Dosen: Ir. Suroso Dipl.HE, M.Eng. Dr. Eng. Alwafi Pujiraharjo

Transkripsi

1 KINEMTIK ZT CIR Dosen: Ir. Suroso Dipl.HE, M.Eng. Dr. Eng. lwfi Pujirhrjo Kinemik z cir mempeljri gerk prikel z cir np meninju g ng menebbkn gerk ersebu. Seelh kecepn didp sebgi fungsi wku v f(, mk dp dikehui disribusi eknn dn g ng bekerj. 1

2 Deskripsi dri: gerkn fluid lirn fluid klsifiksi emporl dn spil Pendekn nlisis Lgrnge vs. Euler Du cr unuk menjelskn gerk fluid Lgrngin Descripion (meod Lgrnge Mengikui prikel bergerk Eulrin Descripion (meod Euler Melih fluid melewi iik u seluruh medn erenu Pol lirn Gris rus (sremlines kecepn meninggung gris lirn dx d dz i j k d d d u i vj wk

3 Meod Lgrnge Ssem mehod Meod Euler Conrol volume mehod Mengikui pergerkn individul prikel fluid. Prikel fluid diidenifiksi. Menenukn bgimn sif fluid berkin dengn perubhn prikel sebgi fungs gsi wku. Conoh: T T (

4 Gerkn fluid dienukn dengn penjelsn sif ng lengkp sebgi fungs gsi emp dn wku. Menggunkn konsep medn (field concep. Unuk mendpkn informsi i enng lirndlm erm p ng erjdi pd iik erenu dlm suu emp sebgi lirn fluid melewi iik-iik iu. Conoh: T T ( x,, z, lirn dp diklsifiksikn: lirn invisid dn viskos lirn kompresibel dn k kompresibel lirn lminer dn urbulen lirn mnp (sed flowdn k mnp (unsed flow lirn sergm dn k sergm lirn su, du dn ig dimensi lirn rosionl dn k rosionl. 4

5 lirn sergm 0 s lirn k sergm 0 s lirn mnp 0 lirn k mnp 0 Lminr Turbulen 5

6 isulissilirn dlh pengujin visul medn lirn (flow-field. Pening bik unuk eksperimenfisik mupun penelesin numerik. Beberp meod Sremlines nd sremubes Phlines Sreklines Timelines Refrcive echniques Surfce flow echniques Gris rus(sremlinedlh kurvng dimn sj meninggunginsnneous locl veloci vecor. Diinju pnjng busur dr dxi dj dzk dr hrus sejjrlocl veloci vecor ui vj wk Secr geomeris menghsilkn persmn gris rus dr dx d dz u v w 6

7 Tom Hsu s numericl simulion Idel flow mchine, b 1, b 1 Tbung rus (sremube erdiri dri seberks gris rus. Fluiddlm sremube hrus ep disn dn idk dp melewi bs dri sremube. Dlm lirn idk mnp (unsedflow, pol gris rus dp berubh erhdp wku. debi mellui suu penmpng pd sremube hrus ep sm. 7

8 Phlinedlhlinsn ng dillui oleh individul prikel fluiddlm suu periode wku. Sm dengn vekor posisi meril prikel fluid Lek prikelpd wku : ( xpricle(, pricle(, zpricle( sr x x sr d Eksperimen: pricle imge velocimer (PI melck pricle phlines unuk mengukur veloci field pd seluruh bidng dlm lirn (drin,

9 Flow over clinder Top iew Side iew Sreklinedlh gris ng menghubungkn prikel fluid ng elh melewi iik ep dlm rung. Mudh unuk melkukn eksperimen: z wrn dlm ir u sp dlm lirn udr. 9

10 Timeline dlh seperngk prikel fluid g berdekn g diberi nd pd wku insn ng sm. Timelines dp diunjukkn menggunkn hdrogen bubble wire. 10

11 Timelines produced b hdrogen bubble wire re used o visulize he boundr ler veloci profile shpe. Profile plos of he horizonl componen of veloci s funcion of vericl disnce; flow in he boundr ler growing long horizonl fl ple. 11

