VISCOUS FLOW FIELDS INDUCED BY A BREAKING SOLITARY WAVE OVER A SHELF
|
|
- Hilary Higgins
- 5 years ago
- Views:
Transcription
1 Journal of Marne Scence and echnolog, Vol. 3, No. 6, pp (05) 855 DOI: 0.69/JMS VISCOUS FLOW FIELDS INDUCED BY A BREAKING SOLIARY WAVE OVER A SHELF Chng-Jer Huang,, Yen-sen Ln, and Chun-Yuan Ln Ke words: RANS equatons, partcle level set metd, soltar wave, splash-up, energ balance. ABSRAC hs work nvestgates the vscous flow felds nduced b a soltar wave passng over a shelf or a step. he proposed numercal model solves the unstead two-dmensonal Renolds Averaged Naver-Stokes (RANS) equatons and the turbulence equatons. he fnte-analtcal scheme s used to dscretze the dfferental equatons nvolved n the RANS model. he partcle level set metd s adopted to capture the complex free surface evoluton. Accurac of the proposed model n smulatng breakng soltar wave on a shelf s verfed b comparng numercal wave profles from the ncdent stage to the begnnng of et fall wth the expermental data. Followng verfcaton of the accurac of the proposed numercal model, the surface evoluton, knematc propertes and energ balance nvolved n a breakng soltar wave on the shelf are elucdated n detals. Numercal results ndcate that durng the overturnng of the soltar wave, maxmum veloct of the flud partcles occurs after the frst splash-up and before the second reattachment. I. INRODUCION Paper submtted /0/4; revsed 0/8/5; accepted 06/0/5. Autr for correspondence: Chng-Jer Huang (e-mal: chuang@mal.ncku.edu.tw). Department of Hdraulc and Ocean Engneerng, Natonal Cheng Kung Unverst, anan, awan, R.O.C. Coastal Ocean Montorng Center, Natonal Cheng Kung Unverst, anan, awan, R.O.C. Wave breakng s one of the most commonl observed features of water waves n the coastal zones. When waves break, the momentum of waves s transformed nto the ocean surface laer. Wave breakng thus plas a sgnfcant role n the dsspaton of wave energ. Gven the hgh complext of the phenomena assocated wth wave breakng, earler research focused manl on the evoluton of a breakng soltar wave on a contnental shelf, whch s represented b a vertcal step. Gorng (978) studed the reflecton and transmsson of a soltar wave passng over a shelf and the results were confrmed b expermental data. Losada et al. (989) measured the evoluton of a soltar wave at a step and classfed the evolutons nto four modes concerned manl wth the dstorton, fsson and breakng of the wave. Yasuda et al. (997) nvestgated the knematc propertes of overturnng soltar waves on a step b usng the potental flow model. Surface profles and veloct felds of the flow from the ntal state to the state when the ets that are eected from ther crests plunge nto the front faces were examned. Experments were also performed to verf the accurac of the numercal results for the temporal water surface elevaton before the breakng pont and the spatal water surface profles around the eected et. Despte ts contrbutons, ther stud dd not address the surface evoluton of the breakng soltar wave after the formaton of the eected et, such as re-attachment, splash-up and ar entranment. B solvng the Renolds averaged Naver-Stokes (RANS) equatons, Lu and Cheng (00) studed the evoluton of a soltar wave over a shelf. Both nonbreakng and breakng soltar waves were examned. he breakng waves were smulated b couplng the RANS equatons wth k turbulence equatons. Accordng to ther numercal results, the fsson processes for generatng the second and thrd soltons are qute dfferent for nonbreakng and breakng soltar waves. he aforementoned research focuses manl on the surface evoluton of the breakng soltar waves. However, the knematc behavor and energ balance of the flows assocated wth breakng waves are also crucal for elucdatng the mechansm of the breakng waves. Man expermental studes have explored the knematc behavor assocated wth breakng waves. B usng the Partcle Image Velocmetr technque, Chang and Lu (998) measured the flud partcle veloctes n the overturnng et of a breakng wave. Accordng to ther results, the maxmum flud partcle veloct at the tp of the overturnng et reached.68 tmes of the phase veloct calculated from the lnear wave theor. he complcated free surfaces nvolved n a breakng wave have been smulated usng numercal approaches such as the VOF metd and the smoothed partcle hdrodnamcs (SPH) metd. Recentl, a level set metd (LSM) s developed to capture the nterface between two fluds. he level set metd provdes an effectve means of computng the nterface separaton and combnaton, such as the moton of ar bubbles n water or fallng water drops n ar. However, numercal df-
2 856 Journal of Marne Scence and echnolog, Vol. 3, No. 6 (05) fuson ma occur as tme proceeds, subsequentl affectng the correct capturng of the nterface. Numerous studes have developed a more accurate and effcent soluton algorthm, referred to as the partcle level set metd, to capture the nterface accuratel, subsequentl mprovng the conservaton of mass n the flow doman (Enrght et al., 00). Wang et al. (009) developed a two phase flow model to smulate spllng breakng waves, n whch the level set metd was mplemented for retrevng the ar-water nterface. Accordng to ther results, surface elevaton, locaton of the breakng pont and undertow profles can be captured. Lubn et al. (0) smulated two-dmensonal breakng waves over a slopng beach b solvng the Naver-Stokes equatons, n ar and water, coupled wth the large edd smulaton (LES). her numercal results were compared wth the expermental observatons. hs work develops a numercal model to examne the surface evoluton, knematc propertes, and energ balance nvolved n a breakng soltar wave over a shelf. he numercal model solves the unstead, two-dmensonal Renolds Averaged Naver-Stokes (RANS) equatons and the turbulence equatons. he nterface between the ar and water phases was captured usng the partcle level set metd. II. GOVERNING EQUAIONS hs work develops a numercal model to stud the surface evoluton and knematc behavor nvolved n a breakng soltar wave on a contnental shelf. he contnental shelf s represented b a step wth a vertcal face nstalled n the computatonal doman. For an ncompressble, vscous flud, the contnut equaton n the Cartesan coordnate sstem s wrtten n tensor form as U x O and the unstead Renolds Averaged Naver-Stokes (RANS) equatons are U ( ) U P U uu U t x x x x x () () n whch the edd vscost s determned as k C (4) where C s an emprcal constant; k s the turbulent knetc energ; s the dsspaton rate of turbulent knetc energ; and s Kronecker s delta. In order to take the wall dampng effect nto account, k models for low Renolds number flows are adopted (Patel et al., 985), whch nvolve emprcal constants and addtonal terms expressed as follows: k k k U t x x x x U uu k U t x x x where U C f uu C f E k x k U E ( ) Launder and Spaldng (974) recommended the followng emprcal constants for a full turbulent flow,.e. C = 9; C =.44; C =.9; k = and =.3. Launder and Sharma (974) proposed the followng terms n the k model for low Renolds number flows n boundar laers to modf the general turbulent transport equaton: (5) (6) (7) k C f (8) where the dampng functon f depends on the turbulence Renolds number R accordng to where U denotes tme-averaged mean veloct of the flud, for two-dmensonal flows ranges from to ; x s the coordnates; t s tme; s denst; P s hdrodnamc pressure, whch equals the reducton of the hdrostatc pressure from the total pressure, and uu are the Renolds stress tensor. In the k model of turbulent flud flows, each Renolds stress s related to the correspondng mean rates of stran b an sotropc edd vscost as follows: U U uu k x x 3 (3) where and f 3.4 exp[ ] R /50 R k / (9) (0) f f R, 0.3exp ()
3 C.-J. Huang et al.: Vscous Flow Felds Induced b a Breakng Soltar Wave over a Shelf 857 III. LEVEL SE MEHOD he level set metd s a numercal scheme developed to treat the evoluton of nterfaces and shapes. One advantage of the level set metd s that one can perform numercal computatons nvolvng curves and surfaces usng an Euleran approach (wth a fxed Cartesan grd). In two dmensons, the level set metd represents a close curve Γ n the plane as the zero level set of a two-dmensonal auxlar functon,, Γ ( x, ) ( x, ) 0 () and then manpulates Γ mplctl through the functon. hs functon s called a level set functon. he sgned dstance functon s generall csen as the level set functon. In ths work, the nterface, Γ, between ar and water s the zero level set of a smoothed dstance functon ( x, t, ), n whch < 0 denotes the ar regon and > 0 refers to the water regon. Functon s defned as the sgned normal dstance from the nterface, Γ, and satsfes. Durng tme evoluton, can be vewed as a propert convected wth the flow feld. Hence, U t 0 x (3) However, numercal dffuson ma arse after a fnte amount of computatonal tme,.e., the level set ma become rregular and s no longer a dstance functon. hus, the level set functon must be re-ntalzed at each tme step to ensure that the level set functon mantans a smooth dstance functon. hs can be acheved b teratng the followng partal dfferental equaton to reach a stead state, and then replacng ( x, t, ) wth d( x,, τ ), d S( ) d (4) where s an artfcal tme and S( ) s a smoothed sgned functon expressed as S( ) (5) In the numercal computaton, the thckness of nterface, Δ, s csen at least three grd cells n the drecton normal to the nterface, Γ. hus, the level set functon remans a dstance functon wth convergng to a unt wtut changng ts zero level set. In numercal mplementaton, wever, conservaton of mass ma be volated durng the re-dstancng procedure. Enrght et al. (00) developed the partcle level set metd to enhance the mass conservaton propertes of the conventonal level set metd and to reduce the numercal dffuson. he level set functon near a free surface s adusted b usng Lagrangan marker partcles. IV. BOUNDARY AND INIIAL CONDIIONS AND NUMERICAL MEHOD Solvng the RANS and turbulent transport equatons requres approprate boundar condtons at all boundares of the soluton doman, as well as the ntal condtons at t 0 for the entre doman. he ntal condtons of veloctes, hdrodnamc pressure, and surface dsplacement are set to zero at t 0. he knematc condton requres that flud partcles move wth the free surface. hs concept can be descrbed n terms of the advecton of the level set functon, as descrbed earler n Eq. (3). he dnamc condtons along the nterface, Γ, are as follows: n O (6a) P P atm (6b) where denotes the mean veloct of the flud (U or V), the turbulent knetc energ (k), or the dsspaton rate of turbulent knetc energ (), and n s the drecton normal to the nterface, Γ, n /. Eq. (6a) can be satsfed b solvng the followng partal dfferental equaton, untl the stead state s acheved (Peng et al., 999), S( )( ) O (7) where S( ) s a smoothed sgned functon, as expressed n Eq. (5); s a fcttous tme; and the operator represents ( / x, / ). Furthermore, the computatonal doman s extended wth tme, such that the wave does not reach the downstream boundar of the computatonal doman. In the proposed numercal model, the governng equatons were dscretzed b means of a fnte-analtcal scheme. he coupled veloct and pressure felds were calculated usng the SIMPLER algorthm. he evoluton of level set metd was solved usng the fourth-order VD Runge-Kutta metd and ffth-order WENO scheme. Further detals on the generaton of ncdent soltar wave n a numercal wave flume and the assocated numercal schemes can be found n Huang and Dong (00) and Dong and Huang (004). V. VERIFICAION o confrm the accurac of the ncdent soltar wave and the assocated veloct feld of the flow generated n the computatonal doman, Fg. compares the numercal soltar
4 858 Journal of Marne Scence and echnolog, Vol. 3, No. 6 (05) H H /h o = t/(l eff /c) Fg.. Comparson of numercal soltar wave profle wth that gven from Boussnesq s theor; ( ) Numercal results, ( ) Analtcal results usng Boussnesq s theor. Boundar H = 0.34 m Boundar h o = 0.3 m R= 0.63 m Boundar P P3 P m m Water Contnental Shelf Fg. 3. Schematc dagram of the expermental setup for measurng the evoluton of soltar wave over a shelf (Yasuda et al., 997 ). Boundar H * t/(l eff /c) U (cm/sec) Fg.. Horzontal veloct profles wthn the boundar laer nduced b a soltar wave at dfferent phases; (smbols) results from the proposed numercal model; (---) analtcal solutons obtaned from Huang and Dong (00). wave profle wth an ncdent wave heght of H /h o = 0.5 wth the theoretcal wave profle obtaned from Boussnesq s theor, H h K x ct (8) sec ( ) 3 where K 3 H /4 and c denotes the phase speed of the wave and equals to g( H h o ). Addtonall, h o s the stll water depth, and H and H denote the ncdent and local wave heght, respectvel. In Fg., the tme s normalzed b L eff /c, where L eff s the effectve wavelength of a soltar wave (Dean and Dalrmple, 995). Fg. compares the numercal and theoretcal rzontal veloct profles near the bottom boundar laer nduced b the soltar wave swn n Fg. at dfferent phases. he theoretcal rzontal veloct profles have been provded b Huang and Dong (00). he numercal grds used n the computatonal doman are x = 0. and = 5 except for near the wall regon, where 0 and 0 grds are unforml dstrbuted wthn 0 * < 5 and 5 * 0, respectvel, where * s defned as, 0.5 Kc /. Notabl, accordng to Fgs. and, the numercal wave profle and veloct feld of the flow generated n the computatonal doman are accurate t (sec) Fg. 4. Comparson between the numercal results and expermental data of the wave profle on a contnental shelf; smbols (,, ): wave profles recorded b the wave gauges P to P4, lnes ( ; - - -; ): numercal results; Δx = Δ = 06. o demonstrate the accurac of proposed numercal model n smulatng breakng soltar waves on a shelf, the numercal results of the wave profle, from the ncdent stage to the begnnng of wave overturnng, are compared wth the expermental data. Fg. 3 schematcall depcts the expermental setup of Yasuda et al. (997). he stll water depth, h o, s set to 0.3 m; the heght of the shelf s 0.63 m; and the ncdent soltar wave heght, H, s 0.34 m. Four wave gauges (P to P4) are dstrbuted near the leadng edge of the shelf to record the temporal water surface elevaton. o reduce the computatonal tme, the numercal wave flume s set up n a fnte doman of 0.5 m long and 0.6 m hgh usng unform computaton cells. he upstream boundar condton s appled to generate the desred ncdent soltar wave concdent wth that recorded at staton P n the experments,.e. wth a wave heght of 0.4 h o. he shelf s nstalled at 8.5 m (about 4 tmes that of the effectve wave length) awa from the wave paddle, and the wave probes are arranged at the same relatve locatons to the shelf as n Yasuda s experments. Fg. 4 compares the numercal and expermental water surface elevatons at wave gauges P to P4. he tme axs (t') n Fg. 4 s smpl csen to reflect the tme lag when the wave crest reaches varous wave gauges. he numercal results are computed wth x = = 06. he wave gauge P4 s placed n the vcnt of the breakng pont (B.P.). he lnes n Fg. 4 represent the numercal results and the smbols denote the expermental data. hs comparson reveals that evoluton of
5 C.-J. Huang et al.: Vscous Flow Felds Induced b a Breakng Soltar Wave over a Shelf x/h o (a) x/h o (b) x/h o (c) Fg. 5. Comparsons of the computed water surface profles wth the expermental records at the breakng pont (left curve) and at the et fall ntaton (rght curve) for varous grd cell szes; (a) Δx = Δ = 0, (b) Δx = Δ = 06, (c) Δx = Δ = 043; sold lne: numercal results, smbols: expermental data. the wave profles from the ntal ncdent stage to the begnnng of overturnng s properl smulated usng ths model. hs comparson ndcates also that before wave overturns, the grd cell sze x = = 06 s suffcentl fne to provde an accurate resoluton of the wave profles. Fg. 5 further compares the wave profles after wave breaks for varous grd cell szes. Wth x = = 0 n Fg. 5(a), the grd cell szes decrease to x = = 06 n Fg. 5(b), and to x = = 043 n Fg. 5(c). he tme step t vares wth the grd cell szes to make the Courant number, defned as max(ut/x, Vt/), less than one. B usng a hgh-speed vdeo camera, Yasuda et al. (997) obtaned the spatal wave profle around the eected et. wo wave profles were provded wth the earler one (.e. the left curve) beng that at the breakng pont, whle the latter one (.e. the rght curve) was at the begnnng of the et fall. However, Yasuda et al. (997) dd not provde the tme duraton between these two profles. he numercal wave profle at the breakng pont swn n Fg. 5 s dentcal to the expermental one, as verfed n Fg. 4. Moreover, the latter one s obtaned b smpl cosng the one closest to the expermental data at an tme. Fg. 5 ndcates that wth a fner grd cell sze, the overturnng wave t =.0 s t =.95 s t =.89 s t =.84 s t =.73 s t =.6 s t =.4 s t =.8 s t = 0.70 s x/h o Fg. 6. Evoluton of a breakng soltar wave on a shelf at dfferent tmes, where h o = 0.3 m, H /h o = 0.44, R/h o = 48. profle can be properl smulated b the proposed numercal model. Addtonall, the grd cell szes n Fg. 5(b) are fne enough to capture the expermental wave profles. Hence, n the latter computaton, the grd cell szes are set to x = = 06. VI. SURFACE EVOLUION AND KINEMAIC PROPERIES OF FLOWS Fg. 6 presents the evoluton of the breakng soltar wave on the contnental shelf from the ntal ncdent wave at t = 0.70 s, to t =.0 s, when the second splash-up occurs. he ncdent wave condtons and geometr of the shelf n Fg. 6 are the same as tse presented n Fg. 3. Fg. 6 ndcates that when the soltar wave propagates over the shelf, the leadng part of the wave rses due to the salng effect. For shallow water waves, the phase speed of the wave ncreases wth the water depth. Hence, the bulged porton of the wave propagates at a faster speed than the front part of the wave. hs propagaton causes the wave to steepen towards the front, at t =.73 s, eventuall topplng over at t =.84 s. hs topplng effect gves rse to the tpcal pcture of a plungng breaker. Owng to gravt, a seres of splash-up occurs subsequentl. Fg. 6 clearl reveals the reattachment and splash-up process of the overturnng waves at t =.89 s,.95 s, and.0 s. Accordng to Fg. 6, the proposed numercal model can elucdate complex phenomena nvolved n the wave breakng, such as the overturnng of wave, reattachments, and splash-ups.
