Numerical Simulation of Spiral Flow and Heat Transfer in Hydrate Pipeline with Long Twisted Band

The DPM model (discrete phase model) considering the motion of solid particles was used to simulate the complex spiral flow characteristics of hydrate in the pipe spinning up with long twisted band. The deposition and heat transfer characteristics of gas hydrate particles in the pipe spiral flow were studied. The velocity distribution, pressure drop distribution, heat transfer characteristics and particle settling characteristics of the flow field in the pipeline were investigated. The numerical results show that, compared with the straight flow of light pipe without twisted band, two obvious eddies are formed in the flow field under the spinning action of twisted band, and the velocities are maximum at the center of the eddies. Along the direction of the pipe, the two vortices move towards the pipe wall from near the twisted band, which can effectively carry the hydrate particles deposited on the pipe wall. With the same Reynolds number, the greater the twist ratio, the weaker the spiral strength, the smaller the tangential velocity of the spiral flow, and the smaller the pressure drop of the pipe. Therefore, the pressure loss can be reduced as much as possible while ensuring the spinning effect of the spiral flow. In a straight light pipe flow, the Nusser number is in a parabolic shape with the opening downwards. At the center of the pipe, the Nusser number gradually decreases towards the pipe wall at the maximum, and at the near wall, the attenuation gradient of Nu is large. For spiral flow, the curve presented by Nusserr number shows a trough at the center of the pipe and a peak at 1/2 of the pipe diameter. With the reduction of twist rate, the Nussel number becomes larger and larger. Therefore, the spiral flow can make the temperature distribution in the flow field in the pipeline more even, and prevent the large temperature difference resulting in the mass formation of hydrate particles in the pipeline wall. Spiral flow has a good carrying effect. Under the same working condition, the spiral flow carries hydrate particles at a distance about 3-4 times that of the straight flow.


Introduction
M ixed p ipelin e of natural gas h ydrate p lu ggin g p rob lem s mo re and mo re seriou s, hy drate b lo cka ge b locks th e f lo w of natural ga s makes the part ial p ressure of p ip eline damage to p ip eline equ ipment , cont ro l hyd rate p lu ggin g gradually becom e an impo rtant p rob lem to en su re the safety of p ipelin e op erat ion . The trad it iona l m ethod s to prevent hyd rates from b lock in g p ipelin es are to chan ge the form ation co nd it ion s of hyd rates by heat in g and lo werin g the p ressu re, o r to inh ib it t he fo rmation of hyd rates by inj ect in g t hermod ynamic inh ib ito rs. Th ese meth ods n ot on ly co st a lot b ut a lso cause p o llut ion t o the env iron ment . The cu rrent research is not foc used on hyd rate supp ression but on th e generatio n of hydrate to ensure the safe flow of hydrate to achieve the purpose of risk control.
There are many k in ds of sp iral rotatin g dev ices, su ch as sp ira l t wisted band , imp eller and sp iral gu ide ba r. Acco rd in g to the d ifferent use co nd it ion s and purposes need t o u se d ifferent rotat in g dev ice, there are th ree met hod s for th e conv ent iona l generatio n of sp iral f lo w: tangent ial in let flo w, in stallat ion of f lo w gu id e and sp iral p ipe. Wan g et al. 1-2 made a comparat ive analy sis of variou s sp iral f lo w rotatin g dev ices and carried o ut experim ental stud ies . Team 3 used PH OENIC S computat ional f lu id soft wa re to n umerica lly simu late the fo rmat ion and attenuation of sp ira l flo w in a p ipelin e wit h a v elocity an gle of 5~70 °. It is found that wh en t he velo city an gle chan ges bet ween 5 ° and 30°, t he resu lt in g sp ira l flo w has a su itab le tan gent ial and ax ial velocity , wh ich is also con duciv e to t he remo val of depo sited impu rit ies and water in t he p ipeline. Dou et al. 4 analy zed th e liq u id -so lid t wo-phase f lo w in the tube wit h built -in sp rin g. Com pared with the f lo w in the non -helical t ube, th e helical f lo w n ot on ly enhanced h eat transf er, b ut also had t he effect of cleanin g d irt . Zhan g et al. 5 stud ied the attenuation charact erist ics of t he sp ira l f lo w of th e f lat axis round tub e gen erated by th e local generator th rou gh exp eriment s, and he con clud ed t hat the tan gent ia l v elocit y and the st ren gth of th e sp ira l flo w d ecreased with t he in crease of t he d istance. In co nclu sion , sp iral f lo w not on ly has stron g carry in g capacity , but also has impo rtant application valu e fo r safe transp ortat ion of NGH. Th e research grou p also u sed t he R NG k-ε model to numerically simu late the f lo w charact erist ics of swirl flo w rotated by th e vane in th e horizontal p ip e 6 . The R eyno lds nu mber had a great inf luen ce on swirl inten sity . Th e swirl int ensit y wou ld increase , and swirl inten sity attenuation rate decrease , when R e numb er increased . Mo reover, th e sp iral f lo w can enhance th e heat transfer bet ween phases, wh ich is a co ntro llable techn iqu e fo r th e fo rmation and p revent io n of h yd rate in th e pipeline.
