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LA4JR -73 7/3 -..~1-..-.

TITLE: EFFECTSOF TURBULENCEON LOWALTITUDEFIREBALLSAT LATE TIMES,“

AUTHOR(S): H. M. Ruppel and R, A. Gentry

SUBMITTED TO: PROCEEDINGS EFFECTSSYMPOSIUMOF DNAATMOSPHERIC

OV .Omptan- of thle artlok for pub!katlon, tho pubiidwrrwognkas W Qowrnnmt’B [Ilosnao)rlghtt In my mpyrightand tho OotmrnrmntS@ Its sahorlwd roprwantathm hmmunrwtdatd debt to roproduaoIn who10or In psrt said@rtlalaundsrsw COp@@t wwod w IIW publMor,

Tho Los AJsmosM.ntlflu Lobormow rsqu..t. that tkpubhtw Idantlfy thl. srllaio m work p.rforrwd under thomnpiomof W U. 8, Atomlo Snwgv CommMon,

1)alcimos

LOS .41 AM()$, NCW MEXICO 07S44

hrm NoiKU!St, No, m91/73

I

EFFECTSOF TURBULENCEON

LOWALTITUDEFIREBALLSAT LATE TIMES* (U)

H. M. Ruppal and R. A. GentryLos Alamoe Scientific Laboratory

University of CaliforniaLos Alamoa, New Mexico 87544

Let us procada a d~ecusaion of the effects of turbulence on th~ dynamicsof fireballs with a review of the turbul.ancg modol currently in USQat LosAlamoa.l The equations ws SOIVS ●re$

tho maas equation

tha momantumaquation

and the turbulence mergy equation

In the abovo

D

and

-- p(lij 1A%j + ~ %k %j + ‘%j ‘

A dmtailcd liot of tho symbols u~od is includ~d ●s Appmdix A,

Tha .ali@nt fgat,ura of this an~l .woral othgr ●lmilar modols now in usa

is t~, transport aquation for tha ~;urbulanca ●wgy. This ●quation containsartation duo to buoyancy ●nd #h*art ●nd dissipation ●nd diffusion. Considorin particular tho buoyancy tmm, sincm this has ●gandorgd aoma coaunant intht r~uant pact. In thim aonnoction nota that orm modalo corrdationg b+twm components ~f vtlocity and othor sualar functions ●s

JJ J

-3-

-gaf-pac

J

Hence a nicetribution to

a#- -gp.‘j

physical interpretation of this term is to view It as the con-the change in turbulence enercy from changes in the potential

energy due to the correlation of fluctuations of density and velocity In agravitational field. Note that in order to have creation rather than de-struction of turbulence energy, the density and preasura gradiants must bsof opposite sign.

An assumption which is made in the derivation of this modal 10 that thareexists Immedistgly a atata of equilibrium betwaan ●ddtae of all sizaso Waaa-Sumst in othar words, that tha timo takan to cquilibrata the caacado procassby which ●nargy As transferred from tha largest eddies wher~ it io craatad totha smallest cddlw whers it is dissipated is ●all compar~d to the times that

msttar in the problem~ Currant eatimatm for this equilibration tim~ in fir@-balls vary from parhaps on. tanth to ona torus formation time, but thaaa num-bara aro uncertain.

Anotlm ●osumption which mutit ba mada in calculation. with this model isth~ s180 of th, integral .calo - that is thm ●lzo of tha largmt or snargycarrying QddioaO What wc uoa for tha .caio ie ● phcnowmolo~ical form fittedby Bart Daly ●t Los Alamoa to tho ●xparimonta of Wy$nandci ●nd Ficdlar.aThey m~amrad thg scalo ●nd tho mamn vertical valocity profil~a of fraa jots.

It was po.nibh to fit thair data rather wall with tho form

●(r,z) n 0.14 d(g) (2 -~) ,

-4-

UA D UBq/S2 D

where A and B are combinations of constants and mean flow quantities. Ifthen the mean flow is roughly independent of the scale, this resulte in

Thie argument is uo be taken only as an indication of ths order of the effectr,fthe scale on the turbulence energy. In the mample of the large scalecaaa ths total turbulence anergy romaina at about 1% of tha total kineticcnargy in tha mesh.

Ror tha valu~ of u that we usa it Sa intar~oting to not- that tha rim●ltitud-, ●s defined by tho position of tha CS1l with the maximum Intarnal●orgy, is littla affact~d by changes in the scales Figura 3 diuplaya the●ltitudo ● ● function of tinm for two scala~~ The u?ti ware obtainad with ascalo lar~ar than th solid curva, tha incraaao baing 50%; howovar, ●t 210soco thm Is otd.y ● 1/2 km dlffmmco in height. Ther~ appaara to b. nodiffmamca in tha two calculation for timas 1*OO than 75 sacs. Thio las:point hao bean ● conaietant finding in our calculations - that tho turbulmc,ham virtually no offoct on dimensional data ●t lass than 7S S*CS and only ●

sll~~ht●ffact tharoaftaz. Thit conclusion may depend on tha rathar smallvalw for U that we ●ra uain~.

Although tharo is ●naral aeraomant of modda of this typa that u mayb. ●xprasatd ●. u = 13ak q, thg valuao of B diff,r ●mong tho various lnvaa-ti$ator8. Wa currantly uao ● valua of $ = 0.02 which valua ia bao~d on thawotk of Lmundm, Moraa, Rodiz ●nd Spaldinu, ‘ They comparad six turbulancgmodtl~ h the prediction of frao shsar flow-. In thomodol which they calltho Ptandtl ●ergy modol thay dofina ● turbulonco viocosity which is ●nal-o$oue to tho above u ●nd in comparison with ●xpmimmt they ●rriw ●t tho valuafor B which W, ●ra currently usins. Daly than porformad ●n indapa~dont chockby tmttns this rauult ●catnot tha chann~l flow etud~os of Laufar, who moas-urad both tho Raynolds #trorno and tho gradimt of tha mtan velocity. U8ingt}m flux approxima&ien ono can rolat~ kha twa to obtain G. Thio wa. done forRoynelcis numbcm in &ha rango 10” to 10’.

Anothr point whiah muet ba addr,aaad ia tha oaeding of tho initial tur-buionao. From tho ●quation for th, tu~bulcnao ●nar~y it ia Qhar that tnordar to ~an~rato turbulanco it io nocacsary that oomo turbulonaa bo ●lraadyprwont. In tha rgal fir~ball, inatabilitien aarva to initiatg th~ turbu-loncm. In our numariaul simulation wo must saad th turbulonca in oorno way.

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methods of seeding yield marked differences in level and configuration ini-tially, but by 30 sees they have coaleacsd into a single dietribution~ Whathas happened is that the turbulanca hao decayed away in regions which cannotsupport it and has grown in thoee placea where shear and buoyancy can supportit.

Figure 5 indicates how rathsr local the ohear creation, in fact, is;tha oame IS true of the buoyancy creation~ Moreover, the region of largestshear creation is ●t the upper ●dge of tha fireball, and hence turbulence ismest pronounced in the ragion of ●teapemt temperature gradiente. CM might●xpcct that the turbulence will reducs tha maximum grsclionts ●nd that io in-deed what WQ find. In Fig. 6 thara im ● comparison of tho maximum gradientof interual ●nergy calculated with ●nd without turbulmce. Both of the-owart ~arri~d out with w fino grid ●nd Iudicata what is pvobably the majoreffact ws will find that turbulmco hamtha degrading of tempmatura ●nd don-slty gradients.

Of courso tho turbulmaca itmlf dapondo crucially on tha gradienta ofthe mean flow~ both tho #hoar ●nd tha buoyancy craation ●a pr~ducta of maanflow gradiants. It it this which causaa ua to dwote such ●ffort to improvaour non-turbul~nt calculationc~ particularly ● rh~y ●ffect temperature anddansity gradionto. If thma ●ra ovmly diffusad by numerical ,ffccta, littlala gained by simply ●dding turbulanca to tho hydrodynamic. TO ●chiw@ thiswc uaa ●n AI&liko codos which allow tha CO1lS to follow tho fluid motion ●smuch ●s io poaoiblao This minimism tho ●ount of fluxing in tha rozon,procma and raducoa th~ diffusion of all tha physical quantitioo snd thgirgradiontn.

