Effect of expansion angle on turbulent swirling flow

Indian Journal or Engineering & M:lleriab Scicnu:, Vol. 6. Dcn:mhcr 1999. pp, 32.,-329

Effect of expansion angle on turbulent swi rlin g flow

Sh()",kal J,lhan Chowdhury & Md, Sajjad MayccLi

Dcp:1rt1l1enl or i\ Icch:lJlic:1I r:ngi nccri IIg. 13:lJlgl:ldc,h lIni I er,il y or Engi neeri ng 8:. TLTI1I111I11g), i)I1,lk:l- I ()( Hl. I',III~ LI,k,11 Hen'il'"" 17 /J('('{'lIlhl'J' 1\1\18; 1/('('(,/>11'<15 NOI"'llIh/'/' 1\1\1\1

This p:lpcr presents tllc IIUlllCriGII ,tudl' 01' swirlillg turhulellt ^!lClII through dificrellt e,\p:III'HIIl ,11I~k', 1IIIIl'II h,II,' Illany prallic:1I applic<llio!l', ill ga, turhlllc<" conlhu<,IOIS, Clc, The .l'ol'erning ditfercntial eqll:llion', II 11IL'I1 111,'011">1.11,: ',-l' llIrhulcncc 1l1odelcl()<,ure, :II'C ,oiled h~ a ulI1trol-\,()lu1l1c ha<,cd itclatiI'C rinilc dil'fcrclIl'L' tcchnlquL', "redll'lnl dlSlnhullllil

1'01' Ihe mcan lelucille<,. Iurhulencc klnellc cnerg) and slrca1l1lin,' plo\<, arc prc,cnlcd, C01l1[lUI,llllllh :11,' dl>Il,' 1<'1 dlliL'I\'1I1 slI'lIl lIumhers lip 10 I .. ~ and luI' dilferl'llI cXl'amlOn ~In.l'les helll'ecn 30" :lIlti ')(), \\,ilit lite IIICIC,IS,' .. I '"111 '1Il'II~lh,

,ccolldar) 11Il-:1\1<, rCl'lrL'ul,lllOl1 is uh<,ellcd in addilionlotilc plim:lry corncr rcclrcul:IIHllI, SWlrll'rodu,"', I.II~"I 1IIII>ul'II,'"

kinclic energ) and CnlI.IIICC' 111I\ill'-' 1:lll', lilli' 1\:LJuirill,l' slHlIler c01l1huslor Icnglh, FOI :111) P:llliclIi,1I 'IIII'I '1Il'II~111 1,,'ldlld Ihc Iranslll()11 I :>ille. :11 slll:Ii In L \1'dll<,lon :111!,'Ic, illgiln lUI hllkllL'e kinclil' energy gL'lIl'ldl ion :lIld l (1I1','qlll'lll i~ I >,'lll'l 1111 \ Ill"

is lou lid, The l'llinputcd rc<,ulh hdl'c hL'L'll l(lulld 10 he cOI1lI'dr~lhiL' 10 Ihc :\1':lilahk C\\,l'lllIll'III:1I d,lLI

Turbulent swirling f'lll\"S through ,In ,1>,iSYlllllll'tric expansion ha ve wide appl icat iuns in the ric Id or engineering, particularl)- to indu\trial furnaces, gas turbines and jet-engine cOlllbustorsl

-', The expansion geometry pr(JduC's mixing rates dOwllstrealll or the expansion that arc substantially. higher than those that would be obtained at the same Reynolds numher at the entrance region or a pipe, The elevated Illixing rates (Ire due to very high ic"els or turbuicnce kinetic energy generated by sheari ng as the core flow issues into the larger pipe, car the tube wall, where the length scales are small, dissipation dominates because it is inversely proportional to the length scale, But in the high-shear regions away from the wall, length scales are large and dissipation rates consequently arc low, Hence, turbulence kinetic energy generated in such shear layer dissipates relatively slowly, and its levels are much higher than would be found in the ordinary pipe flow where no such internal shear layer exists,

