Prediction of Tank Fuel Sloshing during Jettison

Transcription

1 Andé Baeen EADS, Miliay Aicaf, 8 Munic, Gemany ande.baeen@m.eads.ne Rupe Gleissl EADS, Miliay Aicaf, 8 Munic, Gemany upe.gleissl@m.eads.ne ABSTRACT Sepaaion Cleaances fo anks povide in geneal e mos limiing condiions fo e emegency jeison envelope of a fige aicaf. Tanks ae almos wide body bu lig weiged soes wi poo aeodynamic caaceisics as fa as sabiliy is concened. Especially wen paially filled, e pysical caaceisics of e esidual fuel become an addiional dive fo e sepaaion beavio. Tee, is pysical popeies become a funcion of e aicaf flig aiude, depending on angle of aack, flig pa angle and bank angle. Duing e ajecoy iself ese popeies apidly cange in dependence of e ank moion. Teefoe soe sepaaion analysis of paially filled fuel anks always epesens a delicae poblem. Te age of is pape is o iglig a sceme a allows e epesenaion of fuel slosing effecs in a fuel ank duing sepaaion. Te concep of is sceme consiss of wo seps, a seady sae calculaion using finie elemens fo e fuel volume, and a dynamic analysis using a sae of e a sepaaion code used a EADS Deuscland (SSP).I will be sown a e cene of gaviy and e momens of ineia apidly cange in dependence of e ank moion. In ode o epesen ese effecs, analyical esuls fo a slosing liquid in cylindical volumes ae used o pedic e effecive slosing mass, depending on e oaion ae of e body and e body geomey. Duing a jeison pocess e elaaion ime fo e ig acceleaions and aes ae aken ino accoun as deviaion fom ei pseudo-seady posiion. Fiing is sceme ino e sepaaion code, ajecoies wi / wiou slosing fuel mass effecs of an eenal ank ae pesened and e diffeences ae lined ou. Pape pesened a e RTO AVT Symposium on Funcional and Mecanical Inegaion of Weapons and Land and Ai Veicles, eld in Williamsbug, VA, USA, 7-9 June, and publised in RTO-MP-AVT. RTO-MP-AVT 8 -

2 . ABBREVIATIONS & SYMBOLS a : sape paamee paaboloid [/m] Q qi : eeio foces [N] b : ais paamee paaboloid [m] q i : genealized coodinaes (Lagange s fomula) c : ais paamee plane [m] R : cylinde adius [m] E kin : kineic enegy [kj] i : adius quasi-paicle i fom (//) [m] E po : poenial enegy [kj] I,j : loop indices [-] ij : adius quasi-paicle i o quasi-paicle j [m] I / I / I : momens of Ineia aound - / y- / z ais [kg*m ] I eff : effecive momen of Ineia [kg*m ] I solid : momen of Ineia of a igid body [kg*m ] U ij : Lennad-Jones poenial funcion [kj] v i : velociy quasi-paicle i [m / s], y, z : Caesian coodinaes [m] cg, y cg, z cg : cene of gaviy [m] L : L E kin E po (Lagange s fomula) i, y i, z i : quasi-paicle coodinaes [m] L i, eff L eff : quasi-paicle effecive angula y, y, z, z : limis of inegaion [m] momenum [kg*m / s] α : poenial paamee: α f(m, n) : oveall effecive angula momenum [kg*m / s] ε : equilibium es poenial [kj] L solid : angula momenum [kg*m / s], igid body m : slope [-] m, n : Lennad Jones poenial paamee [-] mass nz N cic N : quasi-paicle mass [kg] : load faco [*g, Ea gaviy] : oveall numbe of cicula segmen elemens [-] : oveall numbe of aial segmen elemens [-] γ : flig pa angle [deg] Ω : angula velociy [ad / s], -ais ϕ : oll angle [deg] Θ : inclinaion angle [deg] σ : quasi-paicle diamee [m] opeaos: I ~ : enso of momens of ineia a b : veco poduc of a and b NT : numbe of quasi-paicles [-] 8 - RTO-MP-AVT

