Numerical Modeling of a Planing Hull Maneuvering in a Regular Wave, Part 1: Dynamic Instability

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1 h Inernaional Conference on Fa Sea Tranporaion FAST, Honolulu, Hawaii, USA, Sepember Numerical Modeling of a Planing Hull Maneuvering in a Regular Wave, Par : Dynamic Inabiliy Ray-Qing Lin and Tim Smih Hydromechanic Deparmen, Naval Surface Warfare Cener, Carderock Diviion (NSWCCD), Maryland, USA ABSTRACT The urf recue boa (SRB) of Unied Sae Coa Guard i a cla of high peed planing boa. Thi 9-meer craf i capable of operaing a peed up o Froude number.7. However, when i begin o maneuver in inciden wave near i maximum peed, dynamic inabiliy occur immediaely. In hi inance, he craf rim and roll o a large heel angle, and Plow-In, even wih mall ampliude inciden wave, and mall urn curve. In hi udy, a fully nonlinear hip moion model named he Digial Selfconien Ship Experimenal Laboraory (DiSSEL) i ued a a numerical ool o underand he phyic ha caue he dynamic inabiliie. DiSSEL howed ha when SRB reached Froude number=.698, acceleraion due o heading change would caue a dynamic force and momen imbalance, reuling in heel and pich moion inabiliie. DiSSEL alo howed ha if he heading i fixed, and oher condiion remain he ame, he inabiliy didn occur. Unforunaely, here i no deailed record of he daa or numerical imulaion of he hip moion in he able and unable region, excep for he decripion of he hip moion by Codega and Lewi (987). The imulaion by DiSSEL agree well wih hi decripion. KEY WORDS Planing Hull, Maneuvering, Inciden wave, Dynamic inabiliy, Numerical modeling. INTRODUCTION High-peed urf recue planing boa were deigned o be ued for urf earch and recue operaion for Unied Sae Coa Guard. Thee planing recue boa are able o operae a peed up o 5.5m/ (Froude number=.7) in 3-meer wave heigh. Thee boa have many advanage; for example, hey are eay o maneuver like diplacemen boa and need le power. However, here i one major problem: when hey maneuver a heir upper peed limi in a eaway, hey ofen capize (Codega and Lewi, 987). The Naval Sea Syem Command (NAVSEA) Comba Syem Engineering Saion, Combaan Craf Engineering Deparmen, wa requeed o reearch he problem. The ranvere inabiliy of high peed planing craf i a common problem; ee Lewandowki (996, 997) and Ikeda and Kaayama (). Many year laer, he reaon for SRB capize even are ill no fully underood.. Numerical Tool In hi udy, we will ue a newly developed hip moion model (DiSSEL) o inveigae hi cae. In 7, he Propulion Syem Demonraor (PSD) wa eleced o evaluae DiSSEL abiliy o predic hip moion in boh he raniion and planing regime (Lin and Hoy, 7). In he ame year, he Unied Sae Marine Corp curren Amphibiou Aaul Vehicle (AAV7A) wa ued o evaluae DiSSEL abiliy o predic he Plow-In phenomenon (Hoy and Lin, 7). Boh udie howed he predicion and daa had very good agreemen; however, he evaluaion were only for fixed heading cae. Recenly, Lin e al () ued DDG-5 Pre-Conrac deign hull form and an experimenal hull form o evaluae DiSSEL abiliy o predic he hip moion when maneuvering in calm waer and in a eaway. The imulaion and daa have good agreemen. Bu boh of hee e hull form are no planing craf. Furhermore, he benchmarking i limied o low peed. Finally, we wan o poin ou ha DiSSEL agreed well wih he ae-of-he-ar Large Ampliude Moion Predicion (LAMP) Model (Lin and Yue, 99); and Lin e al (994) when he Froude number i no greaer han.5 (Lin and Kuang, ). Thi i fir ime DiSSEL i ued o udy planing craf maneuvering in a eaway in planing mode. Hopefully, he dynamically conien model can give u ome anwer. The dynamic inabiliy i dicued in hi paper, while uggeion o avoid he inabiliy are preened in a companion paper, Par : Safey Operaion.. Surf Recue Boa (SRB) The hull form of he SRB i hown in Fig. a. Fig. a. Thi i he SRB hull form. American Sociey of Naval Engineer 857