Swirl is further added to enhance name stability and mixing, Sufficiently strong swirl produces secondary recirculation which is driven by an adverse pressure gradient that results from the VISCOUS

dissipation of the tangential velocity component as the flow proceeds downstream, Although, this recirculation contributes to mixing indirectly through convective processes, the primary enhancement of mixing is assumed to result from the rotational shear strain generating higher levels of turbulence, Any increase in shear strain tends to raise the level of

transfer 01 Illean kinetic enl'rg: to IlII'hlliL'lll'l' l'nl'I:':

Also, in these h igh-she;II' '-l'l'ollllar\ rl'C i rLlI LII 11)11 rcgions a\\'a) rlllllllhe \\,111, di ... ip;llioll r;I!L's ,Irl' 1,)\\

1'01' reasons as explained ahm l', 1-:\p,ln"llll1 ;111:,k .tI"'ll arrccts the growth pI' lhi\ "CC()nddr: rl'l'irclILIII\)1l dlll' to swirl. The ability to prl'dll't till' liL'tdik'd 1l,Illlrl' (1/

such flows \\ould icad to Ihc illlp\'()\'cd dL'''I:'11 III engineering equipmcnt. TlI:-illlicnt I'Ill\\ dll\\ n .. lredlll or an abrupt pipe expansion has hL'l'll "llIdll'd 11:

Amano', but the errcct of s\\'irl i" nllt cllnsidL'rL'd,

The objecti ve or the present In \'est igal inn i" to study the effect of expansion angle al dillerent S\I il'l intensities for the turbuicnt swirling /'Im\, ,\Ithollgil.

sophisticated turbuicnce m(ldd, h;I\'e Ill'l'n dl'\ L'loped.

yet the k-£ model is still widely uSl'd in I ill' industr:

due to its simplicity ami as il ha" ;tlread: heen accommodated into many cLllllIllercially ;I\'ai lahle computer codes, Hence. the /..:-r Illude I pI' LllInder ;Ind Spalding~ has been used in the present illl'L'slig;ltipns,

Basic Equations and NUlllc.-ical Details

All the equations governing Ihe ;Ixisynlilletric.

swirling turbulent flow in cylimlric;tI cO(lrdinalCS using the k-£ model closure of Laundcr ;Ind Spaldillg-I can be written as relation ( I):

I [ () ()

- - (pllrep)+- (p I' rep)

r ()x ()r

-~( I-r !!.fl-~( r ^r

^o¢

)Il= , ..,' . ..

^(I)

0).- ⁰

o x

^{Or °} 0^{1' ~ (;i}

324 ^{INDIAN J. ENG. &} MATER. SCI., DECEMBER ISlSlSl

Here, the flow is assumed to be steady and incompressible. In Eq.( I), the first two terms are the convection terms, third and fourth terms are the diffusion terms and 5¢ is the source term which contains terms describing the generation and consumption of variable ¢. The forms for the source term 59 are given in Table I,

where

5¹¹

=~[p~)+~~ _{ax ax rar} [ IP ~l _ax

5 v = -

a [ au)

p - +- -^I

a [

I J / -

av) ax ar ra,. a,.

... (2)

... (3)

c= ^{P[ 2} {[~)2 _ax +[~)2 _ar +[~ _,. l' } + [ ~+~)' _{a ,. a.x}

+:(~r +(~:r

^{... (4)}

p=C _/1 pk' /E+P _/ and

r

_¢

= p

^/(5 _" ^{... (5)}

The turbulence model constants are assigned the following values⁴ (for continuity equation,

r ¢ =o;

for the momentum equations, ^O'Q= I):

Cp

=

^{0.09, CI}

=

^{1.44, C2}

=

^{1.92, O'k}

=

^{1.0, 0'[}

=

^{1.3 ... (6)}

Table I- Sourcc tcrllls for the ~encral Eq.( I) Value of <i> Namc of Equalion Sourcc Tcrlll, SI'

II

I'

IV

k E

Continuity II-momcnlulll (axial)

v-momelllum (radial)

IF-momcntulll (tangcnlial)

k-equ3lion E-equalion

o

d"

s . . "

-- +

d,

_ d/I + PII" _ 2~IV +S ,.

