash-ups are being generated after the wave plunging. The 3-D interface instability in the spanwise direction is clearly demonstrated in Fig.23(b). The study of the flow over a bump in a shallow water flume by Gui et al.[44,45]showed that the G?rtler type centrifugal instability is the most relevant mechanism for the free surface instabilities. Figures 23(c) and 23(d) show the applications of the G?rtler inviscid instability and Rayleigh instability theories in the stream-wise central plane, respectively. In the wave breaking region, G?rtler stability criterion is violated in most locations and Rayleigh stability criterion is broken only in small regions. These results support the idea that breaking wave instabilities are mainly due to G?rtler type centrifugal instability. Figure 23(e) shows the formation of bubbles/droplets in the process of wave breaking. Power-law scaling for the bubble size distribution was obtained with two different slopes separated by a Hinze radius of 0.0012 m as shown in Fig.23(f). The simulation results are in good agreement with the experimental findings.

5.3 Cavitation

Cavitation degrades the performance of lifting surfaces found on ships, such as propeller blades and rudders and may cause erosion. Past computational models have generally been homogenous mixture models, which average the effects of many bubbles, or discrete bubble models, which model only a limited number of bubbles. In Michael et al.[46]a new sharp interface cavitation model was described within the framework of CFD Ship-Iowa V6.2. The interface is advected using a volume of fluid method with the addition of an additional velocity due to phase change. The phase change component of the interface velocity is modeled using a simplification of the Rayleigh-Plesset equation computed through a volume source term included semi-implicitly in the pressure Poisson equation. A marching cubes method is used to compute the interface area in each computational cell and for the determination of the phase at the cell and face centers. Figure 24(a) shows a time series of cavitation on a 2-D NACA66 hydrofoil at ao6 angle of attack. The details of the shedding process can be seen. Figure24(b) shows the bubble growth, merging, and advection process in the simulation of the same foil in 3-D shortly after cavitation inception. This type of high fidelity simulation offers the opportunity for deeper insight into the physics of cavitating flows.

6. Uncertainty quantification

Initial research focused on development and application of deterministic verification and validation (V&V) methodologies and procedures for high-fidelity CFD simulations. Initial studies for validation methodologies[47]were subsequently extended to verification procedures for deterministic uncertainties stemming from iterative, grid and time-step convergence[48,49]. V&V methodologies and examples were presented at the AVT-147 Symposium on Computational Uncertainty[50]. Recently, the research focus moved to stochastic uncertainty quantification (UQ) methods as an essential part of stochastic design optimization for real ocean environment and operations, such as robust design optimization (RDO) and reliability based design optimization (RBDO). UQ research was undertaken within NATO AVT 191 “Application of Sensitivity Analysis and UQ to Military Vehicle Design”. The objective was the development and validation of efficient UQ methods for application to realistic ship hydrodynamic problems. Non-intrusive UQ methods were addressed with high-fidelity physicsbased CFD solvers. Evaluation metrics for efficient UQ methods were developed, based on deterministic and stochastic convergence criteria and validation versus numerical benchmark[51,52], and efficiency of overall UQ procedure by assessing the number of CFD simulations required to achieved prescribed error thresholds[53]. Numerical benchmarks were provided by statistically convergent MC simulation with direct use of CFD computations. UQ methods included metamodel-based Monte Carlo (MC) simulation, quadrature formulas, and polynomial chaos methods. Applications covered unit studies and advanced industrial problems. Specifically, a unit problem for a NACA 0012 hydrofoil with variable Reynolds number was presented and assessed in Mousaviraad et al.[51]. The highspeed Delft catamaran (DC) advancing in calm water with variable Froude number and geometry was presented and studied in Diez et al.[54]. DC in stochastic irregular and regular head waves (see Fig.25) with variable speed and geometry was assessed in He et al.[55]. A combination of UQ problems for the DC was selected from Diez et al.[54]and He et al.[55]and used for further investigation in He et al.[56], focusing on the polynomial chaos method, and Volpi et al.[53], focusing on dynamic metamodels.

