1 h Inernaional Conference on Sabiliy of Ships and Ocean Vehicles 591 SIMULATION OF WAVE EFFECT ON SHIP HYDRODYNAMICS BY RANSE Qiuxin Gao, Universiy of Srahclyde, UK, Gao.q.x@srah.ac.uk Dracos Vassalos, Universiy of Srahclyde, UK, D.vassalos@na-me.ac.uk ABSTRACT The applicaion of advanced numerical analysis mehods based on soluion of RANS and VOF equaions on ship manoeuvrabiliy hydrodynamics is presened. The es cases seleced are conainer models in oblique moion under he effec of incoming harmonic wave. The compued and measured resuls are compared. The general agreemens beween calculaions and experimens are saisfying. Keywords: RANS, VOF, wave, yaw, sway, heave, pich 1. INTRODUCTION The simulaion of wave effec on ship hydrodynamics by using sae-of-ar CFD is gaining increasing aenion in recen years. The advanage of he approach over radiional srip heory or linear/non-linear poenial heory is improved accuracy and capabiliy on simulaion of ship moion in heavy sea. The disadvanage of demanding compuer resources and effor is becoming less boleneck afer high performance parallel compuing echnology was pu ino use. The wave generaion using RANS mehod is a paramoun ask for he sudy of maneuvering in wave. Numerical wave generaion and diffusion disurb physical wave propagaion and affec he qualiy of numerical maneuvering wave ank (diffracion problem in maneuvering scope). Moreover, dynamic or free moion of he ship sailing in he seaway make numerical simulaion more complicaed (radiaion problem in RASE scope). So far, here is lile relevan work available in he lieraure. There were only a few publicaions addressing added wave resisance using RANS approach. One calculaion was made by Weynouh ec using CFDSHIP-IOWA. They sudied head sea effecs on diffracion problem, forced heaving and piching moions. Uncerainy sudy was carried ou and sysemaic calculaions of parameric effecs were conduced. The comparisons of resuls from RANS code, srip heory, poenial code wih experimen show ha RANSE code performed much beer han oher codes. In his paper, applicaion of compuaional fluid dynamics on sudy of ship manoeuvrabiliy hydrodynamics by solving RANS and VOF equaions is presened. Firsly, numerical formulaions will be described wih he focus on numerical wave maker. Secondly, he mehod will be used o he simulaion of a conainer model running a seady yaw in head wave. Then, he aemp was made for free running model calculaions. The accuracy of numerical resuls will be evaluaed by model es daa. Finally, fuure work for improving numerical qualiy and applicaion o criical ship moion in severe sea will be proposed.
592 2. NUMERICAL FORMULATION The Reynolds averaged Navier-Sokes equaions wih SST Κ-ω urbulence model for closure were solved. VOF mehod was adoped o capure free surface inerface. The governing equaions can be wrien as follows. 1 h Inernaional Conference on Sabiliy of Ships and Ocean Vehicles 2.5 Boundary condiions The inle is locaed a one ship lengh ahead of ship where velociy componens and volume fracion were imposed. The wave was generaed from wave maker a inle using following values: 2.1 Coninuiy equaion The coninuiy equaion is wrien as: u = 2.2 RANS equaion u 1 + u u = g + ρ p ν 2 u (1) (2) Wave lengh λ/l=1. Wave ampliude ζ a /L=.8 Wave number k=2π/λ Wave frequency for deep waer ω= gk Model speed V=1.89m/s Wave encouner frequency ω e =ω+ kv Period T=2π/ω e Wave elevaion a inle ζ =ζasin( ω e) kz X velociy u =ζaωe sin( ω e) kz Z velociy w = ζωe cos( ω ) a e 2.3 Turbulence model μ ( ρk) + ( ρuk) = P ρε + (( μ + T ) K) σ ( ρω) + ( ρuω) = ( Γ ω) + G Y + D + S 2.4 VOF equaion ( rw) + ( rwu ) =. Where: u g τ ρ μ r w K ω P ω ω ω ω ω Velociy vecor Graviy vecor Sress ensor Mixure densiy Mixure viscosiy Volume fracion of waer Turbulence energy Specific dissipaion rae Pressure K (3) (4) (5) From above relaionship, we can obain he wave number is.98 and corresponding angular frequency of incoming wave is 3.1/s. Wave encouner angular frequency is 4.95/s. The period is 1.27 seconds. Wave ampliude is.512m. The incoming wave was generaed a he sar of he calculaion. I akes a few periods o eliminae iniial disurbance. Afer abou 5 periods, he force record becomes periodic wih period 1.27s. The oule is a wo ship lengh behind ship. The hydrosaic pressure is specified. Velociy componens and free surface elevaion were given on side boundary, which is locaed a one ship lengh from cenreplane. Wall funcion was used on hull boundary o save compuer ime. Using hese parameers, he simulaion of wave effec on seady oblique moion was performed. Yaw angles are and 1 degrees.