(),.

,. ,

P"II' II' () - - - ; - -(,.p)

,. ,.' d"

G-CIlP£

( CI£G-C2P£')lk

-- ,

I I I I I

Pri mary corner \

recirculation I

I

~ ^:~

^I

^{J~ P.'}

^I

U· I Secondary on-axis 1

';;'~_jJ _j' _ _ c si:~W':O ~' __ __ _ J "

Swirl Generalor

1 - '

^L ~

Fig. I-Geometry of con lined swirling jct expansion sct-up

The computational domain for confined swirling turbulent flow through different expansiun angles is shown in Fig.l. The flow comes thruugh a smaller pipe of diameter 5.08 cm and then expands into a larger pipe of diameter 9.85 cm. Different expansion angles of 30°,45",60" and 90" are considered. Swirl is also generated in the upstream tuhe just hefore expansion, using a constant vane an~1e swirl generator. Here, the tangential velocity ~It inlet IV"I is calculated as V illtan8 where ^ViII is the axial velucity ,It inlet and 8 is the swirl vane angle. The Reynolds number Rc and swirl number S are defined as:

2V R

R = ^III I

V

f

^{II Ir1 -V W dr}

s=

^{II III III}

f

^{I< '}

R I,.V-d,.

I () LII

.. (7)

... ( -+)

where ^ViII and ^Will are the velocities at i11k t. The swirl number may be physically interpreted as the ratiu (11' the axial fluxes of swirl and linear mOlllentum divided by a characteristic radius.

A staggered mesh finite volume method is used to discretise the differential equations \Vritten in general form as Eq.( I). The computational domain is divided by a 46x34 nonuniform grid "vith finer ~pacing in the regions of large spatial gradients. An example of a nonuniform grid system being employt~d to fit the flow domain is shown in Fig.2. The sloping expansion wall is simulated by a stairstep approximation. The above differential equations are illlegr~lted over their appropriate staggered control volumes ,llld discrctised using a hybrid difference schemeS '0 "lip houndary conditions along with wall functions are dpplied at the solid walls. At inlet, V- and W-velocities ~\1'(':

~Ind the specified. The turbulence kinetic enngy "

dissipation rate £ at inlet are calculated as I-:q. (I):

k _III =A V'

J 111' ^{£, "I --}

""

¹¹¹

A '

^{A,I< .. ( I) )}

where AI and A2 arc two constants haVing values uf

,...Wall Boundary

NJ _ _

1·- , --- - - -

d

1- - ' '--1-

-1- -- ::i=

:t=- -. -_. --I Outlot

Inlol -1lt++tH-l-t-l-l-t-1-+-+-+·-t-f--r--+---

- H

2~H+~~~~-+-+~~-4---1-±j

J= 1 . --=-

=;:;

^'t

1,12 \ Symmotry A'ls

Fig. 2- A Iypical grid ~yslcm heill~ employed III I'il Ihe Illl\\' domain

CHOWDHURY & MAYEED: EFFECT OF EXPANSION ANGLE ON TURBULENT SWIRLING FLOW :\25

0.03 and 0.02, respectively. At the outlet boundary and symmetry axis, zero gradient conditions are applied. The discretised equations with boundary condition modifications are solved using the SIMPLE⁶ and TDMA algorithm. Here, semi-implicit line-by-line relaxation method is employed to obtain converged solutions iteratively. The relaxation factors are also used to promote computational stability.

Results and Discussion

Confined swirling turbulent flow through an axisymmetric expansion as shown in Fig.1 is analyzed numerically using the above computational code.

The flow was also studied experimentally by Dellenback et al.⁷ in a water flow loop for the same test configuration as shown in Fig.l, except that the swirl was generated by a swirl generator at a substantial distance upstream of the expansion section, and had an expansion angle

a.