In conclusion, stochastic UQ methods were found mature for application to realistic stochastic optimization problems. Based on the evaluation metrics, MC with dynamic metamodels was found the most promising method overall. The high computational efficiency of dynamic metamodels, by auto-tuning and adaptive sampling, makes the approach also recommended for stochastic optimization. Metamodel-based UQ has been applied to stochastic design optimization of DC in real ocean environment and operations, as shown in Diez et al.[54]and Tahara et al.[57]. Future extensions include the application of metamodel-based UQ and optimization to multi-disciplinary analysis and optimization (MDA, MDO) of FSI problems.

7. Future research

Fig.25 Comparison of time history distributions from irregular wave (benchmark) and regular wave UQ for the Delft Catamaran in head waves, at sea state 6 and =0.5Fr. Empirical and Normal density functions are shown

The oncoming exascale HPC era is to change ourapproaches to grand scientific and engineering challenges and to transform modeling and simulation into a specified discipline of predictive science. Current mainstream RANS solvers for ship hydrodynamics are expected to continue performing well for even larger grids of up to a few billions of points. However, there will be a threshold that further increase of grid size cannot improve the results anymore because of the inherently limited RANS/DES turbulence models and the widely-used lower-order discretization schemes. High-fidelity, first-principles-based simulations with unprecedented resolution can reveal vast unknown temporal-spatial correlations in multi-scale and multiphysics phenomena that are beyond today’s computing and experimental capabilities. With comprehensive V&V procedures, assisted by targeted physical experiments, and rigorous uncertainty quantification, they are to revolutionize ship hydrodynamics research and, along with optimization techniques, the ship design process for greatly reduced design cycles and cost and much improved operation safety and economy. Therefore, the next-generation, high-fidelity ship hydrodynamics solvers have to be developed aiming at the oncoming exascale computing platforms, and addressing modeling issues, discretization schemes, and HPC memory and scalability restraints at the same time.

Acknowledgments

This work was supported by research Grants from the Office of Naval Research (ONR), with Dr. Patrick Purtell, Dr. Ki-Han Kim, Dr. Thomas Fu, Ms. Kelly Cooper, Dr. Roshdy Barsoum, and Dr. Robert Brizzolara as the program managers. The FSI studies are performed in collaboration with Dr. Joachim Grenestedt of Lehigh University. The WAM-V studies are conducted in collaboration with Dr. Mehdi Ahmadian of Virginia Technology University. The planning hull studies are conducted in collaboration with Dr. Carolyn Judge of USNA. The simulations were performed at the Department of Defense (DOD) Supercomputing Resource Centers (DSRCs) through the High Performance Computing Modernization Program (HPCMP).

The user profile obtained by the 26th International Towing Tank Conference held in 2011 indicated for ship hydrodynamics CFD: 65% universities and model basins, 20% directly industry (shipbuilding or engineering design companies), and 15% other. Respondents rated themselves as intermediate/advance CFD engineers. In addition, most model-basin work is for experimental testing not CFD as requested their customers and likely biased by investments in experimental facilities. Ultimately, it depends on the customers at all levels and regulation agencies.

[1] STERN F., YANG J. and WANG Z. et al. Computational ship hydrodynamics: Nowadays and way forward[J]. International Ship Building Progress, 2013, 60(1-4): 3-105.

[2] ITTC2011. The specialist committee on computational fluid dynamics[C]. Proceedings of 26th International Towing Tank Conference. Rio de Janeiro, Brazil, 2011.

[3] CAMPANA E. F. Ship design under uncertainty via high-fidelity stochastic optimization[C]. Proceedings of Annual General Meeting of the Schiffbautechnische Gesellschaft E.V. Berlin, Germany, 2013.

[4] HUANG J., CARRICA P. M. and STERN F. Semi-coupled air/water immersed boundary approach for curvilinear dynamic overset grids with application to ship hydrodynamics[J]. International Journal for Numerical Methods in Fluids, 2008, 58(6): 591-624.

[5] YANG J., STERN F. Sharp interface immersed-boundary/level-set method for wave-body interactions[J]. Journal of Computational Physics, 2009, 228(17): 6590-6616.

[6] Wang Z., SUH J. and YANG J. et al. Sharp interface LES of breaking waves by an interface piercing body in orthogonal curvilinear coordinates[R]. AIAA paper 2012-1111, 2012.