Research on th e safe f lo w of natu ral gas hyd rate, Zhao et al. 7 con sid ered th e interact ion amon g hyd rate, part icle size d ist ribut ion, part icle v isco sity, t he b iggest interna l phase accumu lat ion rate of the basic ph ysical p rop ert ies, such as based on E-Eu ler dou b le f lu id m odel, th e mathematica l m odel of h yd rate f lo w in p ipelin e wa s estab lish ed , th e resu lt s of th e study sho wed that com pared with M u lhe size mo del, th e part icle size of m odel con sidered th e int eract io n b et ween the h yd rate part icles, th e simu lat ion value is closer to th e ex perim ental va lue. Son g et al. 8 int rod uced a popu lat ion equ ilib rium mod el based on the a ggregat ion dynam ics of h yd rate part icles to simu late th e effects of f lu id f lo w rate and hyd rate v o lume f raction on th e safe f lo w characterist ics of hyd rate slu rry. Then th e popu latio n balance mod el based on so lid hyd rate grain accumu lat ion dynam ics 9 , th e co llision f requen cy , aggregatio n efficiency, fra gm entatio n f req uen cy and sub -part icles size d ist ribut ion fun ct ion after cru sh in g of the hyd rate so lid particles were co nsid ered in t he f lo w process, simu lat ion un der d ifferent cond it ions of hyd rate part icle aggregatio n pro cess, th e simu lation resu lt s were com pared with the calcu lated resu lt s of the hyd rate part icle gro wth mod el. In addit ion , So n g et a l. [10][11] sim u lated th e d epo sit ion ru le of gas hyd rate part icles in th e p ipelin e b y referencin g condensat ion metho d, and estab lish ed the k in et ic model of hyd rate d epo sit ion and hy drate decompo sit ion . Based o n the theo ry of hyd rate part icle dep osit io n, th e st ru ctu ral m odel of h yd rate depo sit ion wa s established, th e ma in mechan ica l parameters were determ ined , and t he f in ite element num erical simu lation met hod was u sed t o calcu late the hyd rate d epo sit ion on th e p ipe wa ll. Son g et a l. 12 estab lished a d ynamic mod el of hy drate a ggregat ion based o n the pop u lation eq u ilibrium equation. From th e dy namic mod el, they gave and fu lly d iscu ssed th e ca lcu lat ion metho d of particle f ra gmentat ion and co llision frequ ency , generation condensat ion eff iciency, f ra gmentat ion f req uen cy and particle size d ist rib ut ion fu nct ion of sub -pa rt icles. The t radit ional so lid-liqu id flo w model is so lved, the effects of flo w rate and hy drate vo lum e f ract ion on h yd rate slurry f lo w charact erist ics in p ip elines of o il and water syst em s were simu lated. Lian g Ju n et al. [13][14] th ro u gh the estab lish ment of th ree-d imen siona l mod el of circu lar p ip e sp iral f lo w , R NG k -ε t urbu len ce mod el and DPM mo del were u sed to sim u late the th ree -d imen siona l t ransient of gas -so lid t wophase sp iral f lo w and heat t ransfer in natura l gas p ipelin e, t he v elocit y f ield , temperature f ield , d ist ribut ion law of hydrate pa rt icle vo lum e fract io n and heat tran sfer law of d ifferent cross sect io ns in natura l gas p ip eline were stud ied . And exp erimenta l research o n characterist ics of th e ga s-so lid t wo phase f lo w spun up b y t he t wisted band in p ipelines is condu cted 15 , and th e effect of gas phase velocity and paramet ers of t wisted band on t he part icle carry in g laws , co llisio n characterist ics , carry in g d istance , part icle v elocit y d ist ribut io n and part icle concent ratio n d ist ribut ion is inv est igated, and f lo w cha racterist ics of gas -so lid t wo phase no n-sp iral f lo w and gas-so lid t wo phase sp ira l f lo w are compared and analyzed. Ca i et a l. 16 u sed the DPM mod el and R SM model to simu late the sp ira l t ransport of ga s hydrate part icles with a t wist ed band . Th e temp erature f ield, v elocit y f ield, t urbu len ce int ensit y and d epo sit ion la w of hydrate part icles und er d ifferent to rsion rates and f lo w rates were examin ed . Chan g et al. 17 carried out th ree dim en sional t ransient num erical simu lation and simu la t ion of gas-so lid t wo -phase sp iral f lo w in natural gas p ip elines, and stud ied th e v o lume co ncentrat ion variatio n characterist ics of h yd rate part icles in natura l gas p ipelin es and th e depo sit ion charact erist ics of hyd rate part icles. Co nsid erin g the fo rmation p rocess of h yd rate, Liu et al. 18 established the equatio n of mass, m oment um and en ergy ba lance. Th e iterat ive meth od and f in it e d ifference m ethod are used t o so lve t he mo del resu lt s, and th e sensit iv ity analy sis of th e impo rtant parameters of the model is ca rried out . Bro wn et al. 19 used a m icromechanical force meter to exp lo re the interact ion bet ween the wax deposit ed on th e su rface and disso lved in t he b u lk p hase and the hyd rate chem ically treated to p rev ent a gglom eration . It is fo und t hat wax can sign if icant ly chan ge the cohesion and a dhesion of hy drate pa rt icles, but the effect of ant i-cakin g agent may vary wit h the compo sit ion of anti-cakin g a gent . Nicho las et a l. 20 exp lo red the deposit ion of saturated natura l gas con den sate contain in g water on the p ipeline wa ll by u sin g sin gle-circu lat ion p ip eline, and fou nd that th e dep osit io n of h yd rate o n the wa ll cou ld cause th e p ipelin e p ressu re drop to rise slo wly. At t he same t ime, th e wa ll sed iment s can in su late th e flu id in side th e tub e, mak in g th e wa ll sed im ent s m igrate do wn st ream. L o ren zo et a l. 21 stud ied the gro wth and depo sit ion of hyd rate on th e wa ll un der the con d it ion of annu lar flo w with sin gle circu lat ion p ipelin e, and fo und that the m emb rane gro wth model un der th e cond it io n of lo w su bcoo lin g cou ld well p red ict th e pressu re d rop of th e loo p after hyd rate fo rmat ion . Ho wever, oth er part icle behav io r characterist ics, su ch as the shedd in g of hyd rate layer, should be considered under the condition of high supercoolin g.