3 . INTRODUCTION Te beaviou of liquids in aeospace veicles like aiplanes, ockes o saellies as always been a delicae poblem. Te fuel povides a significan conibuion o e oveall mass of ese veicles, and eefoe e knowledge of e mass popeies of e fuel is eemely impoan fo pefomance and safey consideaions. In e domain of miliay aicaf, ig acceleaions occu duing flig, wee e fuel is foced o slos wiin e anks, especially in paially filled compamens. In ode o accuaely pedic e ajecoy of a sepaaing fuel ank in viciniy of an aicaf, i is of paamoun impoance o epesen e coec pysical popeies of e ank in combinaion wi e ejecion and e aeodynamic foces inclusively all inefeence effecs. Teeby e liquid moion becomes e diving paamee fo e canging pysical popeies of e anks. Tis pape deals eefoe wi an appoac a allows a vey fas deeminaion and epesenaion of liquid slosing effecs and ems on e jeison of a paially filled eenal fuel ank.. LIQUIDS In conas o a solid body, liquid does no keep is sape wen i is in moion. Te inemolecula foces ae weake an in e cysal gids of a solid, so ee is no global ode a peseves coeence. In conas o a gas wee nealy no coeence a all eiss beween e molecules, ee ae egions wee a ceain numbe of molecules ae closely coeen. Tese egions can easily beak up and e-connec, and eefoe e liquid may ake evey sape e bounday pescibes. Te seng of e inemolecula foces vaies fom liquid o liquid, dominaing a popey a is a diving faco fo all dynamical analysis: viscosiy. Viscosiy songly depends on e liquid empeaue and pessue, weeas in a wide ange of pessue and empeaue, a liquid can be idealized as incompessible. Tus, e volume can be esimaed as consan, weeas e sape canges [].. SIMULATION APPROACHES Te modelling of fuel slosing effecs wiin a ank is a lage aea fo scienific eseac. Seveal appoaces ave been done, analyically and in epeimens, o pedic e effecive slosing mass and e effecive momens of ineia of e liquid, [], [], [], []. Wi a liquid consising of billions of paicles (ions, molecules), molecula dynamics offes in eoy e bes appoac o slosing effecs. Bu wi e eeme big amoun of paicles and e compleiy of solving e govening, paly saisical equaions, oe appoaces ave become moe and moe popula as e compue powe as ise as well. Coninuum fluid mecanics, namely Eule- and Navie-Sokes codes, ave poved o povide accuae models fo gas dynamics and aeodynamic simulaion. Bu in ems of liquids, especially apidly moving liquids, e codes ae eemely ime consuming, due o e eeme small ime seps equied fo pope inegaion. Analyical appoaces ave been done as well, ansfoming e pysical poblem ino a maemaical one. Tese appoaces ae mosly only valid fo idealized liquids (no ficion, incompessible, voe-fee, a.s.o.), so ey ae ofen limied o special poblems []. A id way can be consideed wic deals wi macoscopic paicle cluses, conaining billions of eal molecules. Te popeies of e eal molecules ae ansfomed o e macoscopic paicles, aving dimensions of some E- mees (insead of E- mees fo eal molecules). Some esuls fom is RTO-MP-AVT 8 -

