PECULIARITIES OF THE LIQUID CARGO DYNAMICS MODELING FOR THE CASE OF ROAD TANK TRANSIENT MOVEMENT MODES

Transcription

1 8 h GRAM Inernaonal ongress on omaonal Mechancs Volos, Jl 5 Jl 05 PEULIARIIES O HE LIQUID ARGO DYNAMIS MODELING OR HE ASE O ROAD ANK RANSIEN MOVEMEN MODES Marna G. Knasoa, Aleandr O. Shmanos and Alžbea Saeoá 3 Dearmen of echncal Phscs and Engneerng Mechancs Belarsan Sae Uners of ransor Gomel, 46653, Belars e-mal: marna-n@mal.r; eb age: h://engmech.b Dearmen of echncal Phscs and Engneerng Mechancs Belarsan Sae Uners of ransor Gomel, 46653, Belars e-mal: m.bels@gmal.com; eb age: h://engmech.b 3 Dearmen of Aled Mechancs Uners of Žlna Žlna, 00 6, Sloa Reblc e-mal: albea.saeoa@fsro.na.s; eb age: h://ame.na.s/ Keords: Parall-lled Road an, Lqd argo Oscllaons, Dnamc Vscos, Energ Dssaon, emerare hange. Absrac. he aer deals h comer smlaons of lqd cargo sloshng n reserors of road ans. he esmaon of rblen and scos lqd energ dssaon as done, he deendences of lqd energ dssaon for Neonan and non-neonan models ere obaned. Inflence of lqd cargo dens and scos on lqd energ dssaon and hdrodnamc ressres as analed. he mamal change n emerare drng he frs second afer he sar of road an brang as deermned. he obaned resls alloed o mae recommendaons for comer modelng of a sngle road an ransen moemen. INRODUION A grea amon of lqds s ransored b road ans. A mong road aner h lqd cargo s a comle dnamc ssem and secal aenon shold be ad o he relae dslacemen of lqd cargo, hch can lead o loss of sabl and conrollabl of he car. o rode more safe and ecologcall no dangeros ransoraon rocess here s a need o mroe road an consrcons hch can be realed b comer modelng and deends on lqd cargo scos. he fll accon of he henomena occrrng drng ransen drng modes of he road an reqres o se he model of cargo as a connos lqd. Usall, road ans ransor smlar lqds drng her oeraon lfe. Lqd cargo oscllaons n road ans a ransen moemen modes ma case an ncrease n lqd emerare de o nernal frcon forces (energ dssaon of lqd cargo. A sbsanal lqd emerare change can lead o s scos change. he man rose of he or s o anale he ale of lqd cargo scos dssaon and he emerare dsconn calclaon o mae recommendaons for comer modelng of a sngle road an ransen moemen. DYNAMI EQUAIONS OR LIQUID ARGO MOVEMEN o ae no accon he henomena occrrng drng road an ransen moemen modes s necessar o se he model of ransored lqd as a connos medm. All frher resls ere obaned consderng lqd cargo as ncomressble lqds de o no sgnfcan ressre ales. General relaons characerng he lqd cargo oscllaons n he an reseror are ald for boh Neonan and non-neonan flds and nclde sch dnamc eqaons er mass n, as he eqaon of mass and energ conseraon. he hae he follong form [, ]:

2 Marna G. Knasoa, Aleandr O. Shmanos and Alžbea Saeoá., Ф 0; ; ( ; ( ; ( d Q ( here,, roecons of he fld arcle eloc ecor on,, aes, m/s ;,, roecons of he eernal olme (mass forces, N/m 3 ; lqd dens, g/m 3 ; soroc sress (ressre, Pa; comonens of he sress ensor, Pa. secfc hea a consan lqd ressre, J/(g K; lqd emerare, K; Q secfc rae of eernal hea sorces, J/(g s; Т hermal condc, W/(m К; Φ d ar of he mechancal energ rnng no hea er me n, J/(g s:, d ( µ dnamc scos coeffcen, Pa s. o deermne he moon arameers for a lqd h consan scos s enogh o sole he ssem of he frs for eqaons of he ssem (. Wheren he emerare feld can be calclaed from he ffh eqaon of he ssem sng on he obaned eloc feld. Shear adheson forces beeen arcles of real lqds a her moemen are characered b lqd cargo nernal frcon or scos. Earler nesgaons on he ans dnamcs ere erformed onl for he Neonan lqds [3, 4]. Shear sresses beeen he arcles of he Neonan lqd are drecl rooronal o he relae eloc of s laers moemen and deend on he lqd e. or he non-neonan lqds hs deendence s no drecl rooronal. Accordngl, he lqd scos coeffcen s no consan and can deend on he emerare, ressre and shear rae, s draon and oher facors. In he boos [5, 6, 7] here are resened classfcaons of aros lqd meda and s menoned ha esng sem-emrcal and emrcal rheologcal models can be dded no o de-sread basc es: sedolasc ("rel scos" and sco-lasc enronmens. he ssem of eqaons ( reqres o secf bondar condons corresondng o he analed obec. In he consdered roblems he condons of non- eneraon hrogh sold alls n = 0 and arcles rang of a scos fld = 0 [8] ere aen no accon. he eclar of creaed models s he resence of a lqd-ar nerface. A ehcle moemen along he road s ercal oscllaons alas aear and he become a consan sorce of eddes or arfcal rblers [9, 0]. In addon, a sch ransonal moemen modes as emergenc brang or acceleraon, here s a hdromac acng he an all and o or damng deces. herefore, all smlaons of lqd cargo sloshng a non-saonar moemen modes of ans ere carred o ang no accon he resence of rblen sresses, deendng on he flo rae oscllaons. hs led o he aearance of s ne rblen sress nnons n he frs for eqaons of he ssem (. o deermne hese nnons s necessar o fnd he connecon beeen lsaon and aeraged rae n a rblen flo []:

3 Marna G. Knasoa, Aleandr O. Shmanos and Alžbea Saeoá. 0, 0; ; ; ; here,, roecons of he lqd arcles aeraged rae on,, aes resecel, m/s ;,, roecons of he lqd arcles lse rae on,, aes resecel, m/s ; aeraged sress ensor comonens, Pa. hs can be roded b rblence models. he analss n [] shos ha for he solon of or roblem he - ε rblence model [, ] s more referable o se. I noles solng of o addonal eqaons for he rblen nec energ and rblence energ dssaon rae ε for each fne elemen of lqd a each me se [, ]: ε; σ μ (μ ( ( (4, ε ε ε σ μ (μ ε ( (ε ε ε ε (5 here secfc (er n mass lqd rblen nec energ, m /s ; aeraged eloc, m/s;,,,, some dmensonless emrcal consans; secfc (er n mass dssaon rae of lqd rblen nec energ, m /s 3 ; rblence edd scos, Pas:. (6 Analcal solon of eqaons (3 has no been receed e for he roblems of he lqd flos for random nal and bondar condons, so her analss s sall done sng nmercal mehods. We e sed ANSYS X sofare as a ool for solng he aboe-menoned eqaons. In ANSYS s ossble o deermne onl he secfc (er n mass ales of lqd energ dssaon rae. In general case s necessar o ae no consderaon he neenness of fne elemen mesh, as ell as he resence of lqd or ar. herefore, e sggesed he mehod of oal rblen energ dssaon calclaon for lqd sloshng n reseror hch ncldes follong ses: fne elemen modelng of he ransored lqd cargo oscllaons n he an for a ceran me erod; fndng he rblen energ dssaon rae, corresondng o a arclar mese, as he oal mass of each fne elemen and s energ dssaon rae mllcaon; 3 deermnng a cmlae oal of lqd energ dssaon er ccle of oscllaons as he sm of he energ dssaon rae and he mese mllcaon. So, all of he resened comaonal resls for lqd cargo energ dssaon ere obaned sng he menoned echnqe. 3 ANALYSIS O HE ADEQUAY O OMPUER SIMULAION RESULS O HE EXPERIMENAL DAA o anale he adeqac of he real rocesses o he modelng echnqes sed n he ANSYS Worbench enronmen as creaed a fne elemen model of he aer-flled an mong h acceleraon n o aes (3

4 Marna G. Knasoa, Aleandr O. Shmanos and Alžbea Saeoá. (laeral and ranserse or hch as decelerang a rn. he geomercal dmensons of he an are shon n gre. Insde he rooe road an here ere nsalled hree ranserse arons of shercal shae h a hole n he mddle [3, 4]. In eermenal sdes, descrbed n deal n [4], measremens and calclaons ere carred o for dfferen fllng leels of he an. Also, calclaons ere erformed for he reseror ho arons and arons h fla and cone shae, some of hch had holes. he creaed comer model ncldng more han 0 hosand of fne elemens as sed for he comarson h eermenal daa descrbed n [3]. In he calclaons, he lnear acceleraon along he longdnal as of he an s eqal o 0.3g, along he ranserse as 0.5g, he fllng leel of he an as eqal o 40 %. gre : Geomerc arameers of he an h hree arons [3] he comarson of obaned ales of lqd ressre forces corresondng o he longdnal and laeral forces acng he an, h he eermenal and heorecal resls resened n [3], has shon ha he do no dffer b more han 3. %. hs confrms he ald of he mehodolog sed n he erformed smlaons. 4 ANALYSIS O ENERGY EQUAION NUMERIAL SOLUION OR LIQUID ARGO OSILLAIONS IN ROAD ANK RESERVOIRS Lqd cargo oscllaons n he road an a s ransen moemen modes ma be accomaned b a lqd emerare ncrease cased b he nernal frcon forces (lqd cargo energ dssaon. A sbsanal change n he emerare of he ransored cargo can lead o s scos change. he energ dssaon of lqd s dded n o ars: scos and rblen. rblen energ dssaon of lqd cargo deends on he degree of flo orc and s a ar of he orces mechancal energ, conered no hea. o esmae he effecs of lqd rblen and scos dssaon a road an brang here ere carred o he smlaons of lqd cargo oscllaons n he 4 m lengh reseror of he recanglar cross-secon h dmensons.5 m for lqds of Pa s dnamc scos. he reseror as arall-flled, s fllng leel as 50 %. he obaned comaonal resls shoed ha he ale of lqd rblen energ dssaon comonen ncreases for he 80 0 Pas lqd dnamc scos and hen decreases (gre, a. he ales of scos energ dssaon a lqd lo scoses ( o Pas ncrease n drec rooron o he ale of scos, b hen deends nonlnearl. When he dnamc scos ncreases n he range of 00 Pa s he scos energ dssaon ncreases consderabl, hen remans almos consan (n he range of J, and hen decreases gradall, de o a er small relae eloc of he lqd arcles (gre, b. Generall, he lqd scos energ dssaon s % of he oal lqd scos energ dssaon for dfferen ales of he dnamc scos. herefore, can be negleced n comarson h he rblen comonen a comer modelng for cases of road an brang. a b gre : rblen (a and scos (b lqd (h aer dens energ dssaon a brang of an h