2 The ma of SRB i kg, he maximum lengh i 9.6m, and he beam i.794m; draf in calm waer wih zero peed i.957m. A eed, he cener of graviy wa Xlcg=-.63m, cg=., vcg=.34m. The ma momen of ineria were aken a: Rxx/B=.385, Ryy/L=.47, and Rzz/L=.46. The rudder dimenion were: lengh =.633m, op widh=.397m, and ip widh=.9m. The waerje force i hown in Fig. b. Force (kg) Thru Waerjec Waerje Force Drive Lif Ship Speed (Fr) Fig. b. Waerje force by hip peed of he SRB Fig. a and Fig. b how ha he SRB i a lighweigh boa, requiring le propulion force han many oher planing craf, uch a PSD and AAV. The running rim in calm waer i hown in Fig. c. Running Trim Angle (deg) Running Trim Ship Speed (Fr) Fig. c. SRB running rim by hip peed. The running heave in calm waer i hown in Fig. d. DiSSEL Daa Heave Moion (m) Running Heave Froude Number (Fr) Fig. d. SRB running heave by hip peed. DiSSEL Daa Fig. c and Fig. d how ha he running rim and running heave prediced by DiSSEL in calm waer agree well wih he daa (Codega and Lewi, 987).. DiSSEL SHIP MOTION MODEL DiSSEL i compoed of wo main componen. The fir componen handle he hip-wave ineracion and compue he flow around he hip including he influence from he waer free urface, he preure diribuion on he hip hull, and he hydrodynamic force on he hip. The econd componen olve he olid body moion and ue he preure compued by he hip-wave ineracion componen o predic he ix-degree-of-freedom moion of he hip by olving he equaion of moion in he ime domain. The rudder conribuion i included a an exra componen of he force erm in he rigid body moion componen of he code. Furher deail of he model can be found in Lin e al (5) and Lin and Kuang (6, and ). DiSSEL i baed on a hybrid-flow mehod, unlike a pure poenial flow; i include wave breaking and eparaion effec, which are very imporan for predicing hip moion when a hip maneuver in a eaway. The calculaion of eparaion effec in poenial flow can be decribed imply a follow: When a flow pae an objec, he oal preure lo due o eparaion on he objec can be obained by inegraing he preure over he blocking area ( A b ). If he preure in he abence of vicoiy and urbulence i P(), and he preure wih vicoiy and urbulence i P * (), hen he oal force on he objec in hybrid-flow mehod i: A A * n P d np ( ) d, b ( ) A Where A i oal flow impaced by he urface area, n i normal vecor of objec. A b varie wih hip moion, wave ampliude and wave number (Lin and Kuang, 8 and Lin e al, ). The wave breaking funcion varie wih wave ampliude, wave number, hip peed, hip-wave ineracion (Lin and Kuang, 7). 858 American Sociey of Naval Engineer

3 . Ship-Wave Ineracion Model The hip-wave ineracion componen i compued in a fluid domain of deph, H, widh, D, and lengh, L. Excep for he free urface and boom boundary, all oher boundarie are open, which allow fluid o freely pa hrough hee face. Such boundarie no only allow he ue of a mall compuaional domain, bu alo increae accuracy. For an incompreible fluid, h for H z () z The dynamic and kinemaic boundary condiion a z = are P ( u vh) g () ( uvh) x h ( h ) ( h u v h ) (3) z where u i hip forward peed, v h i he horizonal componen of hip repone ranlaional moion of v, φ i he velociy poenial, p i he preure, i he fluid deniy, η i he free urface elevaion, i he kinemaic vicoiy (here repreening he wave breaking effec), g i graviaional acceleraion, i ime, and x i he poiion vecor of a poin in pace. For a purely poenial flow, he vicou diipaion in () vanihe. The above equaion are olved wih an impenerable boundary condiion. A he boom, z = -H, ( hh) ( h u vh) z If one ue he pecral mehod, i require h H, and on he hip hull: n u (5) u i he oal velociy and equal: p c u u v Ω x x (6) where Ω i he hip angular velociy, n i he normal vecor, x p i an arbirary poin on he hip hull urface, x c i he ma cener. (4) The far field boundarie are open boundary condiion ha preerve he conervaion of ma and are implemened a: ( u v ), e h e where e and elevaion of he environmenal wave, and (7) e are he velociy poenial and urface are he correponding quaniie of oher wave aociaed wih he hip (e.g., hip generaed wave and he wave ariing from he hip-environmenal wave ineracion). The over bar indicae