PARAMETRIC STUDY ON AIR CORE PHENOMENA AT LIQUID DRAINING FROM CYLINDRICAL TANK

Transcription

1 Blucher Mechancal Engneerng Proceedngs May 2014, vol. 1, num. 1 PARAMETRIC STUDY ON AIR CORE PHENOMENA AT LIQUID DRAINING FROM CYLINDRICAL TANK I. S. Park 1, C. H. Sohn 1 1 School of Mechancal Engneerng, Kyungpook Natonal Unversty (correspondngensten@knu.ac.kr) Abstract. An ar core phenomenon observed from lavatory bowl dranng n our daly lves has a very mportant scentfc meanng because t s also observed from many ndustral applcatons and related wth a natural phenomenon such as tornado. Moreover snce the ar core affects the dran speed, t s deeply connected wth a dsaster such as flood from local heavy ran. Thus many studes preventng the ar core from formng have been conducted and varous types of vortex suppressor have been suggested. In ths paper, the numercal smulaton on ar core phenomenon s ntroduced and a lot of smulatng results such as cross-sectonal flow feld, ar-core-formaton tme and so on are dscussed n vew of the reason of formng the ar core. Smulatons on varous szed tanks and dran ports, and the ntal rotatng speed of cylnder wall have been conducted (total 56 cases). The contaner level heghts frstly formng the ar core were compared from each other case. From dmensonal analyses, four non-dmensonal parameters and the relatng equaton among them were determned. Keywords: Ar core, Swrl velocty, Dranng. 1. INTRODUCTION The ar core can be observed n the varous ndustral felds such as the molten steel tundsh n a contnuous-casng process and the sump pump staton. The phenomenon s also connected wth the sewerage desgn because the ar core could severely decrease the dranng flow rate. Despte consderable research efforts [1-8] n the hydraulc engneerng feld to elucdate the ar core vortexng phenomenon, t stll requres the more enhanced theores and expermental bases. In ths study, the phenomenon s fully numercally nvestgated. We test the free dranng from the cylndrcal tank. The progresson of the free surface and the flud flow nsde the tank are numercally vsualzed at varous tmes. For preventng or suppressng the generaton of the ar core, the varous attempts have been appled by the prevous researchers [9-12]. However, we focused on the observng the physcs nsde the phenomenon rather than suggestng the new-type vortex suppressors be-

2 cause the detaled understand for the phenomenon s more helpful to devse the hgh performance suppressor. We vared the tank and dran port dameters as well as the swrl veloctes so as to establsh the crteron for the ar core generaton. Through a parametrc study for those factors, the nfluence of each factor was apprased. For these, the tme that the dp fully penetrates the lqud nsde (the crtcal tme) and the level dfference between the ntal state and the crtcal tme (the ar core generaton dstance or crtcal dstance) are measured numercally for varous cases. Moreover by dvdng the crtcal dstance by the crtcal tme, the new concept of the crtcal speed for ar core genernaton was develped. Several non-dmensonal parameters such as the dameter rato for the tank and the dran port, the Reynolds number, the Froude number, the Weber number, and the nondmensonal ar core generaton speed are suggested from the dmensonal analyss. A correlaton for the dmensonless parameters was completed to determne the vortex core generaton for dfferent cases. 2. NUMERICAL ANALYSIS For the transent, ncompressble, lamnar, and free-surface flows n an axsymmetrc assumpton, the followng conservaton equatons for mass and momentum were selected as the set of governng equatons. ( u ) 0 x (1) ( u) p u u j ( uu ) g t xj xj x j xj x j Here, x s the poston vector of the coordnate system, u the velocty vector, t the tme, p the pressure, the densty, and the dynamc vscosty. The cylndrcal tank frstly was rotated for 10 seconds. We replaced the event as rotatng the tank sde wall wth a constant angular velocty. Next the rotatng wall was stoped. The free rotatng and vscous dsspatng process was retaned for 3 seconds. Fnally the dran port was opened and the dranng was started. The present flow pattern can be assumed to have no crcumferental gradent of the flow varables. However the flow obvously has the crcumferental component of velocty, whch has a spatal dstrbuton n the tank and slowly decays as tme goes on. To fnd the swrl velocty component n a two-dmensonal grd system, the followng conservaton equaton for the tangental momentum was appled n addton to the basc axsymmetrc governng equaton set, Eq. (1) and (2). u 1 u ( r uzu ) ( r uru ) r r 3 uru (3) z r z z r r r r Here, z s the axal component of the coordnate system, r the radal coordnate component, u r the radal velocty component, and u the tangental velocty component. Eq. (2)

