francis h. harlow- turbulence

8/3/2019 Francis H. Harlow- Turbulence

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lwA-lJR -87-1235 Po d LA-UR--87-1235 . IDE87 008993

LOS Ahmos N~llonal Laboratory IS oPormwd by Iha Unrvwty 01 Cali fornia !W NM Uni lOd Slsros DOBaflmWN 0! Enorw under Conlracl W.740$EN13.36

TITLE: TURBULENCE

AUTHOR(S): Francis H. Harlow

WBMITTED TO: DNA Numericnl Methcd~ Sympo~ium, SRI International,Menlo Park, California, April 28-29, 1987

INSCLAIMERThh report wm pmpma! Mnm mxount of work -pmorod by sn asoncy or Ihc Unltod SIWW(Jwornnmrt. FJellhor the Unkd SIaIeB Uovornrnant nor qy sgtncy Ihoroof, nor mry or tholr


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TURBULENCE

Franc is H. HarlowGroup T-3, Theoretic al DivisionThe University of CaliforniaLos Alamos National LaboratoryLos Alamos, New Mexico 87545

1. BRIEF DESCRIPTION OFTHE WORKCurrent t heories fo r ma te ria l m ixing inc lude mult iphase interpene tra tion and

single -fie ld turbulence t ranspo rt w it h la rge density va ria tions. Ne it he r app roach byitse lf is adequa te fo r current p roblem-so lving needs, but in comb ina tion they o ffe rtremendous oppo rtunitie s fo r the ana lysis o f comp lex mate ria l d ynamics. Multi-p ha se theory c ontrib utes the o rd ere d jets o r p artic ula te tra je cto rie s tha t p ene -tra te in wave -like fa shion; turbulence transport superimposes the impo rtant non-linear d iffusive component to the m ixing . Shear impedance and ene rgy transpotiarise naturally in this combined analysis.

Two app ro ache s fo r c ombining the se theorie s a re being investig ate d. o nebeg ins w ith multiphase flow and adds turbulence e~]hancement , the o the r is basedon sing le -fie ld turbulence transpo rt w ith c lo sure guidance from multiphase flow


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formid ab le, b ut the emp loyment o f this p owe rful c omb ira tio ~ in o ur numeric alinvest igat ions holds high promise of paying handsome div idends.2. EXAMPLES

Numerous c ircumstances occur in nature for which instab ilit y, turbu lence, andinte rp enetra tion a re sig nific ant p arts o f the d ynamic s. Some examp les a re thefollowing.

No rmal a c ce le ra tio n o f a d isc ontinuity in d ensity c a n re sult in the unsta b leg rowth o f p erturb a tio ns, fo llowed b y m ixing o f the tw o mate ria ls. One o f themost exc iting and significant recent d iscove ries in the fie ld o f fluid dynam ics istha t t he we ll-deve loped nonlinea r phase o f this p rocess p roceeds in a mannerindependent o f the initia l pe rturba tions. Constant acce le ra tion, fo r examp le ,results in self-simila r growth of the mix layer; sing le or multip le shoc lca cc elera tion is followed b y wa ve-like multip ha se interp enetra tion p lusd iffusion-like turbu lence t ransport o f mass, momentum, and energy.Ob lique intersec tion o f a shock w ith a mate ria l interface results in ma te ria l slipacross t l-.e contact d iscont inuity and acrossthe slip surface behind trip le-shockinte rse ctio n if Mach re fle ctio n o cc urs. Insta b ility c a n le ad to both mate ria lm ixing and sign ificant turbu lent shear impedance.


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These a re just a samp ling o f the numerous examp les tha t can be c ited in whichthe se the ore tic a l te chniq ue s a re c entra l to the a c complishment o f meaning fulanalysis.3. ADVANTAGES AND LIMITATIONS TO THE THEORY

The p rinc ipa l advantage is the ultima te confidence in p red ic tab ility a ffo rdedby this type o f fundamenta l irlve stig a tio n o f c omp lic a ted fluid flows. O the r advan-tagesa re the w ide scopeo f app licab ility o f the theories, and the insight they furnishinto the processes that are taking place. Possib le d isadvantages are the necessity forpowe rful compute rs to ob ta in so lutions, and some residua l unce rta inties tha t maya lways be p resent in t he moment closures fo r the d iso rde red pa rt o f the turbulence .A t p re sent, howeve r, the re is little a lte rna tive to the use o f theore tic a l te chniqueslike tho se d esc rib ed in this p re se nta tio n, in the a tta inment o f useful re sults fo rcha llenging problems.4, FUTURE DEVELOPMENTS

