Still wat St water dead zone & collimat dead zone & col - PowerPoint PPT Presentation

Still wat St water dead zone & collimat dead zone & col mated ej ed eject ecta in g in granula lar jet im jet impact ct Wendy W. We W. Zh Zhang Ni Nicholas G Guttenberg, He Herve T Turlier, Jake E Jake Ellowitz, Si Sidney R R. Nagel Physics De Ph Department & James Fr Franck Institute Un University of Chi Chicago cago No Nonequilibrium Dy Dynamics in A in Astrophysics and M strophysics and Material Science aterial Science Kyoto, Japan 2011 Ky

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Preview Preview Im Impact pact of of dense dense granul granular ar je jet • C Collim llimated ted (liq (liquid id-lik -like) e) ej ejecta & interior dead zone • D Differ ifferen ent in t inter terio ior s str tructu cture e  sa same ejecta e  pe • L Liq iquid id-lik -like r e res esponse perfect fluid flow dissipationless flow di dissipation = fr frictional fl fluid jet continuum flow remains no co non-Newtonian in in limit to lim it towards d dis issip ipatio tionle less p perfe fect flu t fluid id flo flow jet

Outline Outline 1. 1. Introduction Introduction 2. 2. Ba Background 3. 3. Ex Experiments & simulation 4. 4. Mo Model 5. 5. Discussion iscussion & Conclusion onclusion jet jet

Bac Backgr kgrou ound: gr d: gran anular ar j jet i impac pact  col ollimat ated (l d (liqu quid-l d-like ke) e ) ejecta non-cohesive particles non-cohesive glass beads Cheng et al. PRL 07 target jet jet target holder loosely packed jet dense jet dense jet  ej ejecta co collimated  shower of recoils hollow conical hollow conical sheet sheet

Ej Ejecta s a sheet an angl gle c chan ange ges wi with D Tar ar /D /D Je Jet redu ducing g D Ta Tar /D /D Je Jet  w wate ter Gran anular ar e ejecta an a angl gle ψ 0  g gla lass beads b agr agree n numerical ally wi with val alues for or wat water j jet  liqu quid-l d-like ke e ejecta

Did i d impac pact c creat ate a l a liqu quid ph d phas ase? dimensionless reaction force Mome Mo mentum m balance " 0 = 1 # A ( D Tar / D Jet ) 2 1 # B ( D Tar / D Jet ) 2  w wate ter  g gla lass dimensionless drag force beads b When D Ta Wh Tar < << D Je Jet jet ) ( D Tar / D Jet ) 2 ( " 0 # 1 $ A $ B jet Sam ame ψ 0  sam ame A-B -B Bu But i indi dividu dual al v val alues of A an of A and B m d B may ay di diffe ffer

Con Context xt • E Ellip lliptic flo tic flow: co : collim llimated ted ejecta ejecta fr from co collis llisio ion o of gol gold d io ions at relativistic speeds  Liq iquid quark- gl gluon uon phase phase with h New ewtoni onian an vi viscosi scosity? y? • F Formatio tion o of p f pla lanetis etismals ls fr from d dust a t aggreg egates tes via col vi a collisi sion ons Pozkanser, Voloshin, Ritter... 2008 APS Bonner prize talk Romatschke & Romatschke PRL 2007 Teiser & Wurm, Mon. Not. R. Astron. Soc. 2009

Outline Outline 1. 1. Introduction Introduction 2. 2. Ba Background 3. 3. Ex Experiments & simulation jet jet

Experiment  jet i Expe interior or i is n not ot l liqu quid-l d-like ke Look at ook at i impac pact of h of hal alf a j f a jet | u |/U 0 pressed agai pr d against gl glas ass 1 0.5 d e a 0 target side de-v -view of j w of jet i interior or d z o n e

Experiment  dead z Expe ad zon one i is c col old tran anspar parent t tar arge get (b) 1 θ eff = T eff / max(T eff ) 0.4 0.5 <u r (z=0)> m/s 0 0.2 0.25 0 0.25 r /D Jet 0 0.25 0.25 0 r /D Jet

liqu quid-l d-like ke ejecta ejecta ? jet interior or structure structure target jet ) ( D Tar / D Jet ) 2 ( " 0 # 1 $ A $ B reac action on drag dr ag force for for force

