Whole-field flow measurement inside a stirred mixer using Tomographic PIV technique

7/24/2019 Whole-field flow measurement inside a stirred mixer using Tomographic PIV technique

1/18

11TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY PIV15Santa Barbara, Califrnia, S!"t!#b!r 1$%1&, '(15

Whole-field flow measurement inside a stirred mixer using TomographicPIV technique#

Chandra Shekhar! "aunao Takahashi$! Taku%a &atsunaga'and "oichi (ishino$1Heat and Fluid Dynamics Laboratory, IHI Corporation, Yokohama, Japan

chandraiitk @ yahoo.co.in

Department o! "echanical #n$ineerin$, Yokohama %ational &ni'ersity, Yokohama, Japan(Department o! )ystems Inno'ation, *he &ni'ersity o! *okyo, *okyo, Japan

ABSTRACT

)! "!rfr#!* "+a!%l-.!*, t+i-.%/l0#! t#ra"+i- #!a0r!#!nt ini*! a fl2 #i3!r4 T+! t+i-.n! f t+!

#!a0r!#!nt /l0#! i $( mm, t+! 2r.in fl0i* i 2at!r, an* t+! fl2 i tirr!* b an i#"!ll!r 2it+ t+r!! "it-+!* bla*!4

T+! i#"!ll!r rtat! at t+! -ntant an0lar "!!* f 15( RPM4 T+! R!nl* n0#b!r ba!* n t+! i#"!ll!r *ia#!t!r an*

t+! ti" /!l-it f t+! i#"!ll!r bla*! i 56$((4 In ttal, 2! "!rfr#!* f0r "+a!%l-.!* t#ra"+i- PIV #!a0r!#!nt,at f0r *iff!r!nt an0lar "itin f t+! rtatin bla*!, fll2!* b -#binin t+! r!0lt t btain fl2 70antiti! in t+!

!ntir! 1'(2a.! r!in t+at fll2 t+! l!a*in i#"!ll!r bla*!4 Sin-! t+! bla*! ar! i*!nti-al, t+! fl2 70antiti! in t+!2a.! r!in b!+in* t+! t+!r t2 bla*! 20l* al b! t+! a#!8 an*, t+0, !ff!-ti/!l, t+i t0* i/! 0 ini+t int t+!

b!+a/ir f t+! fl2 ini*! t+! !ntir! fl2 *#ain4 T+! -#bin!* r!0lt -0l* 0--!f0ll -a"t0r! t+! ti"%/rti-!, 2+i-+

!3t!n* !/!n b!n* t+! fll2in bla*!4 )! 20l* al "r!!nt t0rb0l!n-! .in!ti- !n!r an* t0rb0l!n-! *ii"atin rat!

in t+! 2a.! r!in, a 2!ll a 20l* a! 70antitati/! a--0ra- f tatiti-al fl2 70antiti! b -#"arin t+!# 2it+

t!r! PIV r!0lt4

Keywords:t+i-.%/l0#! #!a0r!#!nt, t#ra"+i- PIV, tirr!* #i3!r, /rti-al tr0-t0r!, t0rb0l!n-! tatiti-

1. INTRODUCTION

Mi3!r ar! 2i*!l 0!* in /ari0 in*0trial 0nit an* 00all *ri/!n b an i#"!ll!r4 T"! f t+! 0!* i#"!ll!r r!atl

aff!-t t+! nat0r! f t+! #i3in an* t+!r fl2 "r"!rti!4 T"i-all, in*0trial #i3!r 0! t b! -lin*ri-al in +a"!, 2it+

#0lti"l! narr2, /!rti-al baffl! "lat! atta-+!* t it inn!r 0rfa-!4 T+!! baffl! "lat! inifi-antl !n+an-! #a-r l!/!l

#i3in4

In !n!ral, i#"!ll!r -an b! *i/i*!* int t2 t"!9 ra*ial%fl2 t"! an* a3ial%fl2 t"!4 Ra*ial fl2 t"! i#"!ll!r -nit

f /!rti-al "a**l!, 2+i-+ rtat! ab0t a i/!n a3i t !n+an-! t+! #i3in4 T+!! i#"!ll!r ar! .n2n t "r/i*! a +i+l!/!l f #i3in at #*!rat! rtatin "!!*4 On! f t+! 2i*!l r!!ar-+!* ra*ial fl2 t"! #i3!r -nit f R0tn

t0rbin!, "!r+a" *0! t it i#"liti- *!in4 Bt+ n0#!ri-al an* !3"!ri#!ntal t!-+ni70! ar! 0!*4