[7] WANG Z., YANG J. and STERN F. A new volume-offluid method with a constructed distance function on general structured grids[J]. Journal of Computaional Physics, 2012, 231(9): 3703-3722.

[8] WANG Z., YANG J. and STERN F. A simple and conservative operator-splitting semi-Lagrangian volumeof-fluid advection scheme[J]. Journal of Computational Physics, 2012, 231(15): 4981-4992.

[9] YANG J., BHUSHAN S. and SUH J. et al. Large-eddy simulation of ship flows with wall-layer models on Cartesian grids[C]. Proceedings of 27th Symposium on Naval Hydrodynamics. Seoul, Korea, 2008.

[10] LARSSON L., STERN F. and VISONNEAU M. Numerical ship hydrodynamics: An assessment of the gothenburg 2010 workshop[M]. Gothenburg, Sweden: Springer, 2014, 318.

[11] STERN F., AGDRUP K. and KIM S. Y. et al. Experience from SIMMAN 2008-The first workshop on verification and validation of ship maneuvering simulation methods[J]. Journal of Ship Research, 2011, 55(2): 135-147.

[12] WU P. C., SADAT-HOSSEINI H. and TODA Y. et al. URANS studies of ship-ship interactions in shallow water[C]. Proceedings of 3rd Intl. Conference on Ship Manoeuvring in Shallow and Confined Water. Ghent, Belgium, 2013.

[13] SADAT-HOSSEINI H., CHEN X. and KIM D. H. et al. CFD and system-based prediction of Delft catamaran maneuvering and course stability in calm water[C]. Proceedings of 12th International Conference on Fast Sea Transportation. Amsterdam, The Netherlands, 2013.

[14] ARAKI M., SADAT-HOSSEINI H. and SANADA Y. et al. System identification using CFD captive and free running tests in severe stern waves[C]. Proceedings of 13th International Ship Stability Workshop. Brest, France, 2013.

[15] SANADA Y., TANIMOTO K. and TAKAGI K., et al.Trajectories for ONR Tumblehome maneuvering in calm water and waves[J]. Ocean Engineering, 2013, 72: 45-65.

[16] SANADA, Y., ELSHIEKH, H., TODA Y. et al. Effects of waves on course keeping and maneuvering for surface combatant ONR tumblehome[C]. Proceedings of 30th Symposium on Naval Hydrodynamics. Hobart, Tasmania, Australia, 2014.

[17] SADAT-HOSSEINI H., WU P. C. and CARRICA P. M. et al. CFD simulations of KVLCC2 maneuvering with different propeller modeling[C]. Proceedings of SIMMAN2014 Workshop. Copenhagen, Denmark, 2014.

[18] SADAT-HOSSEINI H., STERN F. System based and CFD simulations of 5415M maneuvering[C]. Proceedings of SIMMAN2014 Workshop. Copenhagen, Denmark, 2014.

[19] SADAT-HOSSEINI H., KIM D. H. and TAYLOR G. L. et al. Vortical structures and instability analysis for Athena in turning maneuver with full-scale validation[C]. Proceedings of 30th Symposium on Naval Hydrodynamics. Hobart, Tasmania, Australia, 2014.

[20] BHUSHAN S., XING T. and STERN F. Vortical structures and instability analysis for Athena wetted transom flow with full-scale validation[J]. Journal of Fluids Engineering, 2012, 134(3): 031201.

[21] STERN F., TOXOPEUS S. Chapter 1–Experimental and computational studies of course keeping in waves for naval surface combatant[R]. Technical Report 161, NATO AVT, 2013.

[22] SADAT-HOSSEINI H., STERN F. and TOXOPEUS S. CFD simulations of course keeping in irregular waves for 5415M[J]. Ocean Engineering, 2014, in Preparation.

[23] SADAT-HOSSEINI H., KIM D. H. and LEE S. K. et al. CFD and EFD study of damaged ship stability in regular waves[J]. Ocean Engineering, 2014, in Preparation.

[24] YOON H., GUI L. and BHUSHAN S. et al. Tomographic PIV measurements for a surface combatant at straight ahead and static drift conditions[C]. Proceedings of 30th Symposium on Naval Hydrodynamics. Hobart, Tasmania, Australia, 2014.