⁼ 90°

Consequently, the swirling flow in the smaller tube was almost fully developed by the time it reached the expansion section. The flow had a Reynolds number of 30000 and swirl number of S=0.98. Experimental measurements were performed using a Laser Doppler Anemometer. The computational code is first used to simulate the turbulent swirling flow for the experimental conditions of Dellenback el af.7 Values for U and W-velocity at the inlet boundary of the computational domain are taken from available experimental data at X/I? = -0.5. The numerical

1.0

~O.6 cr .,; ,

:.g 0.4 cr

0.2

0.5

D D:J CI D Experimentul Dote of Dellenbock ct ol.

- Prc::;cnt Numerical rrf~dictillll.

r "X/"~ 1.0

I

⁰

[ I _ ^{• I}

o i

" I I

X/H-0.2 X/H:=Q.7

1.5 -O.!) 0.5 1.5 -0.5 O.~ 15

Axial Velocily, u/Uu

I i

fo ^!

X/R .. O.2 X/R.O.7l

} _J ^I _{f _}

,

..

1.5 -0.5 o.~ 1.5 ·0.5 0.5 15

Tangential Velocity. W/UD

Fig. 3--Comparison or computcd dimcnsionlcss mcan axial and tangential yelocity prolilcs with experimental data (j'=O.YX)

predictions are compared to the experilllental results in Fig. 3. Here, the solid lines correspond to thc computational results and the boxcs correspond to the experimental data of Dellenback e/ u/⁷ Thc distribution of the dimensionless Ille:tn axial and tangential velocity across the flow. as prcdictcd by thc present computational model and that 01' the reportcd results⁷ at different sections. are shown in this figme.

Here, X is the axial distance frolll the sudden expansion and I? is the radius of thc largcr pipc. Thc velocities are nondimensionalizcd with thc aiel of thc reference velocity U", which is the avcragc axial velocity at inlet. The predictions of the present modcl are in good agreement with thc experimental data. Hence, it may be concluded that the present numcrical model has the capability of prcdicting swirling turbulent flows with reasonablc accuracy.

The computational model is lIsed to analyzc thc flow of Fig. I having constant angle swirl vanes for swirl generation at inlet just beforc cxpansion (unlikc to the experimental condition of Dcllcnhack ('/ iII'.).

and uniform inlet axial velocity of 0.56 m/s :It a Reynolds number of JOOOO. Thc Icngth of the calculation domain, L is taken as 0.5 Ill. Computations are done for different vane angles. 8 = 0".24". -"1,1".56"

and 66" corresponding to swirl nUlllbcrs or

s =

O. O.J. 0.5, 1.0 and 1.5 respectively. at expansion angles

a.

= 30", 60" and 90". The results are prescntcd in Figs 4-12.

To study the effect or grid-sizc variati()n.

computations are done for swirl vane anglc 8 = 56"

(S

=

1.0) anel expansion angle ^('f.

=

90" ror hoth grid sizes 46 x 34 and 62 x 46. and the results arc presentcd in Fig. 4. The dimensionless proriles 1'01' Illcan axial velocity, tangential velocity and turbulencc kinctic energy at X//? = 0.6 have been shown 1'01' both grid sizes. It is observed that the computational rcsults for both the cases almost overlap. Hcncc. it may be concluded that mesh size or 46 x:\..j. pmvides grid- independent solution and so will bc used ror latcr computations.

The streamline plots for expansion angle rJ. ^{= :\()"}

and different swirl vane angles or 0".24". J1". 56" and 66°, are shown in FigS For svvirl vanc :lIlglc 8 = 0"

(non-swirling flow), we observe only primary corner recirculation due to the expansion. As thc swirl vanc angle is changed to 8 = 24" corresponding to which the swirl number is S=O.J (low swirillow). the length or the corner recirculation decreascs. 1-"01' vanc anglc 8=37" (moderate swirl). the primary corncr I'ccircuiatiun

326 ^INDIAN J. ENG. & MATER. SCI., DECEMBER 1999

1.0.--,--,- - -

~

^'1·-0.