4 paicle appoac ae pesened in figues 7 o 9 in ode o demonsae ei elevance fo a slosing moion. Aloug is paicle appoac povides vey good esuls fo slos pedicions, see figue 8 and 9, i sill consumes moe CPU ime an acceped fo an effecive ajecoy analysis. Teefoe a special concep based on elemens deived fom quasi paicle cloud models is used wiin is pape in ode o compue ajecoies in easonable compuing imes and muc fase an acievable wi e classical appoaces.. STEADY STATE MODEL To pedic e cene of gaviy sif due o e moion of e liquid wiin e ank, an analyical model as been consideed fo a ypical ee-compamen ank. Wiin e consideaion, e oveall ank volume is divided up ino ee compamens, one cenal, main, cylindical compamen and wo paabolic ones a e eemiies (figue ). Te compamens ae enumeaed as followed: fon compamen: compamen middle compamen: compamen ea compamen: compamen Eac of ese compamens can be individually and abiaily filled. In ou pesen eample, eac compamen is assumed o be filled a e same fuel level. Inclining e ank as sown in figue e volume occupied by e liquid becomes a funcion of e fee suface inesecion of e liquid wi e solid walls and e inclinaion angle. Sepaaing e fuel volume ino finie elemens, e cene of gaviy and e momens of ineia fo eac elemen ae compued and summed up o oveall values fo e paially filled ank a is inclinaion. In suc a way, seady sae mass caaceisics of e fuel can be obained a seveal diffeen inclinaions. Wi e ank paially filled, e fuel will ave a fee suface a is always oienaed vs. Ea gaviy field. Supposing e liquid in equilibium a evey ime sep, e cene of gaviy canges wi inclinaion of e ank, due o e cange of e liquid sape, see figue. Te ee compamens ave diffeen geomey and can be filled individually. Tus, eac compamen as o be analysed isolaed fom e oes and e esuling cene of gaviy fo e oveall liquid volume is obained by supeposiion. Wi e ank and e liquid moving in Degees of Feedom afe jeison, slosing effecs in ee dimensions ave o be consideed. Beaing in mind e assumpion of a smoo, fee suface of e liquid, always oiened vs. Ea gaviy field, e oienaion of e ank walls is diffeen fom e oienaion of e fee liquid suface, see figue. Teefoe a coodinae ansfomaion is necessay o bing e wo mass sysems ino conguency so a e soe ajecoy can be compued fo e oveall sysem consising of ank walls and liquid.. Finie Elemens Appoac Te fuel akes e volume beween e fee suface and e ank walls. In maemaics, e volume is e inegal beween a plane (epesening e fee suface) and a bounday funcion (epesening e ank sape). 8 - RTO-MP-AVT

5 Fo e wo paabolic compamens, e oveall volume occupied by fuel is given by e volume inegal y z ( y, z) Vol dy dz (ais oienaion as sown in figues and ) Paaboloid y In Caesian coodinaes, can be epessed as a funcion of y and z a ( y z ) b wi b denoing e ais paamee in -diecion and a being a coefficien fo e sape of e paaboloid. Wi R epesening e adius of e cylindical compamen of e ank, a is a funcion of b and R: b a R In e pesen eample, e values fo R, a and b ae R.7m, a.8, b. A plane, oienaed owads e ank walls by an inclinaion angle Θ, epesens e fee liquid suface. In Caesian coodinaes, is plane is given by m y c Ais oienaion is e same as fo e paaboloid. m denoes e plane inclinaion, c e ais paamee wi e -ais. m is given by m an( 9 Θ), c depends on e fill level of e compamen. Te plane bounday inesecion in z-diecion is ( y z ) b m y c a z ± y m b c y a a Te inesecion in -diecion is y m a b c y a y, m ± a m a b c a Te liquid volume fo e paabolic compamens en esuls in RTO-MP-AVT 8 -

6 Vol m a m m b c y z y y ( y, z) a a a a ( Paaboloid( y, z) Plane( y, z) ) dy dz y a m b c a a z m b c m b c y y a a An analogous fomula aises fo e cylindical compamen, eplacing e paaboloid by e bounday funcion fo a cylinde. Tis volume inegal canno be evaluaed easily bu as o be valid fo e oveall definiion seco fo an(θ) and e squae funcions, wic is, obviously, no possible. An analogous fomula aises wen deiving e momens of ineia fo e liquid volume. Teefoe, an appoimaion is inoduced wic allows an accuae and fas compuaion of e cene of gaviy and e momens of ineia: Te volume is sepaaed in finie elemens (see figue).... Disceisaion Saing fom e volume inegal, e liquid volume is disceized wi finie elemens. To simplify e compuaion of e momens of ineia, finie elemens of ecangula geomey ave been cosen. By is, e finie volume can be evaluaed easily and e momens of ineia ae well defined. Teefoe, bas ae used o epesen e liquid volume in e compamens. Te volume inegal is spli of in wo plane inegals, one wi espec o e -y plane and e oe one wi espec o e y-z plane (fo e ais oienaion see figues and ). As e ank body is aially symmeical, evey inesecion of e liquid plane and e bounday in e y-z plane fo a given is a cicle segmen. Te aea of is segmen is compued using e apezoidal ule wi N cic seps. Disceizing e liquid volume in -diecion in e same way using N seps, and summing up e discee cicle segmens fo all gives e oveall volume of e liquid. Fo e compuaion, e following disceizaion as been used: N cic, N, N compamen. elemens Depending on e desied fill level e volume of e liquid is adjused by vaiaion of e ais paamee of e fee suface plane, c. Fo e compuaion of e volume, fis a sa ais paamee as o be cosen and e volume wiin is inesecion space is compued. Te paamee is vaied if e volume compued does no fi o e desied volume. Tus, e final ais paamee is deemined by an ieaion loop. Wi e paamee fied, e cene of gaviy of e liquid can be compued using e cene-of-mass law. In a second sep, e momens of ineia efeed o is cene of gaviy ae deemined, aking ino accoun e Seine pas of e finie elemens. Tis sceme is epeaed fo evey compamen, e oveall cene of gaviy fo e liquid mass in e ank is obained by supeposiion. Te esuling cene of gaviy fo vaious inclinaion angles Θ is sown in figue. Obviously e cene of gaviy sif in aial diecion is in e ode of. m fo a alf-filled ank... Polynomial Inepolaion Wi e inclinaion angle Θ canging apidly duing jeison, e ieaion loop o compue e liquid suface ais inesecion as o be un fo evey ime sep in e inegaion of e ajecoy. Tis would be vey imeconsuming and ineffecive. Teefoe, e inenion is o povide e mass popeies of e liquid in smoo funcions a can be evaluaed muc fase an an ieaion loop. In ode o deemine ese funcions, e mass popeies (cene of gaviy, momens of ineia) fo seveal inclinaion angles Θ beween 9 deg and 9 deg ave been compued in dependence of e individual fill level fo evey compamen. Te esuls 8 - RTO-MP-AVT

7 fom ese compuaions fo e ea compamen and e fill levels / full, / full, / full ae sown in figues,,. A funcional dependence beween e inclinaion angle Θ, e fill level and e mass popeies of e liquid can be found by polynomial inepolaion: A ode polynomial is used o appoac e dependence accuaely. Wi polynomial funcions being smoo and well defined, e cene of gaviy and momens of ineia can now be povided fo evey inclinaion angle Θ wiin e definiion ineval, see figues,,. In addiion o a, even fill levels a ae no confom o /, / and / ae povided by inepolaion.. DYNAMICAL ANALYSIS. Effecive Momens of Ineia Te momens of ineia compued wi e finie elemen appoac as menioned above ae only valid fo a solid liquid: Te liquid is supposed o be in equilibium, wi a plane fee suface a evey ime sep of e inegaion. Te liquid is supposed o oae a e same oaion ae as e ank body. Real liquids, in conas, ae no in equilibium wen in moion. A lo of e kineic enegy is ansfomed ino inenal enegy. In e molecula domain, is enegy is ansfomed ino oscillaions of e paicles. In egions wee ese oscillaions ae song enoug inemolecula connecions beak up and eunify. Te diving paamee fo e cange of e liquid sape is e moving bounday: Te liquid akes e sape e bounday offes. Tis is ue e.g. fo a ank inclinaion wee e secion walls peven e liquid fom slosing ino e ne compamen. Te secion walls ineac wi e fuel, pusing i ino a new posiion. Te same effec occus fo liquid moion foced by singes o oe elemens of e ank sucue. Te momens of ineia compued wi e finie elemens appoac ae only valid fo is case of a cange of sape foced by e bounday geomey. If ee is no geomey cange diving e liquid moion, e.g. in e case of oll eciaion, supposed ee ae no buffes a keep e liquid oaing, e only diving paamee fo liquid moion is e conac line beween e liquid and e wall. Wi e ficion foces beween e liquid and e wall small bu no equal zeo and e cinemaic viscosiy of e fuel sufficienly small and no equal zeo as well, only e fuel mass close o e wall is foced o oae wi e wall velociy, weeas e fuel mass away fom e walls does no oae a e same level ( diffeenial oaion ). Teefoe, beaing in mind a ajecoy wi quick oaions, e effecive momens of ineia of fuel wi espec o e ank oll ais ae smalle an pediced by e finie elemen appoac. Te effecive momens of ineia depend mainly on e fill level, e acceleaion ae and e geomey of e ank.. Quasi-Paicle Appoac In ode o complee e finie elemen appoac by e effecive momens of ineia I of a liquid, e paicle appoac is now used. Fo is pupose, a sufficien numbe of paicles ave been cosen a epesen e fuel in a paially filled ank. Te equaion of moion of e paicles is given by Lagange s fomula RTO-MP-AVT 8-7