3 Fgure 1. Intal level and crtcal heght. (3) s the conservaton equaton of the crcumferental momentum n a cylndrcal coordnate system by elmnatng all crcumferental gradent terms. Ths s very useful and practcal n terms of the computatonal cost because the hgh level flow nformaton, ncludng all three velocty components can be obtaned on a two-dmensonal mesh system. To capture the shape of ar core, the VOF (Volume Of Flud) scheme [13] was adopted, To update the free surface shape progresson, whle the basc flow felds are beng calculated mplctly, the mplctly free surface updatng and HRIC convectve scheme for the volume fracton equaton are appled for mnmum computatonal costs. The FVM (Fnte Volume Method) based commercal CFD code, Fluent 6.3, was used. For the boundary condton at the opened top of the tank and the dran port ext, the constant pressure condton of 1 atm. was appled. The no-slp condton was appled for all walls. The surface tenson coeffcent between water and ar was kept constant at N/m and the gravtatonal acceleraton was constant a 9.81 m/s 2. The tme step sze was set as ~ 1 10 seconds. A schematc of the system s shown n Fgure 1. The reference cylnder tank had a 90 mm dameter, and a 450 mm heght. The reference dameter of the dran port was 6 mm and ts heght was 15 mm. The tank was ntally flled up wth water to a level ( H ) of 350 mm from the bottom of the tank. And ts top was opened so that the lqud water nterfaces wth ambent ar of 1 atm. For the numercal smulatons, 390 nodes were allocated n the axal drecton and a total of 45 nodes were used n the radal drecton. Of course the number of nodes used n smulatons vared case-by-case accordng to the dmensons of the correspondng cases. However, the ntervals between the neghborng nodes were usually kept wthn 1-2 mm n all cases.

4 3. RESULTS AND DISCUSSIONS Frstly we checked the dran tme for the full dranng. The cases that the sde wall ntally rotates or not, were compared wth each other. The total dran tme had a bg dfference, more than 20 seconds between the cases. The declnng pattern of the water level was dsplayed n Fgure 2. A pecular thng s that the ntally rotatng case shows a deflecton of the water level near at 20 second. On the other hand, the non-rotatng case shows a monotonc decrease of the water level. In the rotatng case, the ar core s generated at around 20 second. The ar core generaton s closely connected wth the dranng flow rate because the effectve dschargng area severly decrease f the vortex core generates. However, the decreasng slops of the water level after 35 second are almost same for both the rotatng or non-rotatng cases. Once the ar core s generated, the core s usually mantaned tll the drangng s fnshed. That means although the vortex core exsts, the dranng flow rate s gettng recovered as the dranng contnues. Fgure 2 also presents the check of grd dependency. A total 25 and 45 grds for radal drecton and 200 and 390 grds for axal drecton are tested for the grd dependency check. All grd systems well smulate the deflecton at around 20 second. Moreover the descendng slops of the water level after the vortex core generaton are predcted smlarly for all cases. However the tmes for the recovery of the dran flow rate are slghtly dfferent. The coarser grd system shows the longer recovery tme. Anyway we used the 45 grds for radal drecton and 390 grds for axal drecton n ths study. Fgure 2. Water level declnng hstory.