In con clusion, academ ics have carried out the num erical simu lation and e xperim ental research of t he comb inat ion of pipeline flo w la w of gas hyd rate in secu rity wo rk , b ut it d id not hy drate pa rt icles in a lon g t wist band un screw th e syst em research to the m ovem ent of the sed imentary ru les, at th e same t im e and heat t ransfer of th e sp iral f lo w syst em of t he la w o n hyd rate fo rmation and th e inf luence of the part icle mov ement is also th e impo rtant int erf erence factors of t he p ipeline operat ion . Therefo re, in t h is paper, th e autho r in v iew of th e current hy drate f lo w characterist ics of common f lo w f ield, th e DPM mod el (d iscrete phase mod el) that con sid ers the m ovem ent of so lid particles is u sed to numerically sim u late the com p lex sp ira l f lo w charact erist ics of hyd rates in side a p ipe swirlin g wit h a lon g t wist ed band , fo cu s on th e d epo sit ion and h eat transf er characterist ics of natu ral gas hyd rate pa rt icles in pip e sp iral f lo w. Invest igate th e velocity d ist ribut ion, p ressu re d rop d ist rib ut ion , heat t ransfer characterist ics and particle sett lin g cha racterist ics of the f lo w f ield in the p ip eline. Prov ide techn ical su ppo rt for th e safe t ranspo rtat ion of natural gas hydrate in pipelines under spiral flow system.

physical model
The fo rmat ion of h yd rate requ ires a series of comp lex p rocesses and do es n ot ex ist d irect ly in th e p ip eline. In th is paper, a series of react ion processes of hyd rate fo rmation are igno red in t he numerical simu lat ion , and it is assumed that hydrate part icles have b een gen erated d irect ly at the entrance of th e p ip eline. In th e num erica l sim u lation , th e shape of hyd rate part icles was set as a po sit ive circle and the part icle size was a lso set as t he same, wh ile th e inf lu ence of p ipe wa ll th ickn ess o n th e fo rmat ion of hy drate was d irect ly ign ored in th e calcu latio n. The calcu latio n model establish ed by C AD soft wa re is sh o wn in Fig.1 . The p ip e d iameter D= 0.0 24m and the len gth L= 2 .5m . At th e same t im e, a gro up of h yd rate pa rt icles with part ia l rotat ion in the sho rt t wisted band was set as a comparison , and th e length of the short twisted band was 0.5m.

geometric model
Twisted band with d ifferent to rsional rates a re set at th e p ipe in let as th e swirler. Th e phy sical mod el of th e t wisted band is sho wn in Fig.2, th e to rsional rates of the sp iral t wist ed band are 6.2, 7.4 and 8 .8 , respect ively . Fig. 3 sho ws a sch ematic d iagram of t he to rsional rate of the t wist ed band. Th e t orsiona l rate is the ratio bet ween t he len gth H of th e twisted band and the width D of the twisted band after a rotation.

boundary conditions
Befo re num erical simu lat ion , th e boun dary con d it ion s of th e geom etric mod el shou ld be set reasonab ly. In the in let end of t he p ip e, th e velo city in let is set as th e bounda ry con d it ion . Th e velo city in let fo r fou r d ifferent rey no ld s numbers is 5 000 , 1000 0, 1 5000 and 20 000 respect ively. In th e out let is sett in g outf lo w expo rt s as the b oundary cond it ion s, no slip wa ll is set to a fixed , the p rob lem is simp lif ied to th ree d imensio nal, con stant ph ysical gas -so lid flo w. Set th e in let t emperatu re Tin of the p ipelin e to 280 K, and th e wa ll t emperature Tw = 277 K. The m odel is Figure 1. The physical model calcu lated u sin g rectan gu lar coo rd inate sy stem. The origin is at t he center of the ent ry interface, the z -ax is is the f lo w direct ion , th e grav ity d irect ion is alo n g th e -y axis, and th e gravit y a cceleratio n is 9 .81m/ s2 . Th e f lu id med iu m is natural gas and hydrate particles, flowing from the left end of the pipeline to the right.