[25] ABDEL-MAKSOUD M., MüLLER V. and XING T. et al. Chapter 7-Experimental and numerical investigations on flow characteristics of the KVLCC2 at 30odrift angle[R]. Technical Report 183, NATO AVT, 2015.

[26] FALCHI M., FELLI M. and GRIZZI S. et al. SPIV measurements around the Delft 372 catamaran in steady drift[J]. Experiments in Fluids, 2014, 55(11): 1844.

[27] MOUSAVIRAAD S. M., SADAT-HOSSEINI S. H. and CARRICA P. M. et al. URANS studies and validation of ship-ship interactions in calm water and waves for replenishment and overtaking conditions[J]. Journal of Ocean Engineering, 2014, Submitted.

[28] SADAT-HOSSEINI H., WU P. C. and TODA Y. et al. URANS studies of ship-ship interactions in shallowwater[C]. Proceedings of 2nd International Conference on Ship Manoeuvring in Shallow and Confined Water. Trondheim, Norway, 2011.

[29] MOUSAVIRAAD S. M., BHUSHAN S. and STERN F. URANS studies of WAM-V multi-body dynamics in calm water and waves[C]. Proceedings of 3rd International Conference on Ship Maneuvering in Shallow and Confined Water. Ghent, Belgium, 2013.

[30] CONGER M., MOUSAVIRAAD S. M. and STERN F. et al. URANS CFD for two-body hydrodynamic simulation of wave adaptive modular vessels (WAM-V) and validation against sea trials[J]. Naval Engineers Journal, 2014, Accepted for Publication, special edition: the current fleet, the next class and the new prototypes.

[31] MOUSAVIRAAD S. M., WANG Z. and STERN F. URANS studies of hydrodynamic performance and slamming loads on high-speed planing hulls in calm water and waves for deep and shallow conditions[C]. Proceedings of 3rd International Conference on Ship Maneuvering in Shallow and Confined Water. Ghent, Belgium, 2013.

[32] MOUSAVIRAAD S. M., WANG Z. and STERN F. URANS studies of hydrodynamic performance and slamming loads on high-speed planing hulls in calm water and waves for deep and shallow conditions[J]. Applied Ocean Research, 2014, Submitted.

[33] FU T. C., BRUCKER K. A. and MOUSAVIRAAD S. M. et al. A computational fluid dynamics study of the hydrodynamics of high-speed planing craft in calm water and waves[C]. Proceedings of 30th Symposium on Naval Hydrodynamics. Hobart, Tasmania, Australia, 2014.

[34] VOLPI S., SADAT-HOSSEINI H. and KIM D. H. et al. Validation high-fidelity CFD/FE FSI for full-scale highspeed planing hull with composite bottom panels slamming[C]. Proceedings of International Conference on Coupled Problems in Science and Engineering. San Servolo Island, Venice, Italy, 2015.

[35] YEON S., YANG J. and STERN F. Large eddy simulation of drag crisis in turbulent flow past a circular cylinder[C]. Proceedings of ITTC Workshop on Wave Run-Up and Vortex Shedding. Nantes, France, 2013.

[36] YOON S. H., KIM D. H. and SADAT-HOSSEINI H. et al. High-fidelity CFD simulation of wave run-up around vertical cylinders in monochromatic waves[C]. Proceedings of ITTC Workshop on Wave Run-Up and Vortex Shedding. Nantes, France, 2013.

[37] KOO B., YANG J. and YEON S. et al. Reynolds and Froude number effect on the flow past an interface-piercing circular cylinder[J]. International Journal of Naval Architecture and Ocean Engineering, 2014, 6(3): 529-561.

[38] YANG J., STERN F. A simple and efficient direct forcing immersed boundary framework for fluid structure interactions[J]. Journal of Computational Physics, 2012, 231(15): 5029-5061.

[39] YANG J., STERN F. Robust and efficient setup procedure for complex triangulations in immersed boundary simulations[J]. Journal of Fluids Engineering, 2013, 135(10): 101107.

[40] YANG J., STERN F. A sharp interface direct forcing immersed boundary approach for fully resolved simulations of particulate flows[J]. Journal of Fluids Engineering, 2014, 136(4): 040904.