1 h Inernaional Conference on Sabiliy of Ships and Ocean Vehicles 2.6 Numerics Second order upwinding inerpolaion was used for convecion flux. SIMPLE mehod was applied o obain pressure. Geomeric reconsrucion of volume fracion was used o calculae wave elevaion. 3. TEST CASEE A conainer model (Hamburg Tes Case) adoped in EU VIRTUE projec was seleced for numerical analysis and validaion. The body plan and profile of bow and sern are shown in Figure 1. The main paricular of he vessel is given in able 1. 593 oher is free sailing moion wih wave effecs. The resuls are given below. 4. CAPTIVE YAW MOTION IN WAVE Manoeuvring in sea wave was radiionally sudied by simplified numerical approach wih model es based empirical formula. The accuracy of simulaion was case dependen. More reliable numerical ools are in demanding. Recen CFD developmen provides an advanced alernaive o ackle he problem. In EU projec VIRTUE, manoeuvring in calm waer and wave were sudied inensively. The resuls of calculaions of manoeuvring in calm waer covering seady yaw, urning, oscillaory sway and yaw were in good agreemen wih model es measuremen. The par of resuls of ship manoeuvring in wave will be presened in he paper. 4.1 Capive yaw angle 1 degrees Figure 1. HTC body plan. The firs case is capive yaw moion (1 degrees) in wave as shown in snapsho below. The harmonic wave was generaed using digial flap maker. The model was in oblique moion a Froude number.238 and yaw angle 1 Table 1. Main pariculars of HTC. The calculaions were carried ou on a 16 processors cluser. The mesh was medium sized wih 1.3m cells. The grid sensiiviy sudies were carried ou on he relevan sudy. The grid effecs are in general small for unseady calculaions. Two es cases were made. One is capive seady yaw moion wih incoming wave. The degrees. The X forces are given in Figure 2, where he resuls from (Red), (Purple) and measuremens (Blue and pink) were compared. The resuls from were obained by a poenial solver wih viscous correcion by PANASSOS. The HSVA experimen resuls
594 include hose wih and wihou wave. As we can clearly see ha surge force is consan wihou wave. The surge force oscillaes a he period given above when here was wave. Boh compued and measured surge forces in waves oscillae around he value from seady measuremen in calm waer. However, as can be seen, he ampliudes of oscillaions were differen. The compued ampliude by FLUENT is close o ha from measuremen. The prediced ampliude by is lower han daa. I seems ha viscous-wave ineracions were underesimaed by poenial solver. X.1.5 -.5 -.1 4 6 8 1 Figure 2. surge force. The sway force in Figure 3 shows similar rend as surge force. The compued sway force from boh and oscillaes periodically afer abou 5 periods when here was incoming wave. The ime record of sway forces from calculaions display sinusoidal feaure. However, he measured sway force exhibis srong high frequency oscillaion. I seems ha wave generaed in model es suffer from shor wave disurbance. The ampliudes of oscillaions beween calculaion and measuremen were generally consisen. The averaged sway forces in one period from calculaion and measuremen are close o ha from seady measuremen. The agreemens beween calculaions and measuremen are accepable. 1 h Inernaional Conference on Sabiliy of Ships and Ocean Vehicles Y.15.1.5 -.5 4 6 8 1 Figure 3. sway force. The yaw momen was shown in Figure 4. The agreemens beween calculaions and measuremen seem prey saisfying. The compued ampliudes and phase angles are close o measured one. The unseady ime records of forces oscillaes around value from seady measuremen. Averaged yaw momen by FLUENT is slighly larger han oher resuls. Similar resuls were obained in he calculaions of seady yaw and urning where prediced yaw momens are slighly larger han measuremen. The similar conclusion could be drawn for yaw momen as for surge and sway forces. N.6.5.4.3.2.1 4 6 8 1 Figure 4. yaw momen. Addiional o calculaion of drif angle 1 degrees, he calculaion of wave effec a sraigh forward condiion (wihou yaw) was performed as well.