0.8 rr 20.6

,;

~. 46XJ4 Grid

62X40 Grid

I I X/R~0.6

:6 0." /

o

L

(C

0.2

o.o~ y~

X!H-O.6

-0.5 0.5 ~.5 -0.5 c.::. I.:) 0.00 C.CS 0.10 0.15

U/U, VI/I., k/U,'

Fig. 4--Comparison of computed results for differelll grid sizes at expansion angle 90" and swirl vane angle 56"

u = D· (S = 0.0 )

0= 24' ( S = 0.3 )

0=37'(5=0.5)

e ⁼ 56' (S~ 1.0 )

0.0 x/It 2.0 4.0 n.O

o = 66° ( s= I.S )

Fig. 5--Streamline plots for expansion angle 30" and different swirl vane angles

vanishes, but secondary on-axis recirculation due to swirl is developed. The swirl strength at which the primary corner recirculation just vanishes completely, is defined as the transition swirl strength. Hence, the swirl strength corresponding to 8

=

37", i.e. 5

=

0.5 has attained the transition value for expansion angle a= 30". Actually, the transition swirl number for a

=

30° has been found to be about 5

=

0.5. As the swirl vane angle at inlet is further increased to 8 = 56(),

1 / iC:~~~ --~

-0.----··-- . __

-=-_1

f--~---~' ""'ij"T"-- - -

n "" 0(> ( S "'" U,II )

o = 24' (S = 03 )

~~

^,,"

/f~~·o ~--o,

_/ (~ ~

LL _ _ _ _ _ _ ., _ _ _ _ _ _ _ _ ____ __ ...

0-37" l S ~ 0.5)

~ ^~

^~~

^~

^{' )}

~---~.-

^{~o --n.I·~--}

,,'" ^-~-'-j

^{. -~ - - -}

^-

~QA -. ... "

---~---

o = 56" ( S - 1.01)

0=66° (S 1.5,

Fig. 6--Streamline plots for expansion ~Inglc (lO" a III I dilTcrcnl swirl vane angles

the on-axis recirculation also grows. At 8 = 66" (high swirl), large on-axis recirculation is developed.

Fig. 6 shows the streamline plots f(lr l'xp;lIlsioll angle a=60" and different s\Virl Valll' ;lllgleS ;It the inlet swirl generator. For vanc angle H = 0". wc find only primary corner recirculation. which dl'crcasc~ in size for 8 = 24", and is similar to that round fur expansion angle a=30". But for 8=1,7". wc ohserve both secondary on-axis recircul;ltion dul' tn swirl and primary corner recirculation. unliJ,;e tll th~lt foulld fm a= 30" in Fig. 5. As the vane angle is increasl'd t(1 8=56", the primary corner recirculatioll vanishes and the secondary on-axis recirculation Ixcoll1es larger.

Thus, the transition swirl strength for ('/. = ()()" is In between 8=37" and 8=56". Actually. the transition swirl number for expansion angle ex == 60" has heen found to be around 5=0.75. COlllpul<itillllS have also been done for expclI1sion angle C'J.=-h ' sho\Ving that the transition swirl number is arolilld S = 0.6. HCllcl'.

with decreasing expansion angle. the magllitude or the transition swirl strength also decreases. Thus, at 10\\'l'r expansion angle, the primary cornci rc-,circulatioll

CHOWDHURY & MAYEED: EFFECT OF EXPANSION ANGLE ON TURBULENT SWIRLING FLOW -:'27

vanishes at the lower swirl strength. At the transition swirl strength, the intensity of the secondary recirculation due to swirl becomes small. As the swirl strength is further increased beyond the transition value, only on-axis recirculation due to swirl is found and keeps growing with the increase of swirl strength. Due to the earlier occurrence of transition swirl strength for lower expansion angle, at any particular swirl strength which is greater than the cOITesponding transition value, on-axis recirculation is bigger for the case of lower expansion angle, as it has more chance to grow after transition. Thus, for vane angle 8 = 56°

(5 = 1.0) which is greater than the transition value, the intensity of the secondary recirculation due to swirl for a

=

60n

is smaller than that for a

=

JOn (Figs 5 and 6). Again, for swirl vane angle 8 = 66^n, the secondary on-axis recirculation due to swirl grows further. But comparing with Fig. 5, it is found that the secondary recirculation for expansion angle a

=

60" at 8

=

66" is smaller than that for a = JOn, because it has less chance to grow as explained above.