8 L L Qq q i q q i i, yi, zi i i ; i,,..., NT fo i T,..., NT wi L E kin E po ; q i i, y i, z i E kin NT mass q& ; and e genealised coodinaes E po U ij j j i Te poenial enegy is given by a Lennad-Jones poenial U ij σ α ε ij m σ ij n wee m denoes e eponen of e epulsing em and n e eponen of e aacive em. Solving Lagange s fomula wi e kineic and poenial enegy menioned above, e equaion of moion esuls in ( qi q j ) Qqi N n m n mass qi n & α ε σ σ m n j n ij ij j i wi e foces Q epesening gaviy, ank acceleaion, a.s.o. qi m Solving is equaion fo evey paicle and inegaing e equaions wi a ode Runge-Kua-Felbeg fomula (able ), e dynamics of e fuel slosing can be pediced vey accuaely. Te following paamees ave been used fo e compuaions (eac compamen filled a /): NT (compamen ), NT (compamen ), NT (compamen ) σ. m, mass. kg, ε. kj, m, n, α Te geomey fo e paicle appoac is sown in figue 7. Te bounday of e ee compamens is epesened by quasi-paicles coloued in ed, e fuel paicles coloued in blue. Summing up e oaional enegy of e paicles wi espec o e ank ais a evey ime sep and building an aveage momenum fo e paicle cluses due o a foced eeio oscillaion yields o e effecive momens of ineia: Te angula momenum of evey paicle is 8-8 RTO-MP-AVT