)0 an* P!tt!rn :1; 0!* La!r


2/18

a""ra-+4 T+! -arri!* 0t t2%*i#!ninal "+a!%l-.!* PIV #!a0r!#!nt in i3 a3i##atri- "lan!, a 2!ll a in an

ai#0t+al "lan! t+at a""r3i#at!l t0-+!* t+! ti" f a rtatin bla*!4 Ba!* n t+! !3"!ri#!ntal r!0lt, t+! *!/!l"!*

#! i#"l! t+!r!ti-al #*!l, 2+i-+ t+! lat!r 0!* in t+!ir R!nl*%a/!ra!* Na/i!r%St.! i#0latin a b0n*ar

-n*itin4 T+! i#0latin r!0lt, +2!/!r, 70antitati/!l *iff!r!* fr# t+! riinal !3"!ri#!ntal r!0lt4

Man r!!ar-+!r al in/!tiat!* a3ial%fl2 #i3!r =in-l0*in in t+! "r!!nt t0*>, b!-a0! a3ial%fl2 #i3!r l!a/!

#all!r +!ar tr! ft"rint in t+! fl2, a 2!ll a t+! -n0#! l! !n!r -#"ar!* t ra*ial%fl2 t"! i#"!ll!r4 S0-+

#i3!r 0tili! "it-+! bla*!, 2+i-+ i!l* +i+ a3ial *i-+ar! rat!8 b0t, in !n!ral, t+! in*0-! all t+! t+r!! /!l-it

-#"n!nt in t+! fl24 S+!n !t al :5; -arri!* 0t t2%*i#!ninal PIV #!a0r!#!nt in an a3i##!tri- "lan! f ar0n* baffl!* tan., in 2+i-+ t+! fl2 2a aitat!* b a f0r%bla*! "it-+!* i#"!ll!r4 T+! -#"ar!* t+! btain!* #!an

/!l-it an* #! i#"l! t0rb0l!n-! tatiti- 2it+ t+! n0#!ri-al i#0latin t+at t+! -arri!* 0t 0n*!r i#ilar -n*itin

an* aft!r !ttin t+! b0n*ar -n*itin ba!* n t+! !3"!ri#!ntal r!0lt4 T+! f0n* t+at t+! -#"0t!* #!an /!l-it

-#"n!nt #at-+ 2!ll 2it+ t+! !3"!ri#!ntal r!0lt, 2+!r!a t+! t0rb0l!n-! tatiti- #at-+ nl in a 70alitati/! !n!4

Ba..!r !t al :&; al 0!* t2%*i#!ninal PIV r!0lt a b0n*ar -n*itin in t+!ir n0#!ri-al i#0latin, an* f0n*t+at t+! r!0lt 2!ll "r!*i-t t+! fl2 b!+a/ir 2+!n it i la#inar4 T+! n0#!ri-al i#0latin "r!*i-t!* t+! #!an /!l-it

-#"n!nt f t0rb0l!nt fl2 al r!anabl 2!ll, b0t f!ll +rt f "r!*i-tin t0rb0l!n-! tatiti-4 +".ar !t al :D; an*

G! !t al :; al t. a i#ilar a""ra-+ 2it+ #r! r l! i#ilar 0t-#!4 All t+!! t0*i! 0!t t+at fl2 in

CONVENTIONS

Fa 9 A "+i-al 70antit, a, in it *i#!ninal fr#4a 9 M!an /al0! f a "+i-al 70antit, a4

aRMS 9 RMS /al0! f a "+i-al 70antit, a4

GREEK ALPHABETS

9 in!#ati- /i-it f t+! 2r.in fl0i*4

t 9 T0rb0l!n-! /i-it4

9 T0rb0l!n-! *ii"atin rat!4

9 I#"!ll!r rtatin "!!* in -l-.2i! *ir!-tin, 15(RPM=154Drad/s>4

ABBREVIATIONS

RMS 9 Rt #!an 70ar!4

RPM 9 R!/l0tin "!r #in0t!4

TKE 9 T0rb0l!n-! .in!ti- !n!r :=uRMS>' J =vRMS>

' J =wRMS>' ;K'4

NOMENCLATURE

D 9 K'4

Q 9 S!-n* in/ariant f t+! #!an /!l-it ra*i!nt t!nr8 Q 1

2UiXj

UjXi

.