initial conditions
The d iameter of th e gas p ip eline D=0 .02 4m, and th e len gth L=2.5m.In the simu latio n, it is con sidered that th e physical propert ies of the hyd rate in the sp ira l f lo w p ipeline a re con stant, th e gas phase is met hane, and the so lid phase is NGH part icles. The basic phy sica l parameters are m easu red at room t emp eratu re. First ly, th e natu ral ga s densit y was set as 0 .77 k g/m3 , the k inemat ic v iscosity of natura l gas was 1 1.0 3 ×10 -6m 2/s, and the h yd rate part icle densit y wa s 9 15k g/m 3.The in it ia l concent ratio n of hyd rate wa s given as 1 %, 2 %, 4 %, 6 % and 8 % in DPM , and th e movem ent of part icles at d ifferent con cent ra t ion s wa s sim u lated. The t emp eratu re of the f lu id and hyd rate part icles in the natu ral gas p ip eline are th e same, and there is n o t emperatu re d ifferen ce. Mo reover, th e hyd rate part icles are set as homo geneou s sph eres wit h the same part icle size in the simu latio n. Data parameters are select ed acco rd in g t o th e research content, as shown in Table 1.  Becau se of th e ex ist ence of the t wist ed band , the un structu red grid is u sed , and the den se processin g of th e p ip e wa ll can bett er perfo rm the tu rbu lence calcu latio n. The m ost su itable grid com put in g was selected t hrou gh th e grid independence test, and the number of grid cells was about 4 million .

mathematical model
The DPM mo del (d iscret e phase mod el) is used in t he simu lation. The d iscrete p hase mo del is a mu lt i -com ponent flo w mo del und er th e eu la -la gran gian metho d. In t he sim u lation , the so lid part icles are t reated as d iscrete phase, wh ile the f lu id is t reated as cont inuou s phase. After the f lu id cont inuou s phase is stabilized in the ca lcu lat ion , th e part icle discret e phase is introduced . In th e d iscrete phase model, the part icle phase is regarded as the d iscret e phase, wh ile the f lu id is on ly regard ed as the cont inuou s phase. Th e pa rt icle vo lu me f ract ion is the mass t ransfer f rom phase q t o phase p. energy equation: Where, , p c ,T and  are gas d en sity, sp ecif ic heat capacity at con stant p ressure, temp erature and therma l conductivity( p c =2.2 05k J/k g.k,  =0.14 W/m k ), u, v and w are all velocities, and t is time.
Where,  , u, and p are gas den sity , velo city, and static pressu re, respect ively; ij is the v iscou s st ress t ensor; t is th e time. Volume fraction equation: Where, aq is the vo lu me f ract ion of phase q, q a S is th e sou rce t erm, pq m is t he mass t ransf er from phase p to phase q, qp m is required to be relatively small, and the solid particle concentration of the discrete phase is generally below 10%.

discrete phase model
The ca lcu lat ion of d iscrete phase model ma in ly co nsists of co nt inuou s phase and d ispersed phase. The DPM mod el can obtain th e part icle m ot ion equat ion by ca lcu lat in g the fo rces on part icles, and th e part icle m ot ion trajecto ry can b e obtained by integratin g th e part icle m ot ion equation of DPM mod el with t ime. The mot ion equat ion of the traject ory of solid particles in the z direction is: Where,u is t he velo city of t he f lu id phase, m/s; Re is defined as the relative Reynolds number as follows: Where, p d is particle diameter, m.

calculation method
C FD soft wa re is usually u sed to so lv e p ract ica l prob lem s in nu merica l simu lat ion . The soft ware is generally compo sed of th ree part s: p ret reatment , calcu lation and data solv in g, and po st -processin g. Pre -p rocessin g is to bu ild a physical mo del and th en co nduct mesh d iv ision . The comp ut in g part in the m idd le is part icu larly impo rtant. Many parameters and algorit hm select ion n eed to be set b efore re -operat ion , amon g wh ich th e select ion of algorith m can imp ro ve the accu racy of sim u lation and comp ut in g eff iciency . The ca lcu lat ion can b e rou gh ly d iv ided into th e follo win g steps: phy sica l mo del select io n, parameter sett in g (grid un it select ion , material def in it io n, phase select ion , boundary cond it ion sett in g, ref erence value sett in g, etc.), a lgo rithm select io n and cont ro l facto r sett in g, in it ializat ion , monitor setting, and time step setting.
The d iscrete phase model is select ed in th e ca lcu lat ion , and the p ressu re base and imp licit so lv er are used to simu late t he tran sient state of t he gas -so lid th ree -d im ensional helical flo w in the gas hyd rate p ipelin e. In t he sim u lated calcu lat ion fo r d iscrete phase, wit h R NG k-Ɛ t urbu len ce mod el, th e SI M PLEC algo rithm is adopted t o th e cou p lin g of pressu re and v elocit y, Th e d iscrete p hase mod el is select ed in the ca lcu lat ion , and th e pressu re base and imp licit so lver a re u sed to simu late t he t ransient state of th e gas -so lid th ree -d im ensional helica l f lo w in th e gas hyd rate pip eline. In th e sim u lated calcu lation fo r d iscrete phase, with R NG k -Ɛ tu rb u len ce mo del, the SI M PLEC algo rithm is adopted to the co up lin g of p ressu re and v elocity , a mu lt id im ensional linear recon stru ct ion met hod is used t o recon struct th e seco nd o rder su rface p ressu re sch eme , pa rt icle mot ion model usin g DPM m odel. In th e DPM mo del, it is also necessary to set som e paramet ers at th e in let of the p ip eline, such as the inject ion pa rt icle sp eed , mass f lo w rate and inject ion pa rt icle num ber, et c. Du rin g th e it erat ive ca lcu lat ion in th e simu lat ion , in o rder to calcu late th e effect of b etter, also n eed to set do wn the relaxation facto r nu merica l range: Ɛp=0.3~0 .7 , Ɛm=0 .5~0 .7 , Ɛk = ƐƐ=0 .4~0 .6 . When the absolute value of residual is below 1×10 -6 , the condition of convergence can be achieved.

grid independence test
Mesh generation is an imp ortant step in th e establishm ent of f in ite elem ent mo del. In th is process, many p rob lem s need to be considered and the wo rk load is v ery heavy. Th e u n it len gth , quant ity and density of the grid have d irect influence on the precision and time of calculation.
In order to meet th e req u irement s of co mputational accu racy and ensure computat ional eff iciency ,8m m, 4mm and 2mm mesh sizes were selected for grid in dep endence verif icat ion . imu lat ion verif ication cond it ion s: p ip e d iameter D=24mm , gas R eyno ld s n umber Re is 2000 0, t wist rate of t wisted band is 6.2, in it ial concent ratio n of part icles is 2%.As sho wn in Fig. 5 , the velo city d ist ribut ion on th e cro ss -sect ion at Z=5 D of t he p ipelin e is select ed fo r comparison . Und er th ese th ree m esh size cond it ions, the v elocity d ist ribut io n cu rves obtained by th e sim u lation are generally sim ilar. H o wever, compared with 2 mm (65 41200 cells) and 4mm (4 20948 0cells), the mesh size of 8m m (286 5700 cells) varies greatly , and th ere a re fewer m esh es near the wa ll, so the calcu lation accu racy is n ot enou gh. On the other hand , th e grid size of 2mm (654 1200 cells) and 4 mm (4209 480cells) is basically th e same, and the accu racy is not imp roved mu ch n ear th e wa ll. In o rder t o imp rov e th e co mput in g eff icie ncy , th e grid size of 4m m (4209480cells) is finally selected as the computational grid.

Experimental verification of gas-solid two-phase spiral flow and heat transfer
The num erical sim u lation resu lts of gas -so lid t wo-phase sp iral f lo w a re compared with th e experim ental resu lts t o verify the feasib ility . Cont rast d ia gram as sho wn in f igu re 6 and 7 are the resu lts of the validat ion , th e p ressu re d ro p of the f lu id (ΔP) and nu sselt n umber (Nu ) wit h the R eyno lds numb er (Re) chan ges in gas -so lid t wo phase f lo w. Th e pip e is 1.2 m lon g, 24 mm in d iamet er and t he part icle size is about 0 .02 mm. The concent rat ion of so lid part icles u sed in th e simu lat ion is th e rat io of so lid v o lume to gas v o lume. From the simu lation and experim ental v erif ication resu lt s, the erro r is v ery small, so the gas -so lid t wo -phase f lo w in th e gas hy drate p ipelin e can be calcu lated by n umerica l simulation method.
The Reynolds number is calculated as follows:  vd = Re (12) Where, d is the d iameter of t he p ipe, v is the average v elocity of part icle f lo w, ρ and μ are the d ensit y and dynamic viscosity of the gas, respectively.

Result Analysis
The deposit ion and heat t ransfer of part icles in sp iral p ipe f lo w were stud ied by u sin g t he sho rt t wisted band mo del. The velo city d ist ribut io n, pressu re d rop d ist ribut io n, part icle deposit ion characterist ics and heat tran sfer characterist ics in th e natura l ga s p ipelin e are ma in ly st ud ied , and t he effects of lon g t wist ed band and no t wist ed band as well as different Reynolds numbers are compared and analyzed. Fig. 8 sho ws th e velocity d ist ribut io n clou d map at each sect ion u nder th e con d it ion of Re=1 5000 and d ifferent torsional rates. It can b e seen f rom th e f igu re that in th e light p ip e with out to rsiona l band f lat DC, t he velo city is maximum in the cent ra l area of th e p ip e and t hen d ecreases u n iform ly to wa rds t he p ip e wa ll, and th e velo city chan ge at each sect ion is not o bv iou s. Ho wev er, in t he p ipe int o the t wist ed band , t wo d ist inct edd ies are fo rmed on bot h sides of th e t wisted band, with th e max imum ve lo city at the cent er of th e vo rtex . Alon g t he d irect ion of the p ipe, th e two vo rt ices mov e fro m the n ear to rsio nal band to ward the wa ll. Compa red wit h t he sho rt t wisted band , t he vo rtex always ex ist s b ecause the lo n g t wisted band is fu ll of the who le p ipe, wh ile in t he sho rt t wisted band p ipe, th e velocity t end s to d ecrease as the part icle t ranspo rtation d istance in creases. And t he lo wer th e t wist rate of t he t wisted band, the greater the velocity of the two vortex centers.   9 sh o ws t he velocity and vecto r graph s at d ifferent sect ion s. Aft er th e velo city d istribut ion is stab ilized, th e velocity cent er can be o bv iou sly ob serv ed at t he far end of th e p ressu re su rface of th e p ip eline, and there is an obv iou s wak e. It can be seen from t he vecto r lin e that t he tangent ial velocity f irst increases and th en stab ilizes. Th e tangent ia l velo city hard ly attenuates in t he p rocess of hyd rate t ransp ortat ion . And th e tan gent ial velocity va lue nea r the wall is th e largest . It is b ecause of the tangent ial velo city that hyd rate part icles la rger tan gent ia l fo rce with th e wa ll, make th e hyd rate part icle is not easy to dep osit , tangent ial v elocit y at the same t ime sp in in the hy drate part icles themselves, make h yd rate part icle is n ot easy to reun ite and dep osit io n, sin ce the lon g t wist ed band rotates a ll t he way , the constant tangential velocity can further expand the sa fe flow boundary of hydrate.  