9 L mass ( v ), L i, eff i i i eff NT i L NT i, eff massi ( i vi ) i Te angula momenum fo a solid fuel is L ~ NT solid I solid Ω an k i wi L e aio ~ eff I eff ~ I ~ I eff solid Ω an k becomes i i mass ~ I ~ I eff solid Ω an k L L eff solid. Te esuls ave been compaed o some analyical invesigaions a ave been caied ou o pedic e effecive momen of ineia of a liquid. One eample fo an effecive momen of ineia is given in figues 8 and 9. Te effecive momen of ineia I, aveaged by a powe meod, is educed o abou pecen of e value fo a solid body. Using is appoac fo seveal acceleaion aes, e effecive momens of ineia wi espec o e -ais ae obained in dependence of angula ae and fill level. Tis funcional dependence is implemened ino e finie elemen sceme, educing e oll momens of ineia fom solid liquid o a eal liquid.. Implemenaion in e Soe Sepaaion Pogam (SSP) Te coe of is invesigaion consiss of e EADS Soe-Sepaaion-Pogam (SSP), a DOF simulaion pogam a compues e moion of jeisoned o launced soes and missiles in any ype of inefeence flow aound e caie aicaf. Tis appoac is based on diffeen maemaical modelling saegies wic ae uilising compued secional loads and aicaf flowfields, as well as measued insalled and on ime accuaely compued End-Of-Soke loads in ode o epesen e aeodynamic effecs. Te eoeical backgound is based on Eule soluions successfully in use a EADS Deuscland fo is special pupose since moe an yeas; see [7], [8]. Te slos subouine is implemened in e SSP main pogam using e acual cene of gaviy and flig pa angles of e ank moion a evey ime sep. Fo ese values, e subouine compues e new cene of gaviy and momens of ineia fo e liquid mass and supeposes ese esuls wi e ank bounday. Te esuling mass popeies ae efeed o e new cene of gaviy. Teefoe e aeodynamic loads and velociies ave o be ansfomed o e new cene of gaviy as well. Afe is ansfomaion, e new posiion and oienaion of e ank ae compued wiin e ne ime sep, e new values ae used again as inpu fo e slos ouine. Tis always elaes e aeodynamic foces o e acual cene of gaviy of e esuling sysem of ank and liquid. Fo e compuaions, e ank popeies in able ave been used. RTO-MP-AVT 8-9

10 RESULTS & CONCLUSION Some ajecoies fo a paially filled ee-compamen ank ae sown in figues o. Fo idenical flig condiions, ank jeison ajecoies fo saig level flig, climb and dive ae pesened. In e pesen eamples, e ank compamens ae equally filled a / fuel level. Te ajecoies ave been compued eie wi e fuel modelled as a solid o as slosing fuel. Te diffeence beween e ajecoies wi / wiou fuel slosing is obvious: Te dynamical modelling of e fuel leads o a songe nose down pic compaed o e solid model due o e slosing fuel mass. Wi e iniial nose down pic momenum due o e Ejecion Release Uni, e fuel in e ee compamens is slosing owads e ank nose. By is, e oveall cene of gaviy also sifs owads e ank nose. Wi e efeence poin fo e momenum compuaion and fo e momens of ineia idenical wi e cene of gaviy, e ank becomes moe sable compaed o a fied cene of gaviy. Tis nose down effec is clealy visible especially fo e climb ajecoy wee e ank eaces quickly an upig posiion. Te disance beween e aicaf and e ank is gowing fase compaed o e pedicion wi solid fuel, poviding a safe jeison aiude. In all ee flig cases, e laeal movemen of e ank wi slosing fuel is nealy educed o zeo compaed o e solid appoac. Beaing in mind e poo aeodynamic popeies of an eenal fuel ank, e fuel slosing educes e aeodynamic insabiliy o a ceain degee, songly dependen on e fill level. In is analysis, e fuel as been egaded as a unifom mass always conneced o e ank walls. In a ne sep, e simulaion will be impoved by a fuel model a akes ino accoun sepaaed fuel mass. Wi e ank acceleaed vey fas by e Ejecion Release Uni, e fuel will sepaae fom e walls and impac on e ank op. By is sock, e ank acceleaion ges a peak, canging e fue ajecoy. Te quasi-paicle model offes a good appoac fo sepaaing fuel masses. Te foces by e sock a e wall can be compued, oo. Consequenly, in a fue sudy, e sock effecs will be analysed in deail, defining paamees fo e sock inensiy a will be implemened in e slos ouine. Ten, e slos model will be almos complee o simulae all elevan fuel slosing effecs accuaely. 8 - RTO-MP-AVT

11 7 FIGURES Empy Tank Empy mass. [kg] Volume. [m ] Xcg / Ycg / Zcg.9 / -. /. [m] Ineia I / Iyy / Izz 8.9 / 9. / 9. [kg * m ] Fuel mass (oal) Res Fuel mass Fuel ca. 8 kg ca..7 kg Empy Tank Fuel oveall mass ca. [kg] Xcg / Ycg / Zcg.7 /. /. [m] Ineia I / Iyy / Izz (solid). / 89./89. [kg * m ] Tank empy wi Res Fuel: Tank full Realisic Flig Condiions. [kg] 9 [kg] Table : Mass popeies of e ank / fuel sysem fo e pesen analysis RTO-MP-AVT 8 -

12 .,,. α, f γ α &. α, γ α f &. α, γ α f &. α, γ α f &. α, γ α f &.7 α, γ α f & ), ( k k k f f k k k Tuncaion Eo: f f ) ( 8 9 & TE No Coec: Take double o alf sepsize, k coec Final Values:,, k k c k f & & & Move:,,, f f k Table : ode Runge-Kua-Felbeg sceme, used fo e paicle appoac 8 - RTO-MP-AVT

13 CG fon CG middle CG ea Z X Z y R CG (elemen) Figue : Tank paially and abiailly filled Z Θ X X CG fon Y Z φ CG (Θ deg) CG (Θ deg) Θ deg φ deg X.m CG ea Figue : Paially filled ank inclined RTO-MP-AVT 8 -

14 ..... d dz d [m]. -. dz [m] Tea [deg] -. Figue : Cene of gaviy sif f ( inclinaion ), eac compamen filled a / cg compamens- compamens- compamens- polynomial polynomial,9,7, cg [m],,,9,7, Tea [deg] Figue : Aial cene of gaviy sif f ( inclinaion, fill level ), compamen 8 - RTO-MP-AVT

15 i f(fill), ea compamen compamens- compamens- compamens- i [kg * m^] Tea [deg] Figue -: I_solid f ( inclinaion, fill level ), compamen iyy f (fill) compamens- compamens- compamens- 8 iyy [kg * m^] Tea [deg] Figue : Iyy_solid f( inclinaion, fill level ), compamen RTO-MP-AVT 8 -

16 Z Y Z X Y X Quasi-Paicle -compamen ank model, D view Quasi-Paicle -compamen ank model, fon view Z Y Y X Z X Quasi-Paicle -compamen ank model, side view Quasi-Paicle -compamen ank model, op view Figue 7: Quasi-Paicle modelling of -compamen ank 8 - RTO-MP-AVT

17 Z Ω Z X Y z X Y y Ω, I_ eff Figue 8: Paially filled ank coss secion, in equilibium (lef) and slosing (ig) I_effecive / I_solid I_eff / I_sol Powe (I_eff / I_sol) I_eff / I_sol,9,8,7,,,,,,,9,8,7,,,,,,,,,,,,,7,8,9,,,,, [s] Figue 9: I_eff / I_solid f ( ), Ω.*Pi [ad/s], compamen, filled a / RTO-MP-AVT 8-7

18 Y(METER) Tank filled a (/, /,/), solid ank filled a (/, /, /) liquid Flugzeugfeses Sysem Epeimenelles Sysem Flugzeugfeses Sysem Epeimenelles Sysem Y(METER) X(METER) X(METER) SSP MA.7 ALFAF.7 SSP MA.7 ALFAF.7 MT BETA. MT BETA. Figue : Tajecoy wiou slosing, paially filled ank, nz g, γ deg Figue : Tajecoy wi slosing, paially filled ank, nz g, γ deg Tank filled a (/, /,/), solid, climb ank filled a (/, /, /) liquid, climb Flugzeugfeses Sysem Epeimenelles Sysem Flugzeugfeses Sysem Epeimenelles Sysem Y(METER) X(METER) Y(METER) X(METER) SSP MA.7 ALFAF.7 SSP MA.7 ALFAF.7 MT BETA. MT BETA. Figue : Tajecoy wiou slosing, paially filled ank, nz g, γ deg, climb Figue : Tajecoy wi slosing, paially filled ank, nz g, γ deg, climb 8-8 RTO-MP-AVT