he paial average of he quaniie. For he far field, DiSSEL employ he peudo-pecrum mehod.. Solid Body Moion Model In hi ecion, he baic equaion decribing he moion of he rigid hip hull are preened. Poiive x i in he forward direcion, poiive y i o por, and poiive z i upward. The origin i a he cener of ma of he hip. In he olid body moion model of DiSSEL, he hip ranlaional moion i expreed a d v p q m hip D ran v F hip F hip (8) d where, m hip i oal hip ma, D ran i he damping p coefficien for ranlaional moion, and Fhip i he oal preure force on he hull a well a on he rudder and appendage, and F i he oal buoyancy force. The q hip olid body roaion i governed by he Liouville equaion and defined in he hip coordinae yem a dω p q I ΩI ΩDroaΩΓhip Γ hip (9) d where I i he oal hip momen of ineria, D roa i he damping coefficien for roaional moion (Lin and Kuang, 8) and Γ i he oal preure momen acing on he p hip q hull, a well a on he rudder and appendage, and Γ hip i he oal buoyancy momen. DiSSEL ue a body exac inegraion by finie elemen/finie difference mehod o calculae he force and momen. A well-behaved, precondiional conjugae reidual ieraive mehod i ued o help wih he dynamical balance beween force and buoyancy force, and momen and buoyancy momen. The roll damping due o he bilge keel i calculaed in DiSSEL uing blocking heory (Lin and Kuang, 8). Applying he blocking heory alo aifie he Kua condiion a he railing edge and he velociy agnaion poin, V TE. The lif force i obained, wih reaonable accuracy, wihin DiSSEL by inegraing he oal preure on he weed urface in he z-direcion. American Sociey of Naval Engineer 859

4 From he velociie in he hip-fixed frame, he drif angle i compued uing: () an () u v v () where v () and v () are x and y componen of v, repecively. The oal heading angle, *, i he yaw angle, 3 plu drif angle : * 3 () A more complee decripion of he formulaion of DiSSEL can be found in Lin e al. (). 3. SHIP INSTABILITY In hi udy, o implify he problem, we avoided he hallow waer effec and only udied he SRB maneuvering in deep waer and focuing on he SRB deign problem. Fir we will udy he hip moion in he able region, hen in he unable region. In each region, we alo imulaed bow ea and quarering ea. Unforunaely, here are no deailed record, daa or numerical imulaion of he hip moion when he SRB i able while maneuvering, or in he proce of capizing. Therefore, he benchmarking i baed on he decripion of Codega and Lewi (987). 3. Sable Region When he SRB forward peed i le han or equal o 5 kno (Fr=.849), he SRB i very able, which mean i can make reaonably large heading change wihou capizing in boh bow ea and quarering ea condiion. 3.. Maneuvering in Bow Sea In he following imulaion, he rudder angle and hip forward peed are inpu daa, and he hip moion are he imulaion oupu. Where λ=wave-lengh/hip-lengh, Hw i wave-heigh, Lw i wave-lengh, and Fr i Froude number. Rudder angle change wih ime i hown in Fig. a. Rudder Angle The acual hip peed which included drifing effec on he hip peed i hown in Fig. b. Ship Speed (Fr) Ship Acual Speed (Daa inpu) Fig. b. Acual hip peed a inpu daa in cae. The imulaion of roll and pich moion are hown in Fig. c. Ship Moion (deg) Ship Moion in Bow Sea (λ=, Hw/Lw=/3, Fr=.849) Roll Moion Pich Moion Fig. c. Numerical imulaion of hip moion by DiSSEL The numerical imulaion of hip rack (way, urge and yaw moion) i hown in Fig. d. 8 Ship Track in Regular Bow Sea (λ=. Hw /Lw =/3, Fr=.849) Rudder Angle (deg) y (m) x 9m) Fig. a. Rudder angle variaion wih repec o ime i inpu daa for imulaion in cae. Fig. d. The imulaion of hip rack, y-coordinae i he original forward direcion; x-coordinae i urning away from original direcion. 86 American Sociey of Naval Engineer