Streng thening the theoretic s! found ations is a high p riority goa l for theinvestigations. Even a t this p resent sta ge the va rious forms of the theory needextensive exe rc ising . The scope o f app lica tions w ill like ly be eno rmous; many w illp roduce use ful re sults in the near future while o the rs w ill re quire added insig ht o r


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present ta lk. Computers will need c onsid era ble memory a nd sp eed for mostapp lica tions. So ftwa re requirement s inc lude the most advanced codes for numer-ica l flu id dynamics invo lv ing la rge d istort ions, in te rface slippage , mesh adap t iv it y,mult i phase in te rpene tra t ion, and a ll the necessary capab ilit y fo r comp lica ted inputand display of results.ACKNOWLEDGMENT

This worb was sup po rte d b y the Unite d Sta te s Dep a rtment o f Ene rg y und erco ntrac t W-7504 -ENG-36.REFERENCET, L. Cook, R. B. Demuth, and F. H. Ha rlow , Mult iphase Inte r ene tra tion o f Shockedrateria ls, Los Alamos Scient if ic Laboratory report LA-7578 1979).T. L. Cook, R. B. Demuth, a nd F, H. Ha rlow, PIC Calc ula tio ns o f Multip ha se Flow, J. Com/)ut. ~@ 41,51 (1981).B. J. Da ly and F. H. Harlow, A Mode l o f Countercu rrent Steam-V4a te r Flow in La rgeHorizontal Pipes, Nu c le a r Sc ie nc e a nd En gin ee rin g 77,273 (1981).T. L. Cook and F. H. Ha rlow, Virtua l Mass in fdultiphase Flow, Intern. J ofMuhiphase Flow 10,691 (1984).T. 1. Coo k a nd F, H. Ha rlow , Vortic es in Bub bly Tw o-Pha se Flow, Intern. J. ofMultip ha se Flo w, 12,35 (1986).T. L. Cook and F, H. Ha rlow , VORT: A Computer Code fo r Bubb ly Two -Phase Flow ,


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D. C . Besna rdand F. H. Ha rlow, Source sofTurbulence inFluid Flow, Lo zNat iona l Labora tory. Inst it ut iona l Support i,lg Research and Deve lopment,Rep ort LA-106OO (1985).D. C. Besnard , F. H. Harlow, N. L. Johnson, R. M. Rauenzahn, and J.Turbulence Transport , Los Alamos Science, Ulam Memorial Issue, 1987.

AlamosAnnual

Wolfe,

D. C . Besna rd , F. H. Ha rlow, and R. M. Rauenzahn, Turbulence and Multip haseInterpenet rat ion, report in preparat ion.D. C . Besnard , J. F. Haas, M. Bonnet , A . Froger, S. Gauthie r, B. St t, and F. H. Harlow,Comparison o f Two Mode ls o f Rayle igh-Taylo r Induced Turbu lent M ixing, Proc . o fthe Los Alamo s/ Limeil Co nfe re nc e o n Ma them atic s and Num eric al Methods,February 2-6, 1987.D. C .Besna rd , R. M. Rauenzahn, and F. H. Ha rlow, Turbulence Theory fo r Ma te ria lMixtures, Proc . of the Los Alamos/ Limeil Conferenc e on Ma thematic s andNumerical Methods, February 2-6, 1987.B.A. Kashiwa, Statist ica l Theory of Turbulent, Incompressib le Mult imateria l Flow, Un iversit y o f Wash ington Docto ra l Disserta t ion, in p repara t ion; degree expec ted inJune, 1987.D. Besna rd and F. H. Ha rlow , Un Mode le de Turbulence c lans Ies Melanges, Pt. 2: Transport d e la Turbulence e t Estab lissement des Me langes, Commissa ria ts ~lEnergie Atomique, France, Special Repot i, 1987,

The fo llowing viewg raphs were used during the ta lk.


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TURBULENCE

F r a n cis H . H ar lowTh eore t ic al Divis ion , Grou p T-3Los Alam os Na t ion a l La bor at ory


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TECHNICAL FOCUSInstability

q Mater ial interfaceq Con ve rgin g s hoc kq Bu rn fron tq Abla t ion fr on tq Pe rt u rba t io n in d ep en d en c e!