Re 9 R!nl* n0#b!r8Re D

'

K' 56$((4U =rU1> 9X%-#"n!nt f t+! intantan!0 fl2 /!l-it4

u 9 T0rb0l!n-! fl0-t0atin in t+! U-#"n!nt f t+! /!l-it8 u U U4

V r=U'> 9 Y%-#"n!nt f t+! intantan!0 fl2 /!l-it4

v 9 T0rb0l!n-! fl0-t0atin in t+! V-#"n!nt f t+! /!l-it8 v V V4

W=r U> 9Z%-#"n!nt f t+! intantan!0 fl2 /!l-it4

w 9 T0rb0l!n-! fl0-t0atin in t+! W-#"n!nt f t+! /!l-it8 w W W4

XYZ=r

X1,X',X>

9 A3! f a ri+t%+an*!* Cart!ian -r*inat! t!#, 2it+ t+! riin l-at!* n t+! -!nt!r f t+! l2!r ti" f

t+! rtatin +aft =n 2+i-+ t+! i#"!ll!r i #0nt!*>4

!"# S"atial "itin f a "int ini*! a -r*inat! t!#X,Y,Z4


3/18

t0rb0l!nt fl2 #i3!r ar! fairl -#"l!3 an* -annt b! "r!*i-t!* b -n/!ntinal t0rb0l!n-! #*!l, 0-+ a, R!nl*%

a/!ra!* Na/i!r%St.! #*!l r $% #*!l4 Rana*! !t al :6;, +2!/!r, r!"rt!* r!anabl #at-+in r!0lt 2it+

!3"!ri#!nt, bt+ in t+! b0l. fl2 r!in an* in t+! n!ar%bla*! r!in4 T+! a*"t!* -#"0tatinal na"+t a""ra-+ :1(;

in t+!ir n0#!ri-al i#0latin4 +an !t al :11; -arri!* 0t t!r! PIV #!a0r!#!nt in a3i##!tri- "lan!, an* f0n* t+at

t+! fl2 a2a fr# t+! bla*! ar! a""r3i#at!l itr"i-, in*i-atin t+at a i#"l!r, t2%*i#!ninal PIV !3"!ri#!nt#a b! a*!70at! t !ti#at! i#"l! t0rb0l!n-! tatiti-4 T+! f0rt+!r b!r/!* t+at ab0t $$? f t+! !n!r tran#itt!* b

t+! i#"!ll!r t t+! fl2 *ii"at! in t+! r!in 0rr0n*in t+! i#"!ll!r4 fl2 #!a0r!#!nt 2it+ "atial

r!l0tin 0ffi-i!nt t r!l/! "atial -al! -#"arabl! t t+! l#r/ l!nt+ -al! f t+! fl2 =2+i-+ i #!ti#!a #all a a f!2 #i-r#!t!r in a "ra-ti-all 0!* #i3!r>4 A r!"rt!* !l!2+!r! :1&;, 2! #!a0r!* all t+! /!l-it

ra*i!nt ini*! a 70ar!%+a"!* fl2 #i3!r t+r0+ a "+a!%l-.!* t#ra"+i- PIV !3"!ri#!nt4 It 2a "!r+a" t+! /!r

firt r!"rt!* intan-! f /l0#!tri- fl2 #!a0r!#!nt ini*! a #i3!r4 M!r !t al, :1D; +2!* t+at t+! fl2 b!+a/ir

ini*! a 70ar! tan. i i#ilar t t+at ini*! a baffl!* r0n* tan., an* t+!r!fr! 0r r!0lt -an b! 0!* t 0n*!rtan* !n!ral

fl2 b!+a/ir ini*! in*0trial #i3!r4 )! aitat!* t+! fl2 0in t+! -##!r-iall a/ailabl! HR%1(( i#"!ll!r4 )!

"r!!nt!* #!an fl2 an* t0rb0l!n-! .in!ti- !n!r *itrib0tin, an* !ti#at!* all t+! nin! -#"n!nt f t+! t0rb0l!n-!

+!ar tr! t!nr4 @r# t+! -#"l!t! t0rb0l!n-! +!ar tr! #atri3, 2! al -al-0lat!* t+! #a3i#0# t0rb0l!n-! +!ar

tr! t+at 20l* b! "r!!nt in t+! fl24 H2!/!r, *0! t t+! i! f t+! int!rratin /l0#! b!in #0-+ lar!r t+an t+!#all -al! #tin f t+! t0rb0l!n-!, t+! !ti#at!* t0rb0l!n-! +!ar tr!! ar! li.!l t b! +0!l 0n*!r!ti#at!* in

#anit0*!4 Lat!r, 2! a""li!* :1; a 0bri*%tr! #*!l =2+i-+ i t+! bai f Lar! E** Si#0latin> n t+! t0rb0l!n-!

*ii"atin rat! t+at i *ir!-tl -al-0lat!* fr# 0r "r!/i0 #!a0r!#!nt :1&;, in r*!r t !ti#at! it tr0! /al0!4 Nt! t+at,i#ilar t t+! t0rb0l!n-! +!ar tr!, t+! t0rb0l!n-! *ii"atin rat! al *!"!n* n #all -al! #tin, an* t+!r!fr! t+!

*ir!-tl -al-0lat!* /al0! 20l* b! +0!l 0n*!r!ti#at!*, a 2!ll4 In a !"arat! "a"!r, 2! al r!"rt!* "r*0-tin,

*iff0in, an* -n/!-tin rat! