and Carl H. Gibson. 3 ... Gibson, Chen and Li:') (1968) have u~ e d this method to cortelate {( ) for a sphere ..... ake flow. For the jet, on ..... Flo, 13, 2193. Stewart.
18 - 1
JET TURBULENCE;
DISSIPATION RATE MEASUREMENTS AND CORREl..ATIONS by
3 Z Carl A. Fri e h e , I C. W. Van A tta and Car l H. G ibson Department of Ae r ospace and MechAnica l Engineering Sci ences U niversity o f Ca l ifo r nia, San Die go La Jolla. Ca li fo r nia 92037
SUMMARY
The rate of viscous dissipation in a turbulent jet is exami:led in some detail. A corre lation o f the mean rate of dissipatio n on the c e nter-line in term s of the orific e Reynolds numb er an d axial position is e stablished. Measureme nts o f the velocity and v e locity d er ivative are describ ed ( or a jet o f orifiee 5 Reynolds nu mbe r of 1.2')( 10 • The spectrum of the squa r e of the v e locity derivative was found to b e similar to tho se obta ined for a tmosphe ric boundar y laye r flows at very large Reynolds num ber s when normalized with Kolmogoro!£ leng th and tim e scales. S p ec t ra o f high er order m ome nts of the velocity de:rivative are also present ed and compare d to Novikov's predictions 01 th e pow er law subr anges. 1.
INTROD UC TION
T he mean ra te 01 viscous dissipati o n of turbulent k.ineti c energy per unit ma55 of f luid, , is .... n important quantity in the energy b uclget lor t he tur bulent jet. Jt is also of importance i n determining t h e line sca l e struc tu re o{ the turbulence . In this pape r Ille d5ssipation rate i n a turbulent jet is eX2. mi ned i n some d etail. Fir s t, a. correlation of ( d in te r ms o f the indepe ndent variables of the; flow is established. From t his and othe r w e ll-known result5 lor the self -preserving jet, r ela ti ons fo r the variations of t he Taylor mieroscale and the Kolmo gorofI l e n g th with Reyn olds number and axia l di s tance Gte derived . Sec ondly , e:x:perimenlal results of th e iluctl.:atio:u of the dissi pation rate in t'. tl,lrbu l e nt jet are presented and compa r e d to s iYnilar measuremen ~s in atYnospherie boundary la yers. Z,
CORRELATIONS
Landau and L\.hhitz ( 1( - k - I -~ , where Il = a conS t ant to be determine d. Th e a t m o spheric measur ements show Il '" 0.3 3 to 0 . 6 4 for th e atmo sph e r iC boundar y l aye r , and).! = 0.85 fo : a l ow Reynold s numb er m i:dr. g laye r (W yngaa rd ana T e m'-e ke s (197 0). It is desirable tha t similar measurements be ma c.e in l a.rge R ey nolds nu:mber non -atmo sphe ric flows, su ch as a je t , to d etermine the un iversa l b ehavior, if any , of KoIrr: og oroff's modifie d t heo:y {StEWart , Wilso n and Bur l ing (l9 70 ) l . I n additi on to a determ i na.ti on of t he con stant J1 ;it;,.n " inte rmediate" Reyno lds number , it is o f interes t to fi nd ou t if the powel' spe ctra o f ¢l normaliz ed w ith K.olm020roff l ength and time sca.le s , coll a ps e o nto a \m i.-ers ... l curve. N oti n g that 1OO ~:< (k ) dk. = «(x -