Fig. 10 sho ws th e relationsh ip b et ween p ipe p ressu re drop and Rey no ld s num ber when a t wisted band with a to rsio n rate of 6 .2 is p laced. It can be seen fro m the figu re that at the same sect ion of the p ipe, th e p ressu re d ro p of th e p ip e in creases with th e increase of Reyno ld s n umber, and t he h igh er the R eyno lds numb er is, the mo re the p ressure d ro p in creases. Alo n g th e d irect ion of th e p ip e, the p ressu re d ecreases mo re obv io usly with the increase of the part i cle transportation distance, and the slope of the curve in the figure is larger and larger, which is similar to a parabola. It can be seen f rom th e figu re that t he p ressure d rop is affected by th e t wist rate. The smaller th e twist rate is, th e greater the p ressure drop of the p ip eline is. Wh en a t wist ed band is p laced in the p ip e , the p ressu re drop will chan ge sign ificantly. The reaso ns are analy zed as fo llo ws: co mpared with the st ra ight light p ip e f lo w, th e torsional b elt p laced in th e p ipe produces resistance to the f lu id, and the sp iral f lo w generated by t he to rsional b elt distu rb s th e bo undary layer of t he p ipe and causes tu rbu lent f lo w. As a resu lt, the p ressu re d rop of th e to rsiona l b elt placed in the pipe is higher than the pipe without torsional belt.

Influence of torsion ratio on pressure drop
In the case of con stant part icle Reyn o lds n umber, t he greater t he to rsion rat io of t he t wisted band p laced in th e p ipe, the weaker the sp ira l f lo w st ren gth , the smaller t he tan gent ial velo city of t he sp iral f lo w and th e smaller the axia l velocity loss, and the smaller the increase in pressure drop of the pipe. Fig. 12 sho ws the t emp eratu re d ist ribut ion cloud map at each sect ion of th e p ipe wit h R e=2000 0 and d ifferent to rsio n rates. As can be seen from the figu re, the temp erature d ist ribut ion in t he p ipe wit hout to rsiona l bands is relat ively unifo rm and layered at the b eginn in g. Alon g the d irect io n of the p ipe, d ue to t he effect of h eat transf er, th e temperature f rom th e center of the p ipe t o th e wa ll decreases gradually, and t he t emperatu re in the cent er of th e p ip e is th e h ighest. After addin g th e t wist ed band , t wo v ort ices will b e fo rm ed o n bot h sides of the t wisted band, and th e temperature at the t wo vo rtex center is the h ighest and gradually decreases fro m the cent er to th e p ip e wall. Wit h th e in crease of the t orsiona l band t wist rate, t he temperature in the vo rt ex center is relat ively sma ller, becau se the smaller the t wist rate, th e stron ger t he sp iral f lo w generated is, th e stron ger t he bo undary layer d ist urbance of th e p ip eline is, wh ich is condu cive to flu id heat t ransfer. Co mpared with t he sho rt t wisted band befo re, th e tem perature of the who le pipe drops slowly.   Fig. 13 sho ws t he change cu rv e of the avera ge Nussel numb er Nu with R e in th e lon g t orsiona l p ip e. In th e p lain DC of the light p ipe witho ut t wisted band, Nu changes litt le with Re and app rox imates a ho rizonta l lin e wh en Re is v ery small. A lon g to rsional belt is p laced in t he p ipeline, and wh en the f lu id f lo ws t hrou gh the int ernal to rsional belt , it will rotate, wh ich enhances th e tangent ial v elocit y of t he f lu id and cont inuou sly scou r the bounda ry layer of th e pip eline. Mean wh ile, th e d istu rbance of t he bou ndary layer is a lso st ren gt hen ed, and the tu rb u len ce intensity of th e flu id n ear th e wall is imp ro ved . The tan gent ial mot i on of th e flu id makes the b oundary layer f lu id and t he ma in bod y mix and st ren gt hen , t hus effect ively en hancin g the con vect ive heat t ransfer of th e f lu id . As yo u can see fro m th e figu re, t he smaller th e t wist rate is, the larger Nu is. Because t he lo wer th e t wist rate, t he more t wist ed th e t wist , th e lon ger th e f lo w. In t he case of t he same mass f lo w rate, the lon ger th e path of the f lu id f lo w is, t he la rger the sp ira l flo w fo rmation and velocity is, and th e greater the tu rbu lence inten sity of th e f lu id is, thu s enhancin g t he heat t ransfer. Fig. 14 sho ws t he Nu d ist rib ut ion curve of all sect ion s un der the cond it ion of d ifferent t orsion rates wh en Re=20 000 . As can be seen from th e f igu re, Nu of th e stra ight light p ipe flo w is a lmo st u nchan ged alon g t he p ipe. When th e twisted tape is p laced in the p ip e, the Nu sser nu mber f irst stren gth en s and th en d ecreases after about 20 D. Since th e twisted band gen erates sp ira l f lo w at th e begin n in g, wh ich enhances th e heat tran sfer of t he p ip e, Nu start s to becom e smaller with the heat exchan ge b et ween t he f lu id and th e p ipe wall. Com pared with the sho rt t wisted band , th e lon g twisted band fills the who le p ipe, so the sp ira l f lo w of the flu id in th e p ipe is mainta ined all th e t im e, so th e attenuation of the Nusser number is relatively small.   