6 Journal of Marne Scence and echnolog, Vol. 3, No. 6 (05 ) x/ (a) g x/ (b) g x/ (c) x/ (d) g.5 x/ (e) moves onsre graduall faster, and eventuall exceeds the speed of waveform, resultng n the curlng of the crest and the eventual breakng of waves. When the wave overturns and reattaches the free surface at t =.84 s (Fg. 7(c)), gravt seems to accelerate the eected et; n addton, the maxmum flow veloct ncreases to.30 Co at the leadng edge of the et. he eected water et then bumps aganst the undsturbed water surface, causng a water splash nto the ar, as swn n Fg. 7(d). Meanwhle, a vod forms as the et bumps nto the water. he splash-up seems to receve energ from the man flow, explanng wh the maxmum veloct occurs at the regon near the reattachment pont wth a hgh speed of.80 Co, whch s ver close to the value of.68 observed b Chang and Lu (997). Fgs. 7(e) and 7(f) sw the successve recurrence of the reattachment and splash-up. he flud wth the maxmum veloct of.8 Co n Fg. 7(d) decreases to.56 Co n Fg. 7(e) and to.53 Co n Fg. 7(f). VII. ENERGY BALANCE IN A BREAKING SOLIARY WAVE ON A SHELF.8 g 0.5 Fgs. 7(a) to (f) sw the contour maps of veloct felds nduced b the breakng soltar wave on a shelf at dfferent tmes to examne the knematc propertes of the overturnng waves. In Fg. 7 the abscssas are not fxed, but are csen to focus on the regon near the front of the waves. Notabl, Fg. 7 reveals that as the front of the wave evolved nto a vertcal shape at t =.73 s, Fg. 7(b), the maxmum flow veloct occurs at the top of the front wth a speed of 0.93 Co (Co = g ). From t =.73 s to.84 s, water at the wave crest.5 he last secton descrbed the evoluton of breakng soltar wave and ts knematc propertes on a shelf. he phscal phenomena nvolved n the breakng waves (e.g., reattachments, splash-ups, and ar entranment) cause energ dsspaton, whch s an mportant effect of the wave breakng and warrants further stud. otal energ of the water waves ( E total ) can be dvded nto the potental energ ( E pot ) and the knetc energ ( E kn ). he wave-nduced potental energ can be determned as follows. 3 E pot x H ( ) g d dx x 0 g d dx (9).6 where x and denote the nterval of ntegraton n the x and axes, respectvel, and represents the stll water depth. he knetc energ s.4.53 g..5.5 x/ (f) Fg. 7. Contour maps of veloctes nduced b a breakng soltar wave on a shelf at dfferent tmes, n whch t = (a).6 sec, (b).73 sec (c).84 sec, (d).89 sec, (e).95 sec, and (f).0 sec. E kn x H ( ) (U V ) d dx (0) where U and V refer to the rzontal and vertcal tmeaveraged mean veloct components, respectvel, and H( ) denotes the smoothed Heavsde functon and s defned as
7 C.-J. Huang et al.: Vscous Flow Felds Induced b a Breakng Soltar Wave over a Shelf 86 E pot E E kn E E total E t (sec) Fg. 8. me evolutons of potental energ (), knetc energ ( ), and total energ () wthn the wle computatonal doman as a soltar wave propagates over a shelf under the same condtons as tse n Fg. 3. de pot dt de kn dt de total dt t (sec) Fg. 9. emporal varaton of tme rate of change of potental energ (), knetc energ ( ), and total energ () as a soltar wave propagates over a shelf. he unt n the vertcal axs s Joule/(s m). he vertcal dashed lnes ndcate some of the tmes of wave profles swn n Fg. 6,.e. t = 0.70 sec,.8 sec,.6 sec,.84 sec,.89 sec, and.95 sec. O f Δ H( ) sn f Δ Δ Δ Δ f Δ () Secton III defnes the level set functon and the thckness. he reflecton coeffcent (K R ) and transmsson coeffcent (K ) are defned as offsre K E / E () R onsre K E / E (3) offsre where E denotes the ncdent wave energ, and E and onsre E are the energ of the wave propagatng n the offsre and onsre drectons, respectvel. he coeffcent of the energ dsspaton, K D, s then determned as follows. K K K (4) D R Fg. 8 presents the tme evoluton of the potental energ, knetc energ and total energ wthn the wle computatonal doman as a soltar wave propagates over a shelf under the same condtons as tse n Fg. 6. Notabl, Fg. 8 reveals that at the ntal state, the knetc energ of the wave s slghtl larger than the potental energ. However, as the wave propagates onto the shelf, the potental energ of the wave ncreases graduall and reaches the maxmum value at t =.4 s, as denoted b the frst vertcal dashed lne. hereafter, the potental energ decreases contnuousl. he decrease n the potental energ results n an ncrease n the knetc energ. he total energ decreases graduall due to the energ dsspaton caused b the nteracton of the wave and the shelf. he second vertcal dashed lne n Fg. 8 denotes the tme when the wave begns to break at t =.73 s. After the wave breaks, the potental energ decreases contnuousl, whle the knetc energ ncreases contnuousl due to the flow motons nduced b reattachments, splash-ups, and vod entranments. However, at the latter stage, e.g., t >.0 s, when two reattachments and two splash-ups have occurred, all three energes decrease contnuousl over tme. As s wdel recognzed, the wave breakng s accompaned b a sudden loss of energ, altugh no expermental data have demonstrated ths assumpton et. In Fg. 6, the wave breakng procedure begns when t >.73 s. Accordng to Fg. 8, no sudden loss of wave energ s assocated wth the wave breakng and, n most of the procedure of wave breakng, the knetc energ of the flud keeps ncreasng, whle the potental energ keeps decreasng. o further examne the energ varaton durng the wave breakng, Fg. 9 dsplas the temporal varaton of the tme rate of change of the potental energ, knetc energ, and total energ as a soltar wave propagates over a shelf. he unt n the vertcal axes of Fg. 9 s Joule /( s m). he vertcal dashed lnes n Fg. 9 ndcate some of the tmes of the wave profles swn n Fg. 6,.e., t = 0.70 s,.8 s,.6 s,.84 s,.89 s, and.95 s. Notabl, before the wave propagates onto the shelf (t < 0.9 s), the tme rate of change of the three energes remans unchanged wth values ver close to zero. he frst maxmum value of the tme rate of change of the potental energ appears at t =.8 s, correspondng to when the leadng part of the wave rses due to the salng effect. he frst maxmum value of the tme rate of change of the knetc energ appears at t =.6 s. Notabl, after the wave overturns and reattaches the free surface at t =.84 s, altugh Fg. 8 reveals no abrupt varatons n the tme evolutons of the potental, knetc, and total energ, Fg. 9 ndcates that the tme rate of change n the potental energ, knetc energ and total energ sgnfcantl var at some partcular nstance. For nstance, after the second reattachment, whch occurs at t =.95 s, de kn /dt ncreases abruptl and de pot /dt decreases rapdl. Immedatel after the second splash-up, t =.0 s, both de kn /dt and de total /dt declne abruptl, whle de pot /dt ncreases rapdl. Notabl,