1 h Inernaional Conference on Sabiliy of Ships and Ocean Vehicles 4.2 Capive sraigh ahead moion in head wave As here was no drif angle in he calculaion, he sway force, roll momen and yaw momen are all zero. Therefore, only surge force, heave force and pich momen are presened. Boh compued and measured surge forces shown in Figure 5 oscillae around he value from seady measuremen. However, as can be seen, he ampliudes of oscillaions were depending on he solvers. The compued ampliude by FLUENT is close o he measured one. However, i is much smaller by s solver. The averaged surge forces from calculaions and measuremen in one period were close o ha from seady measuremen wihou wave. The conclusion for surge force in yaw angle 1 degrees applies o sraigh ahead condiion..1 595 Only calculaion wihou drif was made o reduce he effor and uncerainy. X The surge force was given in Figure 6..1.5 -.5 -.1 2 4 6 8 Figure 6. Surge force in free moion..1 HSVA.5.5 X Heave -.5 -.1 4 6 8 1 Figure 5. surge force in head wave. 5. FREE RUNNING IN WAVE Ship sails in seaway in free running condiion. Ship aiude is no resrained as in capive condiion. The dynamic change of aiude in sea wave was simulaed in he calculaion. Ship speed is consan a 18 knos. Only surge force can be measured in model es. In he secion below, he comparison of calculaion wih measuremen is made. -.5 Figure 7. Heave. 2 4 6 8 The compued and measured surge forces oscillae wih same period 1.27s as in capive condiion. The compued ampliude of oscillaion in free condiion was close o ha in capive condiion while measured ampliude of oscillaion in free condiion was slighly larger han ha in capive condiion. The compued surge force shows numerical wave disurbance while measured surge force oscillaes periodically. The magniude of averaged surge forces in one period in calculaion and measuremen were slighly larger han ha in capive condiion. The sinkage and rim in free condiion ends o increase surge force a few
596 percenage. In general, he agreemens beween compued and measured surge force were good. The.4heave moion was given in Figure 7. Model moves verically wih wave induced heave.2 force. The period of oscillaion was he same as wave period 1.27s. The ampliude of heave moion is deermined by wave induced heave force. The averaged heave moion is relaed o seady hydrodynamic heave force. Pich -.2 The pich moion was given in Figure 8. Figure 8. Pich 2 4 6 8 Model moves wih free piching of period 1.27s. The oscillaion of pich moion in he calculaion was no sricly periodic. There was srong effec from numerical wave. The ampliude of pich moion is deermined by wave induced pich momen. The averaged pich in one period is relaed o seady hydrodynamic pich momen. From maneuvering calculaions in sea wave and comparison wih model ess, he accuracy of CFD ools was generally encouraging. Furher implemenaion of he ool on naval hydrodynamics will be srenghened. 6. FUTURE WORK CFD ools can be effecively used o sudy he wave effec on ship hydrodynamics in variey of moion modes. For he purpose of pracical applicaion, he following work needs o be esablished in he fuure: Model es daa base wih wave and moion signals as well as force componens are needed for validaion of CFD resuls Alhough bow wave can be generaed reliably, following sea as well as oblique sea need o be generaed by RANS approach For he calculaion of large ampliude ship moion, he qualiy of deforming mesh 1 h Inernaional Conference on Sabiliy of Ships and Ocean Vehicles needs o be improve 7. CONCLUSION Based on he compuaional resuls, he following conclusions are drawn: From he comparisons of compued and measured resuls i shows ha he oscillaions of forces in waves depend on he wave ampliude and wave lengh. The effecs of wave on ime-averaged forces from calculaion in capive condiion were small. Averaged X, Y, and N were close o hose from measuremen wihou wave. The forces from measuremen in waves suffer from high frequency disurbance. The reason for his wheher i is due o wall reflecion or wave qualiy needs o be clarified. The compued and measured surge forces in free condiion averaged in one period were slighly larger han hose in capive condiion. 8. REFERENCE Gabriel David Weymouh, Rober Vance Wilson and Frederick Sern: RANS Compuaional Fluid Dynamics Predicions of Pich and Heave Moions in Head Seas, Journal of Ship Research, Vol. 49 No.2, June 25, pp. 8-97 G. Ducroze, F.Bonnefoy, D. Le Touze & P. Ferran : Developmen of a Fully Nonlinear Waer Wave Simulaor based on Higher Order Specral Theory, 2h Workshop on Waer Waves and Floaing Bodies, Norway, 25 A. Cura Hochbaum and M.Vog: Towards he Simulaion of Seakeeping and Manoeuvring based on he Compuaion of he Free Surface Viscous Ship Flow, 24h Symposium on Naval Hydrodynamics, 23