Fig. 15 sh o ws th e Nu d istribut ion cu rv e on t he sect ion Z=5 D when Re=2 0000 . In a st raight light p ipe flo w witho ut torsion band, the Nusser numb er is in a parabo lic shape with the op en in g do wn wards. At t he center of th e p ip e, th e Nusser nu mber gradually d ecreases to wa rd s the p ipe wa ll at th e maximum , and at the n ear wa ll, th e attenuatio n grad ient of Nu is large. Because th ere is no swirl d ist urbance in th e st raight light p ip e flo w, the temperature at th e center of the p ip e is the h igh est , and t he h eat ex chan ge t emperatu re of the p ipe wa ll decreases gradually. In th e p ip e wit h t wist ed tape, t he cu rv e of Nu sserr nu mber app eared a t rou gh in the center of th e p ipe and a p eak at half of th e pip e d iamet er. Because of the p resen ce of the t wisted band, t wo edd ies are fo rmed on both sid es of th e t wisted band to enhance t he max imum heat t ransf er t emp eratu re of t he f lu id , wh ich gradually atten uates to wa rd s the tu be wa ll and the twisted band. With the reduction of the twist rate, the Nussel number becomes larger and larger.  Fig. 16 sho ws th e con cent rat ion d ist ribut ion of hyd rate part icles at d ifferent po sit ion s. It can be seen that th e concent ration d ist ribut io n of h yd rate pa rt icles in the in it ia l sect ion is relativ ely un ifo rm when th e lon g t wisted band is used to sp in. With t he in crease of d istance, t he concent ration of hyd rate part icles p resent s an obv ious sy mmet rica l center d ist ribut ion , and t he hyd rate part icles a re f lun g to th e near p ressu re su rface of th e t wisted band du e t o cent rifu gal fo rce. At the same t ime, because it is located in th e center of the sp iral vo rtex, th e p ressu re is lo w, fo rcin g the su rround in g pa rt icles to concent rate to the lo w p ressu re area. By comparin g d ifferent t wist rates, th e smaller th e twisted rates wa s the mo re o bv iou s in the concent ration area. In th e absen ce of t wisted band s, pa rt icles begin t o depo sit sign if icantly at the po sit ion of 0 .7m and reach th e maxim um part icle co ncentrat ion at th e po sit ion of 1 .5m , ind icatin g t hat th is po int is a possib le location for b locka ge. Wh en the sp iral f lo w is not co mp let ely attenuated, th e concent ration of part icles in each sect io n is a lmo st the same, and t he concent ration of part icles in t he p ip e wa ll reach es t he max imu m and is ev en ly d ist ribut ed. Ho wev er, th ere are some obv io us depo sit s at the 1 .6m po sit ion after the sp iral f lo w attenuat ion . The t ranspo rt d istance has been in creased by mo re than 2 t imes compared wit h th e cond it ion without cy clon e. H o wever, th e con cent ration d ist rib ut ion in all sect io ns rema ined a lmo st t he same du rin g the whole spinning process, indicating that no obvious deposition of particles occurred.  Fig. 17 sho ws th e d ist ribut io n cu rve of the vo lu me fract ion of part icles alon g the p ip e when Y=6.2 and 0=1 %.Th e figu re sho ws the v o lume fract ion of part icle deposit ion in th e lon g to rsio nal b elt und er th ree d ifferent Rey no ld s Numbers of R e=300 0, 5 000 and 100 00. When R e=300 0, th e cu rv e has a p eak valu e at Z=56 D app ro x imately. Th e peak va lue rep resents th e gradual accumu lat ion of part icles here and the p o int is considered as th e depo sit ion p o int of particles. With the in crease of Rey no ld s numb er, wh en the cu rve t end s t o t he ho rizontal lin e with no p eak va lue at Re=5 000 and 1000 0, it can be con sidered that th e part icles a re not d epo sited in t he p ip e. Th e cu rve of Re=5000 is slight ly h igher t han that of Re=1 0000 , wh ich ind icates that the larger th e R eyno lds n umber is, the mo re d ifficu lt it is to dep osit . Th e cu rve of Re=10000 rises slight ly becau se of th e cent rifu ga l mot ion of the part icles in th e lon g torsional band, some of t he part icles will st ick to t he wa ll of the t ube and the tan gent ial fo rce of the sp ir al f lo w is n ot enou gh to make it fly a way. When Y=6.2 and in it ial concentrat ion 0 =1 %, t he crit ica l d epo sit ion Reyn o lds nu mber of particles is with in the ran ge of 3000 -5 000 . Fig. 18 sho ws th e vo lume f ract ion d ist ribut io n cu rv e of part icles alon g th e pip