5 Fgure 3. Velocty vectors and stream lnes for varous tank roaton speeds.

6 In Fgure 3 the tme progresson of the nternal flow structures for three dfferent ntal swrl speeds are presented. To exclude the nfluences of other parameters, the tank dameter s kept at 90 mm and the dran-port dameter at 18 mm. The results for the ntal swrl speeds of 40, 100, and 180 rpm are compared together. As the swrl speed ncreases, the Taylor vortex on the sde wall s generated earler. On the other hand, the case wth lower swrl speed shows the Taylor vortex generaton at a later tme. The flow pattern before the Taylor vortex are structured nsde the tank looks lke the well stratfed free dran and the streamlnes parallel to the axs. The ar core generaton strongly relates to not only the Taylor vortex formaton but also the ts growth. The torus-shape vortex confnes the large parts of the lqud nsde the tank and concentrates the lqud dran nto the centered regon. We smulated a total 56 cases of D = 90 and 120 mm, d = 6, 12, 18, and 24 mm, and the tank rotaton speed = 40, 60, 80, 100, 120, 150, and 180 rpm. We ve check the tme and the water level when the ar core s generated for the frst tme. Next for the generalzaton, we made some non-dmensonal varables,.e., the dameter rato of tank to dran port D*=D/d, the rotatonal Reynolds number Re= D 2, the rotatonal Froude number Fr= D 2 g, 3 2 the rotatonal Weber number We= D, and the non-dmensonal crtcal speed * V Vc D. Here, D s the tank dameter, d the dran port dameter, the densty, the tank roaton speed n rad/sec., the dynamc vscosty, g the gravtatonal acceleraton, the surface tenson coeffcent, and Vc the crtcal velocty. The crtcal velocty s defned by the followng; H H c Vc (4) t here, H s the ntal water level, H c the crtcal heght (.e., the water level when the ar core s generated), t c the crtcal tme (.e., the tme when the ar core s generated). c Fgure 4. Correlaton among non-dmensonal parameters.

7 From the numercal results, we made the followng correlaton among the nondmensonal parameters * * V D Re Fr We (5) 4. CONCLUSIONS The vortexng core phenomenon s fully numercally smulated. The FVM based CFD sklls and the VOF free surface trackng method are appled. The dran tme or the water level descendng speed are checked to prove the consstency of the numercal results. Some characterstc features are well reproduced by the present CFD study. Expandng the calculatng range for the geometrcal dmenson and the tank rotaton speed, we made the correlaton equaton to explan or determne the ar core generaton. Acknowledgements Ths research was supported by Basc Scence Research Program through the Natonal Research Foundaton of Korea (NRF) funded by the Mnstry of Educaton, Scence and Technology (the Grant ). 3. REFERENCES [1] H. O. Anwar, Formaton of a weak vortex. Journal of Hydraulc Research. 4, 1-16, 1966 [2] H. O. Anwar, J. A. Weller, and M. B. Amphlett, Smlarty of free-vortex at horzontal ntake. Journal of Hydraulc Research. 16, , [3] L. L. Daggett, and G. H. Keulegan, Smltude n free-surface vortex formatons. Journal of Hydraulc Dvson-ASCE. 100, , [4] R. Granger, Steady three-dmensonal vortex flow. Journal of Flud Mechancs. 25, , [5] G. E. Hecker, Model-prototype comparson of free surface vortces. Journal of Hydraulc Dvson-ASCE. 7, , [6] A. K. Jan, K. G. R. Raju, and R. J. Garde, Vortex formaton at vertcal ppe ntakes. Journal of Hydraulc Dvson-ASCE. 104, , [7] A. W. Marrs, Theory of the bathtub vortex. Journal of Appled Mechancs, Transactons of the ASME. 34, 11-15, [8] M. Padmanabhan, and G. E. Hecker, Scale effects n pump sump models. Journal of Hydraulc Engneerng-ASCE. 110, , [9] B. H. L. Gowda, P. J. Joshy, and S. Swarnaman, Devce to suppress vortexng durng dranng from cylndrcal tanks. Journal of Spacecraft and Rockets (AIAA). 33, , [10] B. H. L. Gowda, and H. Udhayakumar, Vane-type suppressor to prevent vortexng durng dranng from cylndrcal tanks. Journal of Spacecraft and Rockets (AIAA). 43,

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