Prediction of the Pressure Signature of a Ship in a Seastate

Transcription

1 Prdiction of th Prssur Signatur of a Ship in a Sastat Mark Hyman Thai Nguyn, Knnard Watson Hydromchanics Group, Cod R11 NSWC Coastal Systms Station Panama City, FL 347 phon: (85) fax: (85) mail: hyman@atcf.ncsc.navy.mil Award #: N1498WX3344 LONG-TERM GOAL Prsntly, all US ship min vulnrability studis ar basd on th rstrictiv assumption that th ship is travling through a calm sa. Our goal is to rmov this rstriction and thrby allow a mor accurat assssmnt of ship vulnrability to sa mins. OBJECTIVES W ar dvloping a modl to prdict th prssur fild surrounding a ship advancing in a saway. This prssur fild consists of a stady componnt du to th forward motion of th ship and an unstady componnt du to th oscillatory motions inducd by th incoming wavs. W ar particularly intrstd in prdicting th prssur signatur on th safloor, bcaus this is whr prssur-snsing mins ar typically locatd. Sinc th ship prssur fild dcays with dpth, highfrquncy componnts of that fild ar filtrd to a gratr xtnt as dpth incrass. Additionally, th min sampls th ambint prssur fild at varying but rlativly low frquncy. Both of ths obsrvations suggst th nd for a modl that includs a safloor and is accurat at low frquncis. Most convntional strip thoris assum th fluid to b infinitly dp and ar valid only for high frquncis. Thy ar not appropriat for our purpos, which is why w hav chosn a thrdimnsional formulation. APPROACH Our first stp was to driv th finit-dpth 3D Grn function corrsponding to a translating sourc with an oscillating strngth. W confind our attntion to simulations in th frquncy domain. Ths solutions assum a sufficint tim has passd sinc th ship first ncountrd th wavs, and all motion transints hav dissipatd. Th frquncy-domain formulation is computationally fficint and thrfor mor suitabl for vulnrability assssmnt modls. Nxt, w dvlopd an algorithm to numrically valuat th Grn function. Th intgrals in th Grn function wr valuatd using an adaptiv quadratur. Bfor w could implmnt th Grn function into a panl program, w ndd to prov that th flow fild can b rprsntd by a sourc distribution ovr th submrgd hull surfac and along a contour whr th hull intrscts th fr surfac. This rprsntation is quivalnt to that in th infinit-dpth cas. Onc th flow fild can b rprsntd by a sourc distribution, a panl program can b dvlopd to comput th motions of a ship in wavs and th rsulting prssur fild. WORK COMPLETED Drivd th finit-dpth 3D Grn function for a translating and oscillating sourc. Dvlopd a numrical algorithm to comput th Grn function and its drivativs.

2 Rport Documntation Pag Form Approvd OMB No Public rporting burdn for th collction of information is stimatd to avrag 1 hour pr rspons, including th tim for rviwing instructions, sarching xisting data sourcs, gathring and maintaining th data ndd, and complting and rviwing th collction of information. Snd commnts rgarding this burdn stimat or any othr aspct of this collction of information, including suggstions for rducing this burdn, to Washington Hadquartrs Srvics, Dirctorat for Information Oprations and Rports, 115 Jffrson Davis Highway, Suit 14, Arlington VA -43. Rspondnts should b awar that notwithstanding any othr provision of law, no prson shall b subjct to a pnalty for failing to comply with a collction of information if it dos not display a currntly valid OMB control numbr. 1. REPORT DATE REPORT TYPE 3. DATES COVERED to TITLE AND SUBTITLE Prdiction of th Prssur Signatur of a Ship in a Sastat 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Naval Surfac Warfar Cntr,Coastal Systms Station,Cod R11,Panama City,FL, PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 1. SPONSOR/MONITOR S ACRONYM(S) 1. DISTRIBUTION/AVAILABILITY STATEMENT Approvd for public rlas; distribution unlimitd 13. SUPPLEMENTARY NOTES S also ADM ABSTRACT 11. SPONSOR/MONITOR S REPORT NUMBER(S) 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT a. REPORT unclassifid b. ABSTRACT unclassifid c. THIS PAGE unclassifid Sam as Rport (SAR) 18. NUMBER OF PAGES 4 19a. NAME OF RESPONSIBLE PERSON Standard Form 98 (Rv. 8-98) Prscribd by ANSI Std Z39-18