8 86 Journal of Marne Scence and echnolog, Vol. 3, No. 6 (05) E total E E offsre E E onsre E t (sec) Fg. 0. me evoluton of reflected energ (E offsre /E, ), transmtted energ (E onsre /E, ), and total energ (E total /E, ) as a soltar wave propagates over a shelf. the maxmum negatve value of de total /dt appears at t =.03 s wth a value of 9.03 Joule /( s m), after the second splashup has occurred. As the soltar wave propagates over the shelf, total energ of the ncdent wave s dvded nto the transmtted energ and the reflected energ. o clarf the energ loss durng wave breakng, total energ s dvded nto two parts: the energ of the reflected wave (E offsre ) contaned n the regon from the wave paddle to the leadng edge of the shelf (x 7.7 h o ), and the energ of the transmtted wave (E onsre ) above the shelf from the leadng edge to the downstream of the wave tank (x 4.0 h o ). Fg. 0 presents the tme evoluton of the reflected energ (E offsre /E ) and the transmtted energ (E onsre /E ). Intall, 00% of the total energ was evaluated n front of the shelf. As the wave propagates over the shelf, approxmatel 4.8% of the ncdent wave energ remans n front of the shelf at t =. s. hus, accordng to Eq. (), the reflecton coeffcent K R s Smlarl, the transmtted coeffcent K s Upon completon of the computaton, around 87.3% of the ncdent wave energ remans n the computatonal doman. he energ dsspaton nvolved n the wle process s then.7%. Fg. 8 reveals that before wave breakng (t <.73 s), the dsspated energ s about 5%; whle at the end of computaton (t =. s), the totall dsspated energ ncreases to.7%. hese values ndcate that man part of energ dsspaton occurs n the srt perod after wave breaks. VIII. CONCLUSION hs work develops a numercal model to solve the unstead two-dmensonal Renolds Averaged Naver-Stokes (RANS) equatons and the k turbulence equatons for smulatng the evoluton of breakng soltar waves above a shelf, or a step. he partcle level set metd s adopted to capture the evolvng free surface, begnnng from the steepenng of the wave profle to the wave breakng and the successve reattachments and splash-ups. Based on the numercal results, we conclude the followng.. Numercal results ndcate that the developed numercal model can reveal the complex phenomena nvolved n a breakng soltar wave over a shelf, such as the overturnng of wave, reattachments of the eected et, and splash-ups.. he numercal results of wave profles near the breakng pont and at the stage wth an eected et have been swn to be dentcal to the expermental ones. 3. In the breakng soltar wave, the maxmum local flud veloct appears n the perod between the frst splash-up and the second re-attachment. he contour maps of flow veloctes near the breaker front ndcate that the maxmum local flud veloct s.8 gh o. 4. After the wave breaks, the potental energ frst decreases contnuousl and the knetc energ ncreases contnuousl; whle at the latter stage, the potental energ seems to approach a constant value, but the knetc energ decreases contnuousl n the same manner as that of the total energ. 5. Numercal results ndcate that n the plungng breakng wave, both the reattachment and the splash-up are normall accompaned b an abrupt change n the tme rate of change of knetc energ (de kn /dt) and the tme rate of change of potental energ (de pot /dt). ACKNOWLEDGMENS he autrs would lke to thank the Natonal Scence Councl, awan, for fnancall supportng ths research under Contract No. NSC98--E MY3 REFERENCES Chang, K. A. and P. L. F. Lu (998). Veloct, acceleraton and vortct under a breakng wave. Phscs of Fluds 0, Dean, R. G. and R. A. Dalrmple (995). Water wave mechancs for engneers and scentsts, World Scentfc, Sngapore. Dong, C. M. and C. J. Huang (004). Generaton and propagaton of water waves n a two-dmensonal numercal vscous wave flume. Journal of Waterwa, Port, Coastal, and Ocean Engneerng 30, Enrght, D., R. Fedkw, F. Ferzger and I. Mtchell (00). A hbrd partcle level set metd for mproved nterface capturng. Journal of Computatonal Phscs 83, Gorng, D. G. (978). sunams the propagaton of long waves onto a shelf. echncal Report, KH-R-38, W. M. Keck Laborator, Calforna Insttute of echnolog, Pasadena. Huang, C. J. and C. M. Dong (00). On the nteracton of a soltar wave and a submerged dke. Coastal Engneerng 43, Launder, B. E. and B. I. Sharma (974). Applcaton of the energ-dsspaton model of turbulence to the calculaton of flow near a spnnng dsc. Letters n Heat and Mass ransfer, Launder, B. E. and D. B. Spaldng (974). he numercal computaton of turbulent flows. Computer Metds n Appled Mechancs and Engneerng 3, Lu, P. L. F. and Y. Cheng (00). A numercal stud of the evoluton of a soltar wave over a shelf. Phscs of Fluds 3, Losada, M. A., C. Vdal and R. Medna (989). Expermental stud of the evoluton of a soltar wave at an abrupt uncton. Journal of Geophscal Research 94, Lubn, P., S. Glockner, O. Kmmoun and H. Branger (0). Numercal stud of the hdrodnamcs of regular waves breakng over a slopng beach.
9 C.-J. Huang et al.: Vscous Flow Felds Induced b a Breakng Soltar Wave over a Shelf 863 European Journal of Mechancs B/Fluds 30, Patel, V. C., W. Rod and G. Sheuerer (985). urbulence models for near-wall and low Renolds number flows: a revew. AIAA Journal 3, Peng, D., B. Merrman, S. Osher, H. Zhao and M. Kang (999). A PDE-based fast local level set metd. Journal of Computatonal Phscs 55, Wang, Z., Q. Zou and D. Reeve (009). Smulaton of spllng breakng waves usng a two phase flow CFD model. Computers & Fluds 38, Yasuda,., H. Mutsuda and N. Mzutan (997). Knematcs of overturnng soltar waves and ther relatons to breaker tpes. Coastal Engneerng 9,
Internal Wave Maker for Navier-Stokes Equations in a Three-Dimensional Numerical Model
Journal of Coastal Research SI 64 511-515 ICS2011 (Proceedngs) Poland ISSN 0749-0208 Internal Wave Maker for Naver-Stokes Equatons n a Three-Dmensonal Numercal Model T. Ha, J.W. Lee and Y.-S. Cho Dept.
More informationStudy on coastal bridge under the action of extreme wave
Study on coastal brdge under the acton of extreme wave Bo Huang Bng Zhu Jawe Zhang School of Cvl Engneerng, Southwest Jaotong Unversty, Chengdu 610031, Chna Abstract In order to research the catastrophc
More informationEngineering Analysis of Implementing Pedestrian Scramble Crossing at Traffic Junctions in Singapore
Engneerng Analyss of Implementng Pedestran Scramble Crossng at Traffc Junctons n Sngapore Dr. Lm Wee Chuan Eldn Department of Chemcal & Bomolecular Engneerng, Natonal Unversty of Sngapore, 4 Engneerng
More informationInvestigation on Rudder Hydrodynamics for 470 Class Yacht
Proceedngs Investgaton on Rudder Hydrodynamcs for 470 Class Yacht She Ln 1,, Yong Ma, *, Wetao Zheng, Song Zhang 1,, Xaoshan Le 1, and Yangyng He 1, 1 Graduate School of Wuhan Sports Unversty, Wuhan 430079,
More informationPREDICTIONS OF CIRCULATING CURRENT FIELD AROUND A SUBMERGED BREAKWATER INDUCED BY BREAKING WAVES AND SURFACE ROLLERS. Yoshimitsu Tajima 1
PREDICTIONS O CIRCULATING CURRENT IELD AROUND A SUBMERGED BREAKWATER INDUCED BY BREAKING WAVES AND SURACE ROLLERS Yoshmtsu Tama 1 Ths paper develops a quas-three-dmensonal nearshore current model whch
More informationWave Breaking Energy in Coastal Region
ave Breang Energy n Coastal Regon Ray-Qng Ln and Lwa Ln Dept. of Seaeepng Davd Taylor Model Basn NSCCD U.S. Army Engneer Researc and Development Center. INTERODUCTION Huang 006 suggested tat wave breang
More informationA comparison study on the deck house shape of high speed planing crafts for air resistance reduction
csnak, 2014 Int. J. Nav. Archt. Ocean Eng. (2014) 6:867~875 http://dx.do.org/10.2478/ijnaoe-2013-0218 pissn: 2092-6782, eissn: 2092-6790 A comparson study on the deck house shape of hgh speed planng crafts
More informationSpherical solutions of an underwater explosion bubble
89 Sphercal solutons of an underwater exploson bubble Andrew B. Wardlaw, Jr. Naval Surface Warfare Center, Code 423, Indan Head Dvson, Indan Head, MD 20640-5035, USA E-mal: 423@uwtech.h.navy.ml Hans U.
More informationPredicting Wave Transformation during Extreme Weather Conditions
Predctng Wave Transformaton durng Extreme Weather Condtons Josephus LOPEZ 1, Karlo Marko NARIO 1, Patrck Joshua ROMARES 1, Maro DE LEON, Ryuchro NISHI 3, Hosotan KAZUNORI 4 1 Bachelor of Scence n Cvl Engneerng
More informationDynamic Analysis of the Discharge Valve of the Rotary Compressor
Purdue Unversty Purdue e-pubs Internatonal Compressor Engneerng Conference School of Mechancal Engneerng 8 Dynamc Analyss of the Dscharge Valve of the Rotary Compressor Bo Huang Shangha Htach Electrcal
More informationExperimental And Numerical Investigation Of The Flow Analysis Of The Water-Saving Safety Valve
Expermental And Numercal Investgaton Of The Flow Analyss Of The Water-Savng Safety Valve Muhammed Safa KAMER s PhD Student n Department of Mechancal Engneerng n Kahramanmaras Sutcu Imam Unversty, Turkey.
More informationSpatial Evolution of Water Surface Waves: Numerical Simulation and Experiment of Bichromatic Waves
Proceedngs of the Eleventh (21) nternatonal Offshore and Polar Engneerng Conference Stavanger, Norway, June 17-22, 21 Copyrght 21 by The nternatonal Socety of Offshore and Polar Engneers SBN 1-88653-51-6
More informationReduced drift, high accuracy stable carbon isotope ratio measurements using a reference gas with the Picarro 13 CO 2 G2101-i gas analyzer
Reduced drft, hgh accuracy stable carbon sotope rato measurements usng a reference gas wth the Pcarro 13 CO 2 G2101- gas analyzer Chrs Rella, Ph.D. Drector of Research & Development Pcarro, Inc., Sunnyvale,
More informationNumerical Study of Occupants Evacuation from a Room for Requirements in Codes
Numercal Study of Occupants Evacuaton from a Room for Requrements n Codes HL MU JH SUN Unversty of Scence and Technology of Chna State Key Laboratory of Fre Scence Hefe 2300326, CHINA muhl@mal.ustc.edu.cn
More informationNumerical Analysis of Rapid Gas Decompression in Pure Nitrogen using 1D and 3D Transient Mathematical Models of Gas Flow in Pipes
Internatonal Journal of Chemcal and Bologcal Engneerng 6 01 Numercal Analyss of Rapd as Decompresson n Pure Ntrogen usng 1D and 3D Transent Mathematcal Models of as Flow n Ppes Evgeny Burlutsky Abstract
More informationCFD Simulation of R134a and R410A Two-Phase Flow in the Vertical Header of Microchannel Heat Exchanger
Purdue Unversty Purdue e-pubs Internatonal Refrgeraton and Ar Condtonng Conference School of Mechancal Engneerng 2016 CFD Smulaton of R134a and R410A Two-Phase Flow n the Vertcal Header of Mcrochannel
More informationSEEPAGE AND EROSION MECHANISMS OF OF SANDY GROUND DUE TO AIR BUBBLES
C-14 Fourth Internatonal Conference on Scour and Eroson 28 SEEPAGE AD EROSIO MECHAISMS OF OF SADY GROUD DUE TO AIR BUBBLES Hrotaka SAKAI 1 and Kench MAEDA 2 1 Member of JGS, Dept. of Cvl Eng., agoya Insttute
More informationAerator Performance in Reducing Phenomenon of Cavitation in Supercritical Flow in Steep Channel Bed
Engneerng Internatonal Conference UNNES Conservaton 13 Proceedng Aerator Performance n Reducng Phenomenon of Cavtaton n Supercrtcal Flow n Steep Channel Bed Yer Sutopo 1, Bud Wgnyosukarto, Istarto, dan
More informationInvestigation on Hull Hydrodynamics with Different Draughts for 470 Class Yacht
Proceedngs Investgaton on Hull Hydrodynamcs wth Dfferent Draughts for 470 Class Yacht Yong Ma 1, *, Shje Ln 1,2, Yangyng He 1, Xaoshan Le 1,2 and Song Zhang 1,2 1 School of Sports Engneerng and Informaton
More informationHigh Speed 128-bit BCD Adder Architecture Using CLA
Hgh Speed 128-bt BCD Archtecture Usng CLA J.S.V.Sa Prasanth 1, Y.Yamn Dev 2 PG Student [VLSI&ES], Dept. of ECE, Swamy Vvekananda Engneerng College, Kalavara, Andhrapradesh, Inda 1 Assstant Professor, Dept.
More informationEvaluation of a Center Pivot Variable Rate Irrigation System
Evaluaton of a Center Pvot Varable Rate Irrgaton System Ruxu Su Danel K. Fsher USDA-ARS Crop Producton Systems Research Unt, Stonevlle, Msssspp Abstrat: Unformty of water dstrbuton of a varable rate center
More informationPREDICTION OF POLYDISPERSE STEAM BUBBLE CONDENSATION IN SUB-COOLED WATER USING THE INHOMOGENEOUS MUSIG MODEL
PREDICTION OF POLYDISPERSE STEAM BUBBLE CONDENSATION IN SUB-COOLED WATER USING THE INHOMOGENEOUS MUSIG MODEL C. Lfante *, T. Frank *, A.D. Burns, D. Lucas and E. Krepper * ANSYS Germany GmbH, Staudenfeldweg
More informationEvaluation of Wettability of Solid Surface with Oil/ Refrigerant Mixture
Purdue Unversty Purdue e-pubs Internatonal Compressor Engneerng Conference School of Mechancal Engneerng 16 Evaluaton of Wettablty of Sold Surface wth Ol/ Refrgerant Mxture Mtsuhro Fukuta Shzuoka Unversty,
More informationGAS-LIQUID INTERFACIAL AREA IN OXYGEN ABSORPTION INTO OIL-IN-WATER EMULSIONS
AS-LIQUID INTERFACIAL AREA IN OXYEN ABSORPTION INTO OIL-IN-WATER EMULSIONS ómez-díaz, D. a, omes, N. b, Texera, J.A. b, Belo, I. b a Department of Chemcal Engneerng, Unversty of Santago de Compostela,
More informationA Study on Parametric Wave Estimation Based on Measured Ship Motions
1 A Study on Parametrc Wave Estmaton Based on Measured Shp Motons Ulrk Dam NIELSEN * and Tosho ISEKI ** Abstract The paper studes parametrc wave estmaton based on the wave buoy analogy, and data and results
More informationCross-shore Structure of Longshore Currents during Duck94
CHAPTER 283 Cross-shore Structure of Longshore Currents durng Duck94 Falk Feddersen 1, R.T. Guza 2, Steve Elgar 3, and T.H.C Herbers 4 Abstract The cross-shore structure of the mean longshore current on
More informationA Prediction of Reliability of Suction Valve in Reciprocating Compressor
Purdue Unversty Purdue e-pubs nternatonal Compressor Engneerng Conference School of Mechancal Engneerng 1996 A Predcton of Relablty of Sucton Valve n Recprocatng Compressor W. H. You Samsung Electroncs
More informationMechanical Engineering Journal
56789 Bulletn of the JSME Mechancal Engneerng Journal Vol., o., 6 Measurement of three-dmensonal orentaton of golf club head wth one camera Wataru KIMIZUKA* and Masahde OUKI* * DULOP SPORTS CO. LTD. Waknohama-cho
More informationTerminating Head
Termnatng Head 58246-1 Instructon Sheet for MTA- 100 Receptacle Connectors 408-6929 Usng Dscrete Wre 07 APR 11 Locatng Pawl Feed Slde Tool Base Wre Inserter Adjuster (Inserton Rod) Mass Termnaton Assembly
More informationPeak Field Approximation of Shock Wave Overpressure Based on Sparse Data
Peak Feld Approxmaton of Shock Wave Overpressure Based on Sparse Data Yongl Zhang, Taln Han, Yuqun Chen, Enku Zhang, and Xuan Lu Abstract To obtan the shock wave feld dstrbuton, two knds of calber weapons
More informationComparative Deterministic and Probabilistic Analysis of Two Unsaturated Soil Slope Models after Rainfall Infiltration
Jordan Journal of Cvl Engneerng, Volume 11, No. 1, 2017 Comparatve Determnstc and Probablstc Analyss of Two Unsaturated Sol Slope Models after Ranfall Infltraton Manoj Kr. Sahs 1) and Partha Pratm Bswas
More informationLSSVM Model for Penetration Depth Detection in Underwater Arc Welding Process