0=24° ( S = O.J )

9=37° (5=0.5)

~~ ~ .. . .

~"~ ~

^{_ _ _}

.'~~ ~ ~~ _- _ - _-_ - _ - _ - _ ---i _

0=56° ( s = 1.0 )

0.0 XlR 2~ ~O G.O

e = 66° (S = 1.5 )

Fig. 7-Slrcamlinc plOIS ror cX[l;Jnsion anglc 90" and dirrercnl swirl vanc angles

The streamline plots for expansion angle ^(X = 9()"

and different swirl vane angles arc showll in Fig. 7.

Here again, for vane angle 8 = 0", only prim~lry comer recirculation is observed as for a = -:'0" and 60". For 8=24°, the length of this primary comcr rccirculation decreases. But within this primary recirculation. small counter rotating flow near the wall is ohserved.

Speculation about counter-rotating eddics wcrc also made by Johnston~. As the vane angle is incrcased to 8 = 37", secondary on-axis recirculation duc to swill is developed In addition to thc pl"lmary corner recirculation. With further incrcase of ,'anc angle to 8 = 56° and 66\), the magnitude of the secondary on- axis recirculation increases. But even at tl = 66". small primary corner recirculation exists. This mcans that for a = 90", the transition swirl strength is beyond 8 = 66°.

The distribution of the pred ictcd d i mcnsion less mean axial velocity across the flow for cxpansion angle a = 90" and di ffercnt swi rl vane angles at various sections away from the expansion geometry are shown in Fig. 8 for comparison. Swirl angle zcro means flow without swirl. At 8 = 2-1-" (low swirl). the velocity profiles in t.he initial sections ~Irc similar to those for no swi r1, ha vi ng on I y pri mary cornC("

recirculation. For 8

=

24", at XII<

=

O.i.. the velocity very near to the wall again becomes positive. ~ho\Ving

that there is a counter-rotating flow as observed in Fig. 7. The length of the primary corncr recircui<ltion zone for 8=0" is about 8.2J step heights while that for 8

=

24" is about 6.40 step heights. As the swirl vanc angle is increased to J7" (5=0.5). negative velocities near the centerline are fOllnd, which means that the flow is having secondary on-axis recirculation due to swirl as was observed in Fig. 7. in addition to tile primary corner recirculation. With further incrcase 01"

inlet swirl vane angle, the Illagnitude of the secondary on-axis recirculation due to swirl increases \.vhilc the primary corner recirculation decreases. At high swirl.

8 = 66°, the primary corner recirculation almost vanishes. Beyond XIR = 2.0. the mean axial velocities for moderate and high swirl cases becoille almost identical. The axial velocity profiles for cxpansion angle a=JO" and 60" also show similar bchaviour. hut are not shown here.

Fig. 9 shows the variation or the dilllensioniess mean tangential velocity profiles for expansion angle a= 90" and different swirl vane angles. At

e

^{= 2-1-"}

(low swirl), secondary on-axis recirculation c1l1e to

1.0 \ '

0.8

'"

~O.6

:g g 0.4

'"

0.2

0.8

~O.6 a:

g

.~ 0.'

'" _0.2

0.0 -0.5

"

I I I

0.5 X/R-O.2

- Vane ang'e 0⁰ --_ .. _ .. Vane ong:e 24°

---Vane angie 37"

-- - Vane angle! 56°

- - Vane angle 66"

\\ :

" ^'. , / X/R=O.6 ^/ '-(I

'lX:;"\

^{, '}

I, . ..:

/ / , /

"

{

:1 1.5 -O.~ C.5

Axial Veloc.ity, U/U_o

Axial Velocity, U/ug

t

11 ,l

)/

) ~ i

0.5 05 1.5

Fig. 8--Comparison of dimensionless mcan axial velocity proliles for expansion angle 90"

--_ .. _ .. Vane angle 2'°

---Vane angle 37°

-- - _Vane angle 5bo - - Vane angle 66°

1.0 -.