5 Marna G. Knasoa, Aleandr O. Shmanos and Alžbea Saeoá. recanglar cross-secon o anale he nflence of lqd cargo rheologcal roeres on s sloshng n he road an h baffles and on he ales of hdrodnamc ressres and lqd energ dssaon here ere erformed he smlaons for brang (nal eloc 5 m/s, deceleraon 0.6 g of road an (4 m lengh, m dameer h erforaed baffle (seen holes of 0 cm dameer arall flled h lqd cargo of 967 g / m 3 dens and μ 0 = 0. Pa nal scos. he comaons ere done for hree rheologcal models of lqd cargo behaor: Neonan, de Waele and Bngham-Shedo. Resls shoed ha he oal lqd energ dssaon s mamal for Bngham model and s ce more han he ales obaned for oher models. A he same me, he resls for Neonan and de Waele models dffer less han 0% er one ccle of lqd cargo oscllaons [5]. A he same me, he hdrodnamc ressre n he road an reseror s largel deenden on he lqd dens and hs deendence s almos drecl rooronal. he coeffcens of ressre-dens rooronal for dfferen lqds n comarson h aer are gen n he able. e of lqd cargo Lqd cargo dens Mamal ales of hdrodnamc ressres g/m 3 relae o aer dens Pa relae o aer ressre Nrc acd Gasolne Waer Kerosene Xlol reacle Snfloer ol able : omarson of lqds dens and ressre ales h he corresondng ales for aer In order o anale he effec of he nernal frcon on he lqd emerare change, here ere erformed he comaons of lqd cargo sloshng n road an for lqds of Pa s dnamc scos. Based on or reos calclaons [6], he ehcle of he consdered confgraon sos n 4. seconds a emergenc brang. herefore, smlaons ere erformed secfcall for hs erod of me. Deendence of he lqd aerage emerare mamm ncrease on s scos s shon n gre 3. As can be seen from he fgre, hen he cargo scos ncreases o Pa s can be obsered he mamal aerage emerare ncrease, and hen, h a scos decrease he emerare changes decrease eher de o loer relae eloces of lqd cargo arcles. gre 3: he deendence of aerage emerare ncrease on he lqd cargo scos In general, he mamm emerare deaon from he nal ale as,6. So, f here s a need of comaonal analss for road ans h lqd cargo for one ccle of an ransen moemen he emerare changes can be negleced and he rocess can be consdered o be sohermal. he obaned resls hae shon ha he mamal change n emerare aes lace drng he frs second afer he sar of brang. omaonal resls confrmed he obos fac ha he moemen of lqd n he an becomes more gradall hen lqd scos ncreases (gre 4. I can be elaned b he fac ha he relae eloces of lqd arcles decrease a lqd dnamc scos ncrease.

6 Marna G. Knasoa, Aleandr O. Shmanos and Alžbea Saeoá. gre 4: ree srface oson for lqd h dfferen dnamc scos a road an brang h 0.6g acceleraon 5 ONLUSIONS he comarson of or ales of lqd ressre forces corresondng o he longdnal and laeral forces acng on he an, h he eermenal and heorecal resls resened n [3], has shon ha he do no dffer b more han 3. %. So he mehodolog sed n he erformed smlaons s ald. omaonal resls demonsraed ha lqd scos energ dssaon s % of he oal lqd scos energ dssaon for dfferen ales of he dnamc scos. herefore, can be negleced n comarson h he rblen comonen a comer modelng for cases of road an brang. 3 he resls shoed ha he hdrodnamc ressre n he road an reseror s largel deenden on he lqd dens and hs deendence s almos drecl rooronal. here ere calclaed he coeffcens of ressre-dens rooronal for dfferen lqds n comarson h aer. 4 he obaned resls hae shon ha he mamal change n emerare aes lace drng he frs second afer he sar of brang. In general, he mamm emerare deaon from he nal ale as.6. So, for comaonal analss of road ans h lqd cargo for one ccle of an ransen moemen he rocess can be consdered o be sohermal

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