[41] YANG J., PREIDIKMAN S. and BALARAS E. A strongly coupled, embedded-boundary method for fluid structure interactions of elastically mounted rigid bodies[J]. Journal of Fluids and Structures, 2008, 24(2): 167-182.

[42] WANG Z., YANG J. and STERN F. High-fidelity simulations of bubble, droplet, and spray formation in breaking waves[R]. HPC Insights, 2012, Fall Issue: 5-7.

[43] WANG Z., YANG J. and STERN F. High-fidelity simulations of bubble, droplet, and spray formation in breaking waves[C]. Proceedings of 30th Symposiumon Naval Hydrodynamics. Hobart, Tasmania, Australia, 2014.

[44] GUI L., YOON H. and STERN F. Experimental and theoretical investigation of instabilities for flow over a bump in a shallow water flume with steady downstream wave train[R]. Technical Report 487, IIHR, University of Iowa, 2014.

[45] GUI L., YOON H. and STERN F. Techniques for measuring bulge-scar pattern of free surface deformation and related velocity distribution in shallow water flow over a bump[J]. Experiments in Fluids, 2014, 55(4): 1721.

[46] MICHAEL T., YANG J. and STERN F. Modeling cavitation with a sharp interface[C]. Proceedings of 30th Symposium on Naval Hydrodynamics. Hobart, Tasmania, Australia, 2014.

[47] COLEMAN, H. W., STERN F. Uncertainties and CFD code validation[J]. Journal of Fluids Engineering, 1997, 119(4): 795-803.

[48] STERN F., WILSON R. and SHAO J. Quantitative V&V of CFD simulations and certification of CFD codes[J]. International Journal for Numerical Methods in Fluids, 2006, 50(11): 1335-1355.

[49] XING T., STERN F. Factors of safety for Richardson extrapolation[J]. Journal of Fluids Enginerring, 2010, 132(6): 061403.

[50] STERN F. Quantitative V&V of CFD solutions and certification of CFD codes with examples for ship hydrodynamics[C]. Proceedings of Symposium on Computational Uncertainty, AVT-147. Athens, Greece, 2007.

[51] MOUSAVIRAAD S. M., HE W. and DIEZ M. et al. Framework for convergence and validation of stochastic uncertainty quantification and relationship to deterministic verification and validation[C]. International Journal for Uncertainty Quantification, 2013, 3(5): 371-395.

[52] DIEZ M., CHEN X. and CAMPANA E. F. et al. Reliability-based robust design optimization for ships in real ocean environment[C]. Proceedings of 12th International Conference on Fast Sea Transportation, FAST2013. Amsterdam, The Netherlands, 2013.

[53] VOLPI S., DIEZ M. and GAUL N. J. et al. Development and validation of a dynamic metamodel based on stochastic radial basis functions and uncertainty quantification[J]. Structural Multidisciplinary Optimization, 2014, DOI 10.1007/s00158-014-1128-5, in Press.

[54] DIEZ M., HE W. and CAMPANA E. F. et al. Uncertainty quantification of Delft catamaran resistance, sinkage and trim for variable Froude number and geometry using metamodels, quadrature and Karhunen-Loève expansion[J]. Journal of Marine Science and Technology, 2014, 19(2): 143-169.

[55] HE W., DIEZ M. and ZOU Z. et al. URANS study of Delft catamaran total/added resistance, motions and slamming loads in head sea including irregular wave and uncertainty quantification for variable regular wave and geometry[J]. Ocean Engineering, 2013, 74: 189-217.

[56] HE Wei, DIEZ Matteo and CAMPANA Emilio Fortunato et al. A polynomial chaos method in CFD-based uncertainty quantification study for ship hydrodynamic performance[J]. Journal of Hydrodynamics, 2013, 25(5): 189-217.

[57] TAHARA Y., DIEZ M. and VOLPI S. et al. CFD-based multiobjective stochastic optimization of a water-jet propelled high speed ship[C]. Proceedings of 30th Symposium on Naval Hydrodynamics. Hobart, Tasmania, Australia, 2014.

10.1016/S1001-6058(15)60452-8

* Biography: STERN Frederick (1949-), Male, Ph. D., Professor