\ \

^\ 'I n' ':1 I _~-

0.8

\i

^\ X/R"'U.2 _; ~ I X/H.:...O.6

I \

0- I \1,'

l

'C^O.6 1 ^{\, ~, \}

.,; . ;\ I; ^:;'1 I

I

iii' ^:,."\

~ ::1 I

'00.-4

0

if !T

a: ,

0.1- ,f ¹

'./i :I,I}

r

I/~)I :, .:

V.O ^.J

-0,5 0.5 1.5 -0.5 0.5 1.5 -0.5

Tangential Velocity, W/Uo

Fig. 9----Comparison of dimcnsionless mean tangcntial velocity profilcs for expansion angle <)()"

swirl is absent. So the tangential W-velocity near the centerline is comparatively higher. For higher swirl vane angles, the flows have secondary on-axis recirculation. So, the W-velocities become lower for increasing the pressure and -reate the required adverse pressure gradient for recirculation, specially near the center-line. Similar results are expected for a = 30° and 60°

The distribution of the dimensionless turbulence kinetic energy across the flow at different sections for expansion angle a = 30" and various swirl vane angles are shown in Fig. 10. It is observed that as the swirl strength is increased compared to the no swirl condition, the turbulence kinetic energy increases very much in the initial sections after expansion due to the secondary recirculation resulting in increased

1.0 , - -- - - _ - ,

0.8

~O.6 ^.... 1 \

g ,/

:.r. _o ^0.4

'"

X/R-0.2

0.2 "

>- --

I ';-"::, '

o.D 1.~

- Vor,!'! on')l!! 0"

... Vane angle /"1"

------ VOile ongle J7fJ - - - '/t](,:c angle :ifi"

.- - Var.e angle ob"

r~/'> J;

:, I

: I

:, I , __

; I /

I

' I

: ' , . ~LL_'_' _ t!

0.00 0.05 0.10 0.15 0.00 0.05 U.l0 C.l~ U.OO O.j~ (lIn CoL'i

\ I

Turb. Kin. EncnJY, k/U,,7

X/R==2.0

\ I I

I I

, _I

I

I I

,

I

0.(15 010 O.l~ O.OG O_!'~, (,;.10 015 lurb. Kin. E rH:r:lY, k/ J,,"

Fig. I O--Coillparison of di IllCllsillll less 11lrhlllc/lL'c' ~ilH:til' ellcrt''' proliles for cxpansion angle :l0"

mixing rates in those sections. Hencc. \Ve nccd shorter combustor length for such swirl cascs.

Fig. II shows the variation or the dill1ensionless turbulence kinetic energy across the now 1'01'

expansion angle a

=

^60° Comparing Fi~s. I () ~Ind I I . the turbulence kinetic energies ^1'01' s\virl v;lnc angle 8=56" (5= 1.0) and 8=66" (S= 1.5) ~lrt' roulHJ to he much larger for expansion angle a

=

30" than thosc for a= 60", The reason is that, the Ir~lIlsition swid strength for a=30" occurred at around S=(),5, Earlier.

it was found that at the transition ^S\\ il'l qrcngth. thc secondary recirculation clue to swirl bcconlL's smallcr.

As the swirl vane angle or swirl str'ngth is rurther increased, the secondary recircul~ttiol1 duc to swirl again starts increasing. Generation or turbulence kinetic energy is directly related to this rccirculation.

But, the transition swirl strength I'm (f. = 6()" occurred at 5=0.75, So, the secondary re,-'irculatioll and consequently turbulence kinetic energy <It

e

⁼ 56"

(5 = 1.0) or 66" (5 = I .5) for ex = 3()" lwei Illore chancl' to grow, compared to that for ex = 60". Hence. I'm a particular swirl strength greater th~ln the tr~lIlsition

value, the turbulence kinetic energy and mixing r~lle

will be greater for a lower exp~lIlsion angk

The distribution of the dimcnsionlc,s turhulence kinetic energy for expansion angle a == l)O' is shu\Vn in Fig, 12. Fig. 7 shows that even at tl = 6()" (S= 1.5). t h,-' transition swirl value is not attained. So. \Vith the

CHOWDHURY & MAYEED: EFFECT OF EXPANSION ANGLE ON TURBULENT SWIRLING rLOW l2l)

l.0r -- -- - - - ,

,-

_{; I} ~ 08 ,~ (

~ \" '\

L., 0.6

0.2 , v

"~,r

0.0 ,~ IJ~_" --'-... --"_--'-" i

- Vcnc angle 0"

~---Vane angle 24-"

---.-. Vane angle J7^D --- Vcne angle 56"

. - - Vane angle 66"

X/R 0.6! I

!