3 Showd that th flow fild can b rprsntd by a sourc distribution ovr th submrgd hull surfac and along a contour whr th hull intrscts th fr surfac. This rprsntation is th sam as in th cas whr th dpth is infinit. Dvlopd a panl program that incorporats th Grn function and computs th motions and prssur fild of a ship advancing in wavs. Th program uss th abov rprsntation of th flow fild. RESULTS Th finit-dpth 3D Grn function at th fild point (x,y,z) corrsponds to a translating sourc with an oscillating strngth of frquncy σ locatd at (ξ,η,ζ) and is xprssd as 1 1 G = + r r ik( ωf( dk ( k + σ ) ω + / / kh cosh( k( z + h)) cosh( k( ζ cosh( kh) / ik( ωf( pv ( k σ ) ω ik ( k ) + Cg( k ) ik 4( k 4) Cg( k 4) dk / whr pv indicats th principal valu of th intgral and / ik( ωf( pv ( k + σ ) ω / h = fluid dpth R = (x ξ) + (y η) r = R + (z ζ) r = R + (z+ζ+h) J = Bssl function of th first kind of ordr zro U = spd of th sourc + h)) J ( kr) dk ik1( k1) Cg( k1) ik 3( k 3) + Cg( k 3) Th wav frquncy ω is rlatd to th wav numbr k through th disprsion rlation dk ω = gk tanh( kh) whr g is th gravitational constant. Th group vlocity Cg( is also a function of k and is dfind as Th function F( is Cg ( = ω k

4 ω cosh( k( z + h)) cosh( k( ζ + h)) cos( k( y η)sin ) F( = cosh( kh)sinh( kh) For /, th pols k 1 and k ar th two zros of th dnominator of th fifth trm of G, i.., k 1 and k ar th roots of th quation ( k + σ ) ω = Hr, w assum that k 1 < k. Similarly, k 3 and k 4 ar th two zros of th dnominator of th sixth trm of G. Thy ar th roots of th quation ( k σ ) ω = Th pols k n, n=1,,3,4 ar functions of, and k 3 and k 4 xist for [,/]. Thus, th rang of intgration of th sixth trm and th last two intgrals is from to /. Th pols k 1 and k xist only for [,/], whr is dfind blow. Th fourth and fifth trms of G diffr only in th rang of intgration. Howvr, th fourth trm contains no singularitis and can b intgratd numrically without any difficultis whras th fifth trm contains two singularitis k 1 and k. Th dfinition of is rathr complx. Its valu dpnds on U, h and σ. Whn h and σ ar givn, w can dfin two valus k and U whr k is th solution of th quation and U is givn as ω ( k ) kcg( k ) = σ U = Cg(k ) For U < U, =, and th fourth trm vanishs. All th rmaining intgrations with rspct to ar from to /. For U > U, =cos 1 ( U / U ). W validatd th Grn function and th numrical algorithm usd in its valuation by computing th stady flow around a fully submrgd Rankin body. Th Rankin body was chosn for its simplicity. It can b rprsntd by a singl sourc-sink pair and approximats an undrwatr vhicl fairly wll. Th Grn function for th stady flow problm is a spcial cas of our mor gnral translating and oscillating Grn function. It is obtaind by stting th frquncy in our Grn function to zro. Th figur compars our rsults with thos of Sahin t al. (1994). Th Rankin body in this xampl has a lngth to diamtr ratio of 7 and a lngth to dpth ratio of.5. Th hull cntrlin is locatd at mid-dpth (α= z/d=.5), and th Froud numbr is.7. Th figur shows th axial distribution of bottom prssurs dirctly blow th body (y=). Excllnt agrmnt is obsrvd.

5 .1 Prdiction Sahin t al. (1994).5 C p z α =.5 x (x = at bow) U x / L IMPACT/APPLICATIONS Th primary purpos of this rsarch was to improv th Navy s ability to assss ship vulnrability to sa mins. Howvr, our modl can also b usd to dsign improvd prssur-snsing mins. RELATED PROJECTS Undr a Coastal Systm Station Intrnal Rsarch task, Dr. Thai Nguyn is invstigating th ffcts of a compliant, muddy safloor on th motion of ships in wavs. A diffrnt Grn function was drivd and computd in this cas whr thr xists a thin, dnsr fluid layr, rprsnting th mud layr, blow a lightr uppr fluid layr. Howvr, th sam panl program is usd in both projcts with th xcption of th subroutin computing th Grn function. REFERENCES I. Sahin, M.C. Hyman and T.C. Nguyn. 1994: Thr-dimnsional flow around a submrgd body in finit-dpth watr. Appl. Math. Modlling, 18,