12 Conour plos of he pressure field due o flow impinging on block. 1

13 Koordin Gris rus Koordin gris rus dlh sisim koordinng dienukn dlm erm gris rus dri lirn. Uni vecors : s nd n Menenukn vribel medn (field vriblessebgi fungsi emp dn wku. Pressure field, p p(x,,z, eloci field, ( xz,,, u x,, z, i v x,, z, j w x,, z, k ( ( ( ccelerion field, ( xz,,, x,, z, i x,, z, j x,, z, k ( ( ( x z 1

14 eloci Field(Medn kecepn Kecepn pd sembrng prike keldlm medn lirn (he veloci field dinkn (x,,z, u(x,,z, i v(x,,z, j w(x,,z, k Kecepn prikel dlh lju perubhn vekor posisi dri prikel iu. dr d Diinju prikel fluid dn hukumnewon kedu, F m pricle pricle pricle Percepn prikel dlh urunn kecepn erhdp wku. dpricle pricle d Nmun, kecepn prikel pd suu iik pd sembrng wku dlh sm dengn kecepn fluid, x,, z ( ( ( ( pricle pricle pricle pricle Unuk menurunkn erhdp wku, hrus digunkn chin rule. d dxpricle dpricle dzpricle pricle d x d d z d 14

15 dimn dlh pril derivive operor dn d dlh ol derivive operor. dxpricle dpricle dzpricle bil u, v, w d d d pricle u v w x z Dlm benuk vecor, percepn dp diulis: d ( x,, z, ( i d Term perm disebu locl ccelerion dn idk nol (nonzero hn unuk lirn idk mnp(unsed flows. Term kedu disebu dvecive ccelerion dn memperhiungkn pengruh prikel fluid bergerk ke loksi bru dlm lirn, dimn kecepn berbed. Percepn : lju perubhn kecepn Komponen: Norml perubhn rh Tngenil perubhn kecepn ( s, e d d e d d de d d d s de en d r ( e e s r n 15

16 Koordin Cresin x i j du udx ud udz u u u u u. u v w d x d d z d x z x z k dv vdx vd vdz v v v v v. u v w d xd d z d x z dw wdx wd wdz w w w w w z. u v w d x d d z d x z Convecive Locl Q Qo Q o m / s s Qo Q1 Q o ( m / s π π d ( ( Q / Q m / s 1 L π π d o (0.5 (1 4 4 C.74* 7.49 m / s s 16

17 17 Dikehui: Hiung: Percepn, xz i j k k j i k j i ( ( xz x z z x 0( ( 0( 0 ( 0( ( 0( 0( 0( xz xz w w z w v w u x w x z x xz z v w z v v v u x v xz u w z u v u u x u z x ; ; w xz v u olume re of flow (debi Kecepn konsn pd penmpng Kecepn vrible Mss flow re Q d Q Q d d m ρ ρ ρ ɺ

18 Debi : jumlh z cir ng menglir mellui mpng linng ip sun wku (m /de., lier/de. Q.v (m x m/de m /de Unuk z cir riil v f(r,sehingg dq d.v πr.dr.v Q πv.r.dr Pd prkekn vrisi penmpng dibikn, sehingg v dinggp sergm mk: Q.v Debi: Q Q π rdr 18

19 19 Hn komponen kecepn rh-x (u ng mempuni konribusi pd lirn mellui penmpng Q or d Q or d ud d Q cosθ Hiung: (1 ( R r r v o o ( ( / (1 0 0 o o o o o o R o R o R R Q R R R R r r rdr R r d Q π π π π π π

20 Hiung: Q,, mɺ / Q d d m s Q 5 5 m / s 1 mɺ ρq 1.*5 6 kg / s Z cir k kompresibel menglir secr koninu mk volume z cir ng lew ip sun wku dlh sm di seip penmpng. 0

21 Mss ng msuk mss ng kelur ρ 1.v 1. 1 ρ.v. Z cir k kompresibel ρ 1 ρ, mk v 1. 1 v. pers koninuis Q 1 Q Q 1 Q Q 1.v 1.v 1.v 1.v.v 1