19 Y(METER) Tank filled a (/, /,/), solid, dive ank filled a (/, /, /) liquid, dive Flugzeugfeses Sysem Epeimenelles Sysem Flugzeugfeses Sysem Epeimenelles Sysem X(METER) Y(METER) X(METER) SSP MA.7 ALFAF.7 SSP MA.7 ALFAF.7 MT BETA. MT BETA. Figue : Tajecoy wiou slosing, paially filled ank, nz g, γ - deg, dive Figue : Tajecoy wi slosing, paially filled ank, nz g, γ - deg, dive 7 REFERENCES [] Lamb, H., Si: Hydodynamics, ediion (9), Dove Publicaions [] Tega /Bey / Demcak: Measuemen of Foces due o Liquid Moion in a Popellan Tank, AIAA, 98 [] Abamson, H.M.:Te Dynamic Beaviou of Liquids in Moving Conaines Inoducion, Souwes Reseac Ins. (San Anonio, TX, USA), 9 [] Kule, J.R. / Sigillio, V.G.: Slosing of Liquids in Cylindical Tanks, AIAA Volume, Page 9-, 98 [] Baue, H. F.Effecive momen of ineia of liquids, Z. Flugwiss. Welaumfosc. 9, 98, Hef [] Hasings, L.J. / Toole, L.E.: An Epeimaenal Sudy of e Beaviou of a Slosing Liquid subjeced o a Sudden Reducion in Acceleaion, NASA-TM-X-7, 98 [7] Deslandes, R.: Teoeisce Besimmung de Tajekoien abgeende Flugköpe von Kampfflugzeugen, MBB-UFE, 978 [8] Deslandes, R.: Weieenwicklung des Recenvefaens zu Emilung des Abgangsvealens von Aussenlasen, MBB-UFE-S/R/ / Teil, 98 RTO-MP-AVT 8-9

20 DISCUSSION EDITING Pape No. 8: Auos: Speake: Discusso: Quesion: Andé Baeen, Rupe Gleissl Ande Baeen G. Akoyd How do you accoun fo e effec of ai in e ank? Speake s Reply: Ai in e ank leads o a diffeen fee suface of e fuel and sould be consideed as well in e simulaion. Using e paicle appoac, pessue due o ai in e anks can be implemened by addiional pessue loads on eac paicle close o e fee suface. Tis is a ask fo fue invesigaions wi e paicle appoac and is envisaged fo fue impovemens of e meod. Discusso: Quesion: G. Moei How muc CPU ime is equied fo e ajecoy? Speake s Reply: Te compuaion of a ajecoy using e seady-sae slos subouine, modified by e paicle appoac, akes no longe an a few seconds up o one minue. Te CPU ime equied fo a paicle appoac compuaion depends on e numbe of paicles involved. Fo e pesen eample wi nealy paicles, one second in eal ime equies ca. wo ous CPU ime. Discusso: Quesion: A. Cenko Te pevious pape on ank slosing sowed e ank picing up, yous sows i picing down. How do you accoun fo e discepancy? Speake s Reply: In e cuen soe-elease-pogam, fuel impac on e ank walls is no ye consideed. Te ajecoies pesened ee only ake ino accoun e cene of gaviy sif and canging momens of ineia. Te paicle appoac consides impacs on e walls, soon ese effecs will be implemened in e simulaion ouine as well. Te pic up due o fuel impac is coec and leads o sligly diffeen ajecoies an pesened ee. Discusso: Quesion: F. Ljungbeg Have you analyzed ow paicle size affecs you dynamic esuls? 8 - RTO-MP-AVT

21 Speake s Reply: Yes, seveal paicle sizes ave been used fo idenical fill levels of a cylinde. Te esuls diffe emakably in dependency of e paicle diamee in ems of waves on e suface and sepaaed fuel masses: Fo lage paicles, e dynamics of e liquid is oo esiced due o ineia effecs as e paicle mass inceases wi e diamee. Bu fo a ceain size limi, deails like suface waves o slosing modes ae clealy visible an coespond well o liquid dynamics. RTO-MP-AVT 8 -

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