Chm can aoo the ●ffoat of resolution on turbulanca ●narty by compatifigconto:m plets from ● high raoolution calculation with a low rooolution ra-ault at 20 *SC. ●o in Fis 7-

4Tha fins $rid ualculaticn haa ● maximum turbu-

lonca 9n9x~y of 1.2 x 10- whila the eoarsc grid on ~ha risht hag a uaximumof 8.5 % 10-% Tho total turbulanca ●norgy differs by about tha sanm ratio.6inco tha minlmm otll sim in tha two calculations diff~rs by ● fsctor of2-1/2 ●nd th turbulanc~ anorcy by only 50%, it 10 roaaonabla to ●cmmo thatFurthtr r,fininc of th, sono aisa will not gr,atly ●ff~ct tha amount of tl~rbu-lanaa ●uarty. Not. ●lso that tha configuration of tho tw aalmilacion. inFig. 7 ●. timilar in ●ppaaranao.

A. a rcfarcmao, not~ that the maximumwrtiaal valoaity is ●bout 0.14ka/oao. Th maximum turbulmca ●ar-y aorrosponds to ● Fluatuatins v,loaityof 0.01 lun/caa or rou&hly 10X of KIM maximum man flow wloaity. Finallylat us return to th~ ●ffmt of tuxbulmoo on dimensional data.

-6-

conceivable that as better calculations with sharper gradients are performed,higher levele of turbulence may be supported which increase the net effect.In addition a larger value of ~ would likely lead to more pronounced differ-●ces due to turbulence.

-7-

1. B. J. Daly and F. H. Harlow, Phye. Fluids~ 2634 (1970).

2. 1. Wygnanski and H. Fiedler, J. Fluid Mech. 38, 577 (1969).

3. B. 1!. Launder et al., Imperial College Report lT1/TN/B/19.

4. J. Laufer, NACAReport No. 1053 (19S1).

5, A. A. Anmden●nd C. W, H.irt, “YAQUI$ An Arbitrary Lagrangian-EulerianComputer Program for Fluid Flows at All Speeds, ” Los Alamos ScientificLaboratory report LA-51OO.

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APPENDIXA

Notation

,P=

t-

‘~ “‘J -u“

8-

q“

% -

P“

A-

Pm

%j mI-

deneity

time

jth coordinate

jth component of velocity

turbulence viscosity

integral scale

specific turbulence energy

gravitational acceleration in jth direction

pressure

dilational viscosity

shear viscoeity

Kroneckar delta function

a~acific internal energy

,..,

c●-

1’

s

———— s

[

v(o)= 0.3 2.0-—v(r)

=01*

,01? ~_L_L–l_J_._LLo

Fig. 1. Maximum turbulenceintegral acalos.

50 100

Tim (see)

ener~,y in any computational

.

.

m

●

●

●

●

●

●

m

m

●

.

■

●

●

●

■

●

●

●

m

[

v(o)0.3 2.0- —v(r)

01●

10~4 ~L..L. I L-L_l-A_L_L_L..J-0 50 100

33

30

N25

x

Tim (see)

Fig. 3. Altitude as a function of t- for two scale8, one 502 largerthan the other.

q-tu

q-KE

0.769 X 10-7

t 87.35

b0.25x

c\ iiA

Twbu ence Energy

0.724x o0 7

t88

%)0.824X 10”8

0

0.655 xIO”7

talo

0,272 X 10”7

7

t 83Q

0.272x 10-7

‘Ea

N

I I I I24.6

24.0

23.0

2s.0

22.6

mo

2M

21.0

L~o 088 I ,0 1,6 Ao M

R (km)I

r.

o

o

zoo

150

100

80

00

●

●

●

✚✏

●

●

●

●

I ‘\/\\I \

\

\

\

Alb

9

,

-~ Fine grid

\

\

\

\

\

\

\

\\

Fine grid with turbulence

\●

✼

D

\

\

B

\

\

B \

10 20 30 40 50 60

Time (sac)

I

1-----

24X

24mc

238C

22*C

2Lt

21,0

ID

1

R (km)

I

o

—

210

-1

No turbulence

Whfa turbulence

0-

-i

50 100 I50 200 250