5 3.. Maneuvering in Quarering Sea Similar o bow ea, he rudder angle i inpu daa, a hown in Fig. 3a; reuling peed i hown in Fig 3b. Rudder angle (deg) Rudder Angle y (m) Ship Track in Regular Quarering ea (λ =, Hw/Lw=/3, Fr=.849) x (m) Froude Number (Fr) Fig. 3a. The rudder angle i inpu daa for cae Ship Speed 4 8 Fig. 3b. The acual peed i for cae. Becaue hip peed include he drifing force, he ame acual peed for he hip given peed in quarering ea i maller han hoe in bow ea. Fig. 3d. Simulaion of he hip rack in quarering ea. The previou wo cae howed ha he SRB i very able and can allow large heading change when i acual peed equal 5 kno (Fr=.849). We have eed everal cae, bu included a ingle repreenaive cae for each eaway. 3. Inabiliy Region When he acual peed i increaed o mainain able maneuvering, he SRB need o reduce i heading change (curvaure), which i no hown in hi paper. However, here i a criical poin, beyond which he SRB dynamic inabiliy no longer can be overcome. The imulaion of hip moion a he criical poin are hown in hi ubecion. 3.. Maneuvering in Bow Sea The rudder angle a inpu daa for cae 3 i ime maller han hoe of cae (Fig. a) and cae (Fig. 3a), a hown in Fig. 4a. Rudder Angle Ship Moion (deg) Ship Moion in Regular Quarering Sea (λ=, Hw/Lw=/3, Fr=.849) Roll Moion Pich Moion Fig. 3c. Simulaion of roll and pich moion in quarering ea. Rudder Angle (deg) Fig. 4a. Inpu rudder variaion i for cae 3. American Sociey of Naval Engineer 86

6 Froude Number (Fr) Ship Speed Roll Angle (deg) S hip moion in R egular B ow w ave (λ=, H w /Lw =/3, Fr=.698) Ship Moion (deg) Fig. 4b. The hip acual peed i for cae Ship Track in Bow Sea (λ=, Hw/Lw=/3, Fr=.698) Roll Moion Pich Moion Fig. 4c. Simulaion of roll and pich moion for cae 3. y (m) Ship Track in Regular Bow Sea (λ =, Hw /Lw =/3, Fr=.698) x (m) Fig. 4d. Simulaion of hip rack for Cae 3. Fig. 4 how ha when he SRB maneuvered in bow ea and i acual peed wa equal o 3 kno (Fr=.698), no maer how mall he heading change i, he inabiliy ill occur. The SRB ar o Plow-In and he roll angle reache 9 o which agree well wih he decripion by Codega and Lewi (987). Fig. 4e and Fig. 4f how roll and pich for a fixed heading, wih oher condiion remaining. Fig. 4e. The imulaion of roll moion a a fixed heading. Pich Angle (deg) - Pich moion in Bow Sea (λ=, Hw/Lw=/3, fr=.698) Fig. 4f. The imulaion of pich moion a a fixed heading. The difference beween roll moion (blue line) in Fig.4c and Fig. 4e i wih and wihou heel moion. We can ee heel i dominaing he moion in Fig. 4c and caue he inabiliy. The difference beween pich moion (red line) in Fig. 4c and in Fig. 4f i wih and wihou Plow-In. 3.. Maneuvering in Quarering Sea The previou ubecion howed he hip moion inabiliy in bow ea. Thi ubecion udie he hip moion inabiliy in quarering ea. Fig. 5a how he rudder inpu; Fig. 5b and Fig. 5c how reuling peed and roll/pich moion. Rudder Angle (deg) Rudder Angle Fig. 5a. The rudder angle i for cae American Sociey of Naval Engineer

7 Froude Number (Fr) Ship Moion (deg).5.5 Ship Speed Fig. 5b. The acual hip peed for cae 4. Ship Moion in Reqular Bow Sea (λ=, Hw/Lw=/3, Fr= Roll Moion Pich Moion Fig. 5c. Simulaion of roll and pich moion for cae 4. When he acual hip peed reache 3 kno (Fr=.698), no maer how mall he urning angle, he force and momen loe dynamic balance. The SRB ar o roll violenly and reache 9 o, while pich increae bow down o Plow In, and he SRB capize. Thi i imilar wih he SRB capizing in bow ea (Fig. 4c) and agree wih he decripion of Codega and Lewi (987). y (m) Ship Track in Regular Bow Sea (λ =, Hw/Lw=/3, Fr=.698) X (m) Fig. 5d. The imulaion of hip rack for cae 4. Fig. 5e and Fig. 5f how roll and pich for a fixed heading; all oher condiion remain. Roll Angle (deg) Pich Angle (deg) Roll Moion in Quarering Sea (?