eline wh en Y=6 .2 and 0=8 %.Compared with t he f igure abov e, the part icles were d epo sited wh en Re=4 000 , ind icatin g that the crit ica l depo sit ion Rey no ld s n umber of the part icles wa s 4000 -50 00 when Y=6 .2 and in it ia l concent ration 0=8 %.Becau se th e h igh er the pa rt icle con cent ration is, th e easier it is to depo sit , and the h igher th e crit ical R eyno lds num ber can be deposit ed . By co mparin g th e t wo p ict ures, it can be con clud ed that th e greater th e particle concentration is, the closer the particle deposition is to the pipe inlet, and the more particles are deposited. sho ws t he d ist ribut ion cu rve of vo lume f ract ion of d ifferent t wisted band part icles alon g the p ip e when Re=4 000 and 0 =8 %. Th e t wist ed band wit h a t wist rate of 6.2 sho rt t wisted band and lon g t wisted band as well as flat light tu be with out t wisted band were compa red respect ively , the cu rve in th e f igure sh o ws an increasin g trend . In the st raight light tube f lo w without to rsion band , the part icles were depo sited at Z=12 D, wh ere the vo lume f raction of the part icles is t he largest. In the sho rt t wist ed band with Y=6.2, pa rt icles were depo sited at Z=2 8 D, and the peak value of the cu rve was smaller t han that without t wist ed band. In the lo n g t wisted band wit h Y=6 .2, th e dep osit io n lo cation of part icles is appro x imately at Z=42 D, and th e part icles d epo sited in the p ipeline are the least . It can be seen that the lo n g t wisted band has t he best ca rry in g effect, fo llo wed by the sho rt t wist ed band, who se ca rry in g d istance is about 3 -4 t imes that of th e n on -t wisted band. Th is resu lt p rov id es theoret ica l gu idance fo r t h e safe t ranspo rtat ion of hydrate. In Fig. 19, YL rep resent s the t wist rate of the lo n g t wisted band, and YS rep resents t he t wist rate of th e sho rt twisted band. Figure 19. Volume fraction distribution curve of different twisted band particles along pipeline at Re=4000, 0=8%

Conclusions
(1) In p lain d irect cu rrent of light p ipe without to rsional band , the velocity is maximum in the central area of the pipe and then decreases un iform ly to wards the p ipe wall, and the velocity chan ge at each sect ion is not obv iou s. Ho wev er, in the pip e into the t wisted band, t wo d ist inct edd ies are fo rmed on both sid es o f the t wisted band, with the maximum velocity at the center of the vo rtex. Alon g the d irect ion of the p ip e, the t wo vo rtices move from th e near to rsional band toward the wall, it can effectively carry the hydrate particles deposited on the pipe wall.
(2) At the same section of the p ipe, th e p ressu re d rop of the p ipe increases with the increase of Reyno lds number, and the h igher the Reyno ld s numb er is, the mo re th e p ressu re d rop increases. Alon g the direction of the p ipeline, the p ressure drop becomes more obv ious with the increase of particle t ransport d istance, and the pressu re d rop cu rve is sim ilar to a parabola. In the case of constant part icle Reyno lds number, the greater the torsion ratio of the t wisted band p laced in the pipe, the weaker th e sp iral flo w st ren gth, the smaller the tangent ial velocity of the sp iral flo w and the smaller the ax ial velocity loss, and the smaller the p ressu re d rop of the p ipe. Therefore, the p ressu re lo ss can be reduced as much as possible while the effect of spiral flow can be guaranteed.
(3) In a straight light p ip e flo w without to rsion band, the Nusser number is in a parabolic shape with the open in g down ward s. At the center of the p ipe, the Nusser number gradually decreases to wards the p ipe wa ll at the maximum, and at the near wall, the attenuation gradient of Nu is large. In th e p ipe with t wist ed tape, th e cu rve of Nusserr number appeared a trough in th e center of th e p ipe and a peak at half of the pipe d iameter. With the reduct ion of the t wist rate, the Nu ssel number become s larger and larger. Sp iral flo w can make the temperature d ist ribut ion of the flo w field in the pipeline more even and prevent the large number of formation of hyd rate particles in th e p ipeline wall due to the large temperature difference.
(4) The larger th e Reyno lds number is, the less lik ely th e part icles are to deposit . The larger the particle concent ration is, the clo ser the part icle depo sit ion is to the pip e in let, mo re part icle d eposit ion. When the to rsional rate of the lon g torsional band is 6.2 and the in itia l concent ration of the part icles is bet ween 1% -8 %, the crit ical d eposit ion Reyno ld s number of the part icles is bet ween 3000 -5000. Sp iral flo w has a good carry in g effect. Under the same wo rk in g cond it ion , the spiral flow carries hydrate particles at a distance about 3-4 times that of the flat and straight flow.