Tu rbu l enceq Mixq Sh ea r im p ed an ceq He at d is pe rs al

Mu lt ip h a se In t e r pe n e t ra t io n


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PERTURBATION INDEPENDENCE

Or der jet splus

t u r bu le n t d iffu s io n

w


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INTENSE EXPERIMENTAL ACTIVITYSh ock T u be s

q Sov ie t (And r onov )s F r e n c h (L im e il)q Ca l T ec hq LANL (Ben j am in )

Lase r -Dr ivenq AWRE (fo il s)q F r e n ch (fo ils a n d sp h e r es )q Live rmor eq X-1 (lo ca l a n d Ro ch e s t er )

Low-speedq AWRE (r o ck e t s le d )


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THREE THEORETICAL APPROACHESlMu l t i fi e ld In t e rp en e t r a t i on

q Cook-Demuth -Har lowq Youngsq 13 i n s t o c kq Scannap ieco -Cran f iU

S in g le -F ie ld Tu rb u le n c eq An dron ov e t a l.q Lumleyq 13e sn a rd -Ha r low-Rauenzah n - J a n s senq Lei th

Br u t e -F or ce Nume r ic sq Youngs-Wareingq Sharp-Gl imm


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Mu l t ip h a s e I n t e r p e n e t r a t i on

Tu r b u l e n c e


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Mixin g of

q Massq Momen t umq En e r g y

EFFECTSF or E xa m ple

Ma t e r ia l S p ecie sS h ea r Im p e d an c eH ea t Disp er sa l


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PHYSICAL PROCESSES

C r ea t ion of T u r b u le n ceq F rom Mea n -F low Kin et ic En er gy

She a r I n s t a b ili ty (v or t i ci t y)I n t e r p e n e t r a t i o n I n s t a b ili t y

c ROm I)iffiirentid AcceteratkmP r e s su r e G r a d ie n t s

shocksRarefactionsMult ip l e Acou s t ic Wave sCen t r i f ug i ng

Buoyancy. F r om Chem ic a l o r ~b la t iv e

; =%:*

Su r f a ce I n s t a b ili t y


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PHYSICAL PROCESSESTransport. Mean -F l ow Advec t io n

d i sp l acemen td i l a t ionr o ta t io n (o f t e n so r s)

. DiffisiOnv i scoust u r b u l e n t

..qTu r b u le n t s elf d iffu s io n is n o n -lin e a r !


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PHYSICAL PROCESSES

q

q

q

q

Cas ca d e (la r g e t o sm a ll)o- 0 -OVis cou s d is sip a t ion (sm a ll t o h e a t )

-0: :?:;$: , . . 8.:,?::,b:. 0


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PHYSICAL PROCESSESSummary


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MATHEMATICAL DESCRIPTIONS (CURRENT)Mu l tip h a s e F low. Va r ia b le s for e a ch fie ld. E xch a n ge F u n ct ion sq En t i t y De sc r i p t io n s

Tu r bu l e n c e. Con s t a n t Den s it y. Va r ia b le Den sit y (Low Mach #

T emp e r a t u r e va r ia t io n sD iffe r e n t s p e ci es

q Two -fi eld t u r b u l e n c eR ] ij a n d R2 ij


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q

q

q

9

q

LEVELS OF APPROXIMATION FORTURBULENCE

Gene r a l Non -I s ot r op i cI so t r op i c As sum p t i on

{e~c c Uat ic h +9VMSimplified Closures (&~) ~w. ~uatk

+?WQPo in t F u n c t io n a l (m i xin g le n gt h )E d d y Viscosit y (va r ia b le or con s ta n t )

A m a jor ch a llen ge a t a ll le ve ls :Wh at is S ?

,


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CLOSURESfor exampie:T_A44 f=i w it h Tr a n s p or t E q u a tion


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ORDERED-LIMIT GUIDANCEMu lt iP h a se flow h a s u n iqu e cor r ela t ion b et ween a n d ~ ?.t c

c a n b e %m~qu e ly c a lc u la t e d .

Un ce r t a in t ie s lie in t h e p h ysics ofq e n t i t yc~~ var~ations q!+.:,q entity con~rtions ~w>dlls. e xch an ge fu nct ion s


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THUSC lo su r e t e rm

= (or d er e d fr a ct ion ) (or d er e d closu r e )+

(d i so r d e r e d fr a c t i on ) (t u r b u l en c e c lo su r e )

Wh e r e t u r b u le n ce closu r e is@ Der ived

q Po in t fu n c t io n a lq T r a n s p o r t e d

e P o st u la te d w it h u n ive r sa l con st a n ts d e t er m in ed em pir ica lly

francis h. harlow- turbulence

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