=, Hw/Lw=/3, Fr=.698) Fig. 5e. The roll moion for cae 5, wih fixed heading. Pich Moion in Quarering Sea (λ=, Hw/Lw=/3, Fr=.698) Fig. 5f. The pich moion for cae 5, wih fixed heading. Similar o bow ea, he difference beween roll moion (blue line) in Fig. 5c and ha hown in Fig. 5e i wih and wihou heel moion. The heel moion i he major reaon for capize in Fig. 5c. The differen beween he pich moion (red line) in Fig. 5c and hoe in Fig. 5e i wih and wihou Plow-In. 4. CONCLUSION High-peed planing urf recue boa (SRB) were deigned o be ued a urf earch and recue for Unied Sae Coa Guard. They can operae up o a Froude number equal o.7 and eaily maneuver like a diplacemen boa. However, here are dynamic inabiliie near he maximum peed. Since here aren any deailed recorded daa or any imulaion of he hip moion a high peed, epecially in he capize region, he reaon ha caue capizing have no been fully underood for he la wo decade. In order o underand he phyic ha caue he inabiliie, we ued DiSSEL Ship Moion Model o udy he hip moion in he able and unable region. The DiSSEL howed ha he heel and pich inabiliie are he major caue of capize. A high peed, he urge force, roll and pich reoring momen of he SRB canno counerac he force and momen of acceleraion due o he heading change; herefore, he inabiliy occur and lead o capize. In Fig. 4c and Fig. 5c, he roll moion reache a cerain level, and hen uddenly jump o 9 o. A he ame ime, pich inabiliy occur and lead o Plow-In. The imulaion American Sociey of Naval Engineer 863

8 agree well wih he decripion of hip moion, epecially he capize proce, by Codega and Lewi (987). The imulaion by DiSSEL alo howed ha if he heading i fixed, bu oher condiion remained he ame, he inabiliy didn occur. Thi again ugge ha a he high peed, changing heading, which reul in force and momen acceleraion, can no be balanced by urge force, and roll and pich reore momen. REFERENCES Codega, L. & Lewi, J. (987). A Cae Sudy of Dynamic Inabiliy in a Planing Hull, Marine Technology, Vol. 4, No., pp Hoy, III J. G. and Lin, R.-Q. (7). Numerical Simulaion of he Plow-In Phenomena, Proc. nd Inernaional Conference on Marine Reearch and Tranporaion, Ichia, Ialy,, pp Ikeda, Y. & Kaayama, T. () Sabiliy of High Speed Craf, Conemporary Idea on Ship Sabiliy ELSEVIER Science Ld., pp Lewandowki, E. M. (996). Predicion of he Dynamic Roll Sabiliy of Hard Chine Planing Craf, Journal of Ship Reearch, Vol. 4, No., pp Lewandowki, E. M. (997). Tranvere Dynamic Sabiliy of Planing Craf, Marine Technology, Vol. 34, No., 9-8. Lin, R.-Q., Kuang, W. & Reed, A. M. (5). Numerical Modeling of Nonlinear Ineracion Beween Ship and Surface Graviy Wave I: Ship Wave in Calm Waer, J. Ship Reearch, 49, Number, -. Lin, R.-Q. & Kuang, W. (6). Nonlinear Ship-Wave Ineracion Model, Par : Ship Boundary Condiion, J. Ship Reearch, 5, Number, Lin, R.-Q. & Hoy III, J. G. (7) Fa Ship Moion in Coaal Region, Proceeding of he 7 h Inernaional Conference on Fa Sea Tranporaion, Shanghai, China, Lin, R.-Q. & Kuang, W. (7). Modeling he Effec of Ship Appendage on he Six-Degree-of-Freedom Ship Moion, ICMRT, Ichia, Ialy. Lin, R.-Q., and Kuang, W. (8). Modeling Nonlinear Roll Damping Wih a Self-conien, Srongly Nonlinear Ship Moion Model, J. Marine Science and Technology,3:7-3. Lin, R-Q., Hughe, M. & Smih, T. (). Predicion of Ship Seering Capabiliie wih a Fully Nonlinear Ship Moion Model, Par : Maneuvering in Calm Waer, Marine Science and Technology, pp Lin, R-Q., and Kuang, W. (). A Fully Nonlinear, Dynamically Conien Numerical Model For Solidbody Ship Moion. I. Ship Moion Wih Fixed Heading, Proceeding of The Royal Sociey A (online publihed and hard copy in prin). Lin, W.M., and Yue, D.K.P. (99) Large-ampliude Moion in Time-Domain, Proceeding of h Sympoium of Naval Hydrodynamic, Univeriy of Michigan, Ann Arbor, MI. Lin, W.M., Meinhold, M.J., Salveen, N., & Yue, D.K.P. (994). Large-ampliude Moion and Wave Load for Ship Deign, Proceeding of h Sympoium of Naval Hydrodynamic, Univeriy of California, Sana Barbara, CA. ACKNOWLEDGEMENTS The auhor wih o hank Mr. Terry Applebee, Head of he Seakeeping Diviion, NSWCCD, for hi many ueful commen and uggeion. The auhor wih o hank Mr. William L. Thoma III of he Unied Sae Coa Guard for providing he SRB geomery, loading, and power daa required for hi udy. Thi work and he developmen of DiSSEL Ship Moion Model are uppored by David Taylor Model Bain, Carderock Diviion, Naval Surface Warfare Cener, Independen Laboraory In-Houe Reearch (ILIR) Program adminiered by Dr. Barkyoumb. 864 American Sociey of Naval Engineer