ISS 1746-7659, England, UK Journal of Informaton and Computng Scence Vol. 5, o. 4, 2010, pp. 271-278 LSSVM Model for Penetraton Depth Detecton n Underwater Arc Weldng Process WeMn Zhang 1, 2, GuoRong Wang
More informationInstantaneous Current Prediction for Naval Operations
Instantaneous Current Predcton for Naval Operatons Peter C. Chu Naval Ocean Analyss and Predcton Laboratory, Department of Oceanography Naval Postgraduate School, Monterey, CA 93943 Albert E. Armstrong
More informationOver Steep Topography
JOURNAL OF GEOPHYSCAL RESEARCH, VOL. 88, NO. C1, PAGES 743-750, JANUARY 20, 1983 On the Formaton of Surface to Bottom Fronts Over Steep Topography Y. HSUEH AND BENOT CUSHMAN-ROSN! Department of Oceanography,
More informationADDITIONAL INSTRUCTIONS FOR ISU SYNCHRONIZED SKATING TECHNICAL CONTROLLERS AND TECHNICAL SPECIALISTS
A ADDITIONAL INSTRUCTIONS FOR ISU SYNCHRONIZED SKATING TECHNICAL CONTROLLERS AND TECHNICAL SPECIALISTS DIFFICULTY GROUPS OF FEATURES 1 DEFINITIONS: Change of Rotaton: Refers to TURNS or LINKING STEPS rotatng
More informationNear-inertial internal wave interactions with mesoscale. Craig M. Lee. fronts: Observations and models
JOURNAL OF GEOPHYSCAL RESEARCH, VOL. 102, NO. C2, PAGES 3237-3253, FEBRUARY 15, 1997 Near-nertal nternal wave nteractons wth mesoscale fronts: Observatons and models Crag M. Lee Department of Physcal Oceanography,
More informationITRS 2013 Silicon Platforms + Virtual Platforms = An explosion in SoC design by Gary Smith
ITRS 2013 Slcon Platforms + Vrtual Platforms = An exploson n SoC desgn by Gary Smth 2013 2013 Gary Gary Smth Smth EDA, EDA, Inc. Inc. All All Rghts Rghts Reserved. Reserved. 1 The Fve Desgn Constrants
More informationTwin Gas Jet-assisted Pulsed Green Laser Scribing of Sapphire Substrate
JLMN-Journal of Laser Mcro/Nanoengneerng Vol. 11, No., 16 Twn Gas Jet-asssted Pulsed Green Laser Scrbng of Sapphre Substrate X.Z. Xe, Z.Q. Luo, X. We, F.L. Zhang, W. Hu and Q.L. Ren School of Eletromechancal
More informationOPTIMIZATION OF PRESSURE HULLS OF COMPOSITE MATERIALS
OPTIMIZATION OF PRESSURE HULLS OF COMPOSITE MATERIALS J.Franco a, A.Corz a*.a.peña b a Materal Composte Group. Unversdad de Cadz. Avda/Ramon Puyol s/n. 11205 Algecras (Span) *alcorz@caltech.es b Calpe
More informationSIMULATION OF EXTREME WAVE INTERACTION WITH MONOPILE MOUNTS FOR OFFSHORE WIND TURBINES
SIMULATION OF EXTREME WAVE INTERACTION WITH MONOPILE MOUNTS FOR OFFSHORE WIND TURBINES Feng Gao, Clve Mngha and Derek Causon Extree wave run-up and pacts on onople foundatons ay cause unexpected daage
More informationJournal of Chemical and Pharmaceutical Research, 2014, 6(5): Research Article
Avalable onlne www.jocpr.com Journal of Chemcal and Pharmaceutcal Research, 204, 6(5): 520-526 Research Artcle ISS : 0975-7384 CODE(USA) : JCPRC5 Dgtal Electrcal Resstance Tomography System and ts Expermental
More informationBubble Column Reactor Fluid-dynamic Evaluation at Pilot-plant for Residue and Extra-heavy Crude Oil Upgrading Technology
J. Chem. Chem. Eng. 9 (15) 176-19 do: 1.1765/1934-7375/15.3.3 D DAVID PUBISHING Bubble Column Reactor Flud-dynamc Evaluaton at Plot-plant for Resdue and Extra-heavy Crude Ol Upgradng Technology Rcardo
More informationM.H.Ahn, K.J.Lee Korea Advance Institute of Science and Technology 335 Gwahak-ro, Yuseong-gu, Daejeon , Republic of Korea
The Methodology on Exposure Dose Evaluaton Modelng Related to Arbtrary Accdent n the Temporary Storage Faclty for Low and Intermedate Level Waste - 9133 M.H.Ahn, K.J.Lee Korea Advance Insttute of Scence
More informationThe impact of foreign players on international football performance
MPRA Munch Personal RePEc Archve The mpact of foregn players on nternatonal football performance Orhan Karaca Ekonomst Magazne, Research Department October 008 Onlne at http://mpra.ub.un-muenchen.de/11064/
More informationBubble production by breaking waves
Calhoun: The NPS Insttutonal Archve Theses and Dssertatons Thess Collecton 989-2 Bubble producton by breakng waves Danel, Albert C., Jr. Monterey, Calforna. Naval Postgraduate School http://hdl.handle.net/0945/26903
More informationPedestrian Facilities Planning on Tianjin New Area program
Avalable onlne at www.scencedrect.com ScenceDrect Proceda - Socal and Behavoral Scenc es 96 ( 2013 ) 683 692 13th COTA Internatonal Conference of Transportaton Professonals (CICTP 2013) Pedestran Facltes
More informationNUMERICAL SIMULATION OF EXTREME WAVE GENERATION USING VOF METHOD *
466 010,(4):466-477 DOI: 10.1016/S1001-6058(09)60078-0 NUMERICAL SIMULAION OF EXREME WAVE GENERAION USING VOF MEHOD * ZHAO X-zeng RIAM, Kyushu Unversty, Fukuoka, Jaan State Key Laboratory o Coastal and
More informationAnalysis of Hold Time Models for Total Flooding Clean Extinguishing Agents
Analyss of old Tme Models for Total Floodng Clean Extngushng Agents Todd M. etrck, Al S. Rangwala Department of Fre Protecton Engneerng Worcester Polytechnc Insttute Worcester, MA 69-8 Abstract Ths study
More informationSEAKEEPING BEHAVIOUR OF A FRIGATE-TYPE TRIMARAN
Desgn & Operaton of Trmaran Shps, London, UK SEAKEEPNG BEHAVOUR OF A FRGATE-TYPE TRMARAN W Pastoor, Det Norske Vertas AS, Norway R van 't Veer, Martme Research nsttute Netherlands, The Netherlands E Harmsen,
More informationProceedings of the ASME nd International Conference on Ocean, Offshore and Arctic Engineering OMAE2013 June 9-14, 2013, Nantes, France
Proceedngs of the ASME nd Internatonal Conference on Ocean, Offshore and Arctc Engneerng OMAE June 9-,, Nantes, France OMAE-6 ROLL DAMPING COEFFICIENTS ASSESSMENT AND COMPARISON FOR ROUND BILGE AND HARD
More informationInternational Journal of Engineering and Technology, Vol. 8, No. 5, October Model Systems. Yang Jianjun and Li Wenjin
Internatonal Journal of Engneerng and Technology, Vol. 8, No. 5, October 2016 1 Relablty Optmzaton Desgn of Submarne Free-Runnng Model Systems Yang Janjun and L Wenjn Abstract Wth regard to the relablty
More informationPlanning of production and utility systems under unit performance degradation and alternative resource-constrained cleaning policies
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Plannng of producton and utlty systems under unt performance degradaton
More informationNonlinear Risk Optimization Approach to Gas Lift Allocation Optimization
pubs.acs.org/iecr Nonlnear Rsk Optmzaton Approach to Gas Lft Allocaton Optmzaton Mahd Khshvand and Ehsan Khamehch* Faculty of Petroleum Engneerng, Amrkabr Unversty of Technology, Tehran, Iran ABSTRACT:
More informationFirst digit of chosen number Frequency (f i ) Total 100
1 4. ANALYSING FREQUENCY TABLES Categorcal (nomnal) data are usually summarzed n requency tables. Contnuous numercal data may also be grouped nto ntervals and the requency o observatons n each nterval
More informationMass Spectrometry. Fundamental GC-MS. GC-MS Interfaces
Mass Spectrometry Fundamental GC-MS GC-MS Interfaces Wherever you see ths symbol, t s mportant to access the on-lne course as there s nteractve materal that cannot be fully shown n ths reference manual.