Simulat ation on jet rigid grains rigid grains inelastic collisions inelastic collisions fric frictio tion b betw tween g gra rain ins sticky target sticky target grains immobile after gr co colliding with target red = d = h high gh s spe peed d blue = bl = z zero s o spe peed

Simulat ation on r repr produ oduces e expe xperiment collimated ejecta jet dead zone norm normalized alized velocity velocity red = d = h high gh s spe peed d contours contours bl blue = = z zero s o spe peed agree agree quantitatively quantitatively

No de o dead z ad zon one at at fr friction onless t tar arge get jet coeff. of restitution and/or friction between grains  weak variation Guttenberg (2011)

or  Sam Diffe fferent i interior ame e ejecta 0.01  no 0.008 dead P( ψ−ψ 0 ) zone  dead 0.004 zone 0 ψ−ψ 0 -10 -5 5 10 0 ejecta angle ejecta angle changes changes from rom ejecta ejecta r remains collimated 45 45 ° (w (with dead zone)  40 40 ° (w (without deadzone)

Outline Outline 1. 1. Introduction Introduction 2. 2. Ba Background ) ( D Tar / D Jet ) 2 ( " 0 # 1 $ A $ B 3. Ex 3. Experiments & simulation reac action on drag dr ag force for for force Same ψ 0 Sa 0 i in granular & water jet impact  li liquid phase in granular jet? No No Ejecta ≠ sc Ej scattering pattern (dilute regime) jet De Dense jet impact is different  T To see relevant limit, model as continuum insted of simulating as hard spheres jet

Fr Friction onless t tar arge get s simulat ation on r results  con ontinuum m mode odel of gr of gran anular ar j jet i impac pact 1. 1. Ma Mass conservation 2. 2. En Energy conservation 3. 3. Mo Mome mentum m conservation No Not assuming hydrodynamic limit obtains Ph Phenomenological

Fr Friction onless t tar arge get s simulat ation on r results  con ontinuum m mode odel of gr of gran anular ar j jet i impac pact 1. 1. Ma Mass conservation velocity field  density incom ompr pressibl ble fl flow ow

Fr Friction onless t tar arge get s simulat ation on r results  con ontinuum m mode odel of gr of gran anular ar j jet i impac pact 2. 2. Energy nergy conservation conservation granular granular tem temperature perature T G = = 0 flow

Fr Friction onless t tar arge get s simulat ation on r results  con ontinuum m mode odel of gr of gran anular ar j jet i impac pact 3. 3. Mo Mome mentum m conservation density × acceleration = - pressure gradient + dissipation (shear stress tensor) shear stress = µ pressure e local shear direction phenomenological friction coefficient µ

Fr Friction onless t tar arge get s simulat ation on r results  con ontinuum m mode odel of gr of gran anular ar j jet i impac pact 1. 1. Ma Mass conservation 2. 2. En Energy conservation T G = 0 3. Mo 3. Mome mentum m conservation µ Incom ompr pressibl ble fr friction onal al fl fluid Bo Boundary conditions: At At un unknown j jet surface, normal stress and tangential stress both 0 stress both 0 At At target, tangential and normal velocity both 0

Fr Friction onless t tar arge get s simulat ation on r results  con ontinuum m mode odel of gr of gran anular ar j jet i impac pact 1. 1. Ma Mass conservation 2. En 2. Energy conservation T G = 0 3. 3. Mo Mome mentum m conservation µ Incom ompr pressibl ble fr friction onal al fl fluid hard sphere Choose µ to fit simulation simulated ψ 0 quantitatively reproduces u(x) & p(x) in hard sphere simulation

Fr Friction onless t tar arge get s simulat ation on r results  con ontinuum m mode odel of gr of gran anular ar j jet i impac pact 1. 1. Ma Mass conservation 2. 2. En Energy conservation T G = 0 3. 3. Mo Mome mentum m conservation µ Dissipat pation onless pe perfe fect fl fluid fl d flow e ow emerge ges wh when we we t take ake t the l limit µ  0 Con Continuou ous appr approac oach i instead of abr ad of abrupt pt c chan ange ge

o 0 as µ  0 Deadz adzon one s shrinks ks c con ontinuou ously t to 0 as H DZ H DZ D Tar ✖ µ

Ejecta an Ej a angl gle dom dominat ated by d by con ontribu bution on fr from om reac action on for force A as as µ  0 ) ( D Tar / D Jet ) 2 ( " 0 # 1 $ A $ B reac action on drag dr ag force for force for µ