0.00 0.05 0.10 0.15 0.00 0.05 C.iO 0.15 0.00 0.05 Turb. Kin. Energy, k/U/

X/R=1.0 i

0.10 0.15

Fig. II-Comparison of dimensionless turbulcnce kinetic energy profiles for expansion angle 60"

increase of vane angle up to 66°, the turbulence kinetic energy generation also increases to some extent But, comparing Figs 10, I I and 12, it is observed that the turbulence kinetic energy and consequently mixing rate at

e =

56° and 66° for a

=

30"

is much larger than those for a = 60" or 90".

Conclusions

The present computational model is capable of predicting the swirling turbulent flow through an axisymmetric expansion with reasonable accuracy, With the increase of swirl intensity at inlet, secondary on-axis recirculation may be produced near the centerline, After the transition swirl strength, swirl produces larger turbulence kinetic energy and enhances the desired mixing rate for complete combustion in a shorter combustor length. For a particular swirl strength greater than the transition

'"

(:-0.6 ,,;

"

:.0 0.4 o

X/R-O.2

==

---~~~~ ~~~:~ ~~ Vene anale JIG

..

--- Vane onqle 56"

- - Vane angle 66"

",-". --~ \1('.;;', - /' :,~ ;':/[("'°06 1 \ "

'~,,~~~, ^'I' ! 'X,- l

, ', I

Y' i

X/R==l.C

'1 \ \,\ '. ' :/-'"

^!

r" ' , ,)

O.? • .... ... ..>./ /' / ) i' ^II'

"',4" 'I:' II

,'/ -":: :{ . ::1

o,gooL-'--'-0-"-.O'--"'-0.L'O-U-'-.15 0.0"'0--"-0-'-,05- -0:0 c.;~ o.oo"--"!o-o-:~ ^{- 0,-'-;0- 0';.,}

'"

Turb. Kin. fncrgy. </U./

Fig. 12-Comparison of dimensionlcss turhuicllCC ~il1l:lil' energy profiles for expansion angle <)0"

value, lower the expansion angle, higher the turbulence kinetic energy and mixing r~\lc.

References

I Flllldwnen/als (!t gas I/I/hilll' CllllliJlI.\lillll, ediled hI' Gl'rslein M, NASA-CP-20R7 (NASA Lcwis Rese:IITh Cenler.

C1evcland, Ohio). 197<).

2 Cas IUriJille cOlllbmw!' desigll IJwhielll.L ediled hy Leldwre A H (McGraw-Hili, New Yllr~), IlJXO.

3 AmanoRS,AIAAJ,21(IO)(19X:1) 1400.

4 Launder 8 E & Spalding D 13, COIIlI' MI'I" AI'I,I /\lIn" 1:'lIg. ,~

(1974) 269.

5 Patankar S V, Nlllllerical "eul lIlIri .flilid .floll' (!\fIcC'raw-llill.

New York), 19RO.

6 Gosman A D & Pun W M, Calmllliioll of !'('Ci!'Cllirllillg .fIO)'·S. Rcp. No. HTS1741 12 (Dcparlll1t:nt of Mecl1:lnil';iI Engineering.

Imperial College, London) 1<)7-1.

7 Dcllenback P A, Metzger D E & Neitzel (; 1', rl/A·\ .I. 2()(i)) (1988) 669.

8 Johnslon J P, IlIle/'/llll floll',\', 1II!'lmlell(,(': rOIJics ill 0IIIJ/ied physics, 12th edn (Springer-Verl:lg. New York). I 'J7X.