More informationCOMPARATIVE ANALYSIS OF WAVE WEATHER WINDOWS IN OPERATION AND MAINTENANCE OF OFFSHORE WIND FARMS AT HSINCHU AND CHANGHUA, TAIWAN
Journal of Marne Scence and Technology, Vol. 5, No. 5, pp. 563-570 (07) 563 DOI: 0.69/JMST-07-0703- COMPARATIVE ANALYSIS OF WAVE WEATHER WINDOWS IN OPERATION AND MAINTENANCE OF OFFSHORE WIND FARMS AT HSINCHU
More informationω, would be a JONSWAP
NUMERICAL PSEUDO RANDOM SIMULATION OF SAR SEA AND WIND RESPONSE Eugeno Puglese Carratell (1,), Fabo Dentale (1), and Ferdnando Reale () (1) Unversty of Salerno, Va Ponte Don Melllo, 8484 Fscano, Italy
More informationReport No. FHWA/LA.13/508. University of Louisiana at Lafayette. Department of Civil and Environmental Engineering
TECHNICAL REPORT STANDARD PAGE Report No. FHWA/LA.13/508 4. Ttle and Subttle A Comprehensve Study on Pavement Edge Lne Implementaton 7. Author(s) Xaoduan Sun, Ph.D., P.E. Subassh Das 9. Performng Organzaton
More informationMouhamadou Diop, Frédérick Gagnon, Li Min, and Mario Fafard. Correspondence should be addressed to Mouhamadou Diop;
ISRN Materals Scence Volume 24, Artcle ID 45469, pages http://dx.do.org/.55/24/45469 Research Artcle Gas Bubbles Expanson and Physcal Dependences n Alumnum Electrolyss Cell: From Mcro- to Macroscales Usng
More informationSECOND-ORDER CREST STATISTICS OF REALISTIC SEA STATES
SECOND-ORDER CREST STATISTICS OF REALISTIC SEA STATES MARIOS CHRISTOU Shell Internatonal Exploraton and Producton, 2288 GS Rjswjk, The Netherlands. E-mal: maros.chrstou@shell.com PETER TROMANS Ocean Wave
More informationAalborg Universitet. Published in: 9th ewtec Publication date: Document Version Publisher's PDF, also known as Version of record
Aalborg Unverstet Predctablty of the Power Output of Three Wave Energy Technologes n the Dansh orth Sea Chozas, Jula Fernandez; Jensen,. E. Helstrup; Sørensen, H. C.; Kofoed, Jens Peter; Kabuth, Alna Krstn
More informationA Climbing Robot based on Under Pressure Adhesion for the Inspection of Concrete Walls
A Clmbng Robot based on Under Pressure Adheson for the Inspecton of Concrete Walls K. Berns, C. Hllenbrand, Robotcs Research Lab, Department of Computer Scence, Techncal Unversty of Kaserslautern P.O.
More informationAn intro to PCA: Edge Orientation Estimation. Lecture #09 February 15 th, 2013
An ntro to PCA: Edge Orentaton Estmaton Lecture #09 February 15 th, 2013 Revew: Edges Convoluton wth an edge mask estmates the partal dervatves of the mage surface. The Sobel edge masks are: " #!1 0 1!2
More informationDriver s Decision Model at an Onset of Amber Period at Signalised Intersections
Probablty to stop 1.00 0.90 0.80 0.70 0.60 0.40 0.30 0-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 90-95 95-100 1st veh n platoon 2nd veh n platoon
More informationRisk analysis of natural gas pipeline
Rsk analyss of natural gas ppelne Y.-D. Jo 1, K.-S. Park 1, J. W. Ko, & B. J. Ahn 3 1 Insttute of Gas Safety Technology, Korea Gas Safety Corporaton, South Korea Department of Chemcal Engneerng, Kwangwoon
More informationResponse based sea state estimation for onboard DSS Safe and Efficient Marine Operations
Response based sea state estmaton for onboard DSS Safe and Effcent Marne Operatons Ulrk Dam Nelsen AMOS Workshop, NTNU, Trondhem, 13 th and 14 th November, 2014 Contents Introducton: Context Montorng and
More informationRADIAL STIFFNESS OF A BICYCLE WHEEL AN ANALYTICAL STUDY
ADIAL TIFFE OF A BICYCLE WHEEL - A AALYTICAL TUDY José aría ínguez Dpto. de Físca Aplcada II Facultad de Cenca y Tecnología Unversdad del País Vasco Aptdo. 644 488 Blbao PAI Emal: osemara.mnguez@ehu.es
More informationNumerical Simulation on a Gas Distributor Used In Slurry Column Reactor Yating CAI
2nd Internatonal Conference on Electrcal, Computer Engneerng and Electroncs (ICECEE 2015) Numercal Smulaton on a Gas Dstrbutor Used In Slurry Column Reactor Yatng CAI College of Chemcal Engneerng, Bejng
More informationDegassing of deep groundwater in fractured rock
WATER RESOURCES RESEARCH, VOL. 36, NO. 9, PAGES 2477-2492, SEPTEMBER 2000 Degassng of deep groundwater n fractured rock around boreholes and drfts Jerker Jarsj6 and Georga Destoun Dvson of Water Resources
More informationChinese and foreign men s decathlon performance comparison and structural factor correlation test based on SPSS regression model
ISSN : 0974-7435 Volume 10 Issue 3 Chnese and foregn men s decathlon performance comparson and structural factor correlaton test based on SPSS regresson model Pengfe Zhang*, Jngjng Lu Insttute of Physcal
More informationWheels. Wheels 2. Wheels 4. Wheels 3. Wheels 5. Wheels 6
Wheels 1 Wheels 2 Introductory Queston Wheels The lght turns green and you re n a hurry. Wll your car accelerate faster f you skd your wheels and burn rubber or f you just barely avod skddng your wheels?
More informationThe woman in Figure 10 is taking a deep breath. This action helps
3.2 The Gas Laws Secton 3.2 1 FOCUS Key Concepts What causes gas pressure n a closed contaner? What factors affect gas pressure? How are the temperature, volume, and pressure of a gas related? Vocabulary
More informationPhysical and Geological Studies of the Proposed Bridge-tunnel Crossing of Hampton Roads near Craney Island
College of Wllam and Mary W&M ScholarWorks Reports 8-97 Physcal and Geologcal Studes of the Proposed Brdge-tunnel Crossng of ampton Roads near Craney sland C. S. Fang Vrgna nsttute of Marne Scence B. J.
More informationGeophysical validation of NSCAT winds using atmospheric data and analyses
JOURNAL OF GEOPHYSCAL RESEARCH, VOL. 104, NO. C5, PAGES 11,405-11,424, MAY 15, 1999 Geophyscal valdaton of NSCAT wnds usng atmospherc data and analyses R. Atlas, 1 S.C. Bloom, 2 R. N. Hoffman, 3 E. Brn,
More informationLake Clarity Model: Development of Updated Algorithms to Define Particle Aggregation and Settling in Lake Tahoe
Lake Clarty Model: Development of Updated Algorthms to Defne Partcle Aggregaton and Settlng n Lake Tahoe Goloka B. Sahoo S. Geoffrey Schladow John E. Reuter Danel Nover Davd Jassby Lake Clarty Model Weather
More informationProduct Information. Universal gripper PZN-plus
Product Informaton Unversal grpper PZN-plus PZN-plus Unversal grpper Relable. Robust. Flexble. PZN-plus unversal grpper Unversal 3-Fnger Centrc Grpper wth hgh grppng force and maxmum moments due to mult-tooth
More informationStability Analysis for the Design of 5000-Tonnes Offshore Work Barge
Internatonal Journal of Engneerng and echnology Volume No. 9, September, Stablty Analyss for the Desgn of 5-onnes Offshore Work arge Ntonye Samson a, Ezenwa Ogbonnaya b, uve Ejabefo a a Department of arne
More informationEquilibrium or Simple Rule at Wimbledon? An Empirical Study
Equlbrum or Smple Rule at Wmbledon? An Emprcal Study Shh-Hsun Hsu, Chen-Yng Huang and Cheng-Tao Tang Revson: March 2004 Abstract We follow Walker and Wooders (200) emprcal analyss to collect and study
More informationJournal of Chemical and Pharmaceutical Research, 2014, 6(3): Research Article
Avalable onlne www.ocpr.com Journal of Chemcal and Pharmaceutcal Research, 2014, 6(3):326-332 Research Artcle ISSN : 0975-7384 CODEN(USA) : JCPRC5 Research on comprehensve evaluaton model-based NBA schedule
More informationDevelopment and Validation of Newborn Child Head Numerical Model Dummy for Impact Simulations
Internatonal Journal of Electroncs and Electrcal Engneerng Vol. 4, No. 6, December 2016 Development and Valdaton of Newborn Chld Head Numercal Model Dummy for Impact Smulatons J. M. Nursherda, B. B. Sahar,
More informationInvestigating sailing styles and boat set-up on the performance of a hydrofoiling Moth dinghy
Investgatng salng styles and boat set-up on the performance of a hydrofolng Moth dnghy Abstract M W Fndlay, S R Turnock Flud-Structure Interactons Research Group, School of Engneerng Scences, Unversty
More informationDevelopment of Accident Modification Factors for Rural Frontage Road Segments in Texas
Development of Accdent Modfcaton Factors for Rural Frontage Road Segments n Texas Domnque Lord* Zachry Department of Cvl Engneerng & Center for Transportaton Safety Texas Transportaton Insttute Texas A&M
More informationDETECTION AND REFACTORING OF BAD SMELL
Internatonal Journal of Software Engneerng & Applcatons (IJSEA), Vol.4, No.5, September 2013 DETECTION AND REFACTORING OF BAD SMELL CAUSED BY LARGE SCALE Jang Dexun 1, Ma Pejun 2, Su Xaohong 3, Wang Tantan
More informationA NUMERICAL INVESTIGATION OF SHEET FLOW UNDER NON-BREAKING AND BREAKING WAVES. Abstract
Coatal Dynamc 2017 A NUMERICAL INVESTIGATION OF SHEET FLOW UNDER NON-BREAKING AND BREAKING WAVES Yeulwoo Km 1, Zhen Cheng 2, Tan-Jan Hu 1, Ryan S. Mera 1 and Jack A. Puleo Abtract An Euleran two-phae flow
More informationMass Transfer of CO 2 into Water and Surfactant Solutions
Mass Transfer of CO 2 nto Water and Surfactant Solutons Rouhollah Farajzadeh, Al Barat, Harm A. Dell, Johannes Brunng, Pacell L.J. Ztha Delft Unversty of Technology, Department of Geotechnology, Mjnbouwstraat
More informationENERGY SAVING IN THE HYDRAULIC CIRCUIT FOR AGRICULTURAL TRACTORS: FOCUS ON THE POWER SUPPLY GROUP.
ENERGY SAVING IN THE HYDRAULIC CIRCUIT OR AGRICULTURAL TRACTORS: OCUS ON THE POWER SUPPLY GROUP. Massmo Borgh, Barbara Zardn, rancesco Pntore, Engneerng Department Enzo errar, Unversty of Modena and Reggo
More informationDisplacement-based performance assessment of steel moment resisting frames
Dsplacement-based performance assessment of steel moment resstng frames M. Ferraol, A. Lavno, A.M. Avossa, A. Mandara Seconda Unverstà d Napol, Dpartmento d Ingegnera Cvle, va Roma 9 Aversa (CE), Italy
More informationPropagation of Big Island eddies
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106, NO. C1, PAGES 935-944, JANUARY 15, 2001 Propagaton of Bg Island eddes Chrstna L. Holland and Gary T. Mtchum College of Marne Scence, Unversty of South Florda,
More informationPERFORMANCE AND COMPENSATION ON THE EUROPEAN PGA TOUR: A STATISTICAL ANALYSIS
PERFORMANCE AND COMPENSATION ON THE EUROPEAN PGA TOUR: A STATISTICAL ANALYSIS C. Barry Pftzner and Chrs Spence, Department of Economcs/Busness, Randolph-Macon College, Ashland, VA, bpftzne@rmc.edu, cspence@rmc.edu
More informationComparisons of Means for Estimating Sea States from an Advancing Large Container Ship
Downloaded from orbt.dtu.dk on: Jan 31, 18 Comparsons of Means for Estmatng Sea States from an Advancng Large Contaner Shp Nelsen, Ulrk Dam; Andersen, Ingrd Mare Vncent; Konng, Jos Publshed n: Proceedngs
More informationResearch and Application of Work Roll Contour Technology on Thin Gauge Stainless Steel in Hot Rolling
Send Orders for Reprnts to reprnts@benthamscence.ae The Open Mechancal Engneerng Journal, 215, 9, 111-116 111 Open Access Research and Applcaton of Work Roll Contour Technology on Thn Gauge Stanless Steel
More informationPolyethylene flow prediction with a differential multi-mode Pom-Pom model
Korea-Australa Rheology Journal Vol. 14, No. 1, March 2002 pp. 25-32 Polyethylene flow predcton wth a dfferental mult-mode Pom-Pom model R.P.G. Rutgers*, N. Clemeur, S. Muke 1 and B. Debbaut 2 Department
More informationModeling Low-Pressure Injections in Diesel HCCI Engines
Modelng Low-Pressure Injectons n Desel HCCI Engnes Yong Sun * and Rolf D. Retz Engne Research Center, Department of Mechancal Engneerng Unversty of Wsconsn-Madson Madson, WI 5376-169 USA Abstract Homogeneous
More informationAnimating Bubble Interactions in a Liquid Foam
Anmatng Bubble Interactons n a Lqud Foam Oleksy Busaryev Oho State Unversty Tamal K. Dey Oho State Unversty Huamn Wang Oho State Unversty Zhong Ren Zhejang Unversty Fgure : Coke foam. By representng foam
More informationAalborg Universitet. CLIMA proceedings of the 12th REHVA World Congress Heiselberg, Per Kvols. Publication date: 2016
Aalborg Unverstet CLIMA 2016 - proceedngs of the 12th REHVA World Congress Heselberg, Per Kvols Publcaton date: 2016 Document Verson Publsher's PDF, also known as Verson of record Lnk to publcaton from
More informationOklahoma Corporation Commission Oil & Gas Conservation Division Post Office Box Oklahoma City, Oklahoma Rule 165:
Oklahoma Corporaton Commsson Ol & Gas Conservaton Dvson Post Offce Box 52000 Oklahoma Cty, Oklahoma 73152-2000 Rule 165: 10-3-25 Form 1002A AP No.: 35043231380001 OTC Prod. Unt No.: 043-205416 Completon
More informationarxiv: v1 [cs.ne] 3 Jul 2017
Modelng preference tme n mddle dstance trathlons Iztok Fster, 1 Andres Iglesas, 2 Suash Deb, 3, 4 Dušan Fster, 5 and Iztok Fster Jr. 6 1 Unversty of Marbor, Faculty of Electrcal Engneerng and Computer
More informationAalborg Universitet. Published in: 9th ewtec Publication date: Document Version Accepted author manuscript, peer reviewed version
Aalborg Unverstet Predctablty of the Power Output of Three Wave Energy Technologes n the Dansh orth Sea Chozas, Jula Fernandez; Jensen,. E. Helstrup; Sørensen, H. C.; Kofoed, Jens Peter; Kabuth, Alna Krstn
More informationThis document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore.
Ths document s downloaded from DR-NTU, Nanyang Technologcal Unversty Lbrary, Sngapore. Ttle capacty analyss usng smulaton Author(s) Ctaton Huang, Shell Yng; Hsu, Wen Jng; He, Yuxong; Song, Tancheng; De
More informationLaser Shock Processing influence on local properties and overall tensile behavior of friction stir welded joints
Laser Shock Processng nfluence on local propertes and overall tensle behavor of frcton str welded jonts Mhaela Iordachescu a '*, Andres Valente a, Lus Caballero a, Danut Iordachescu b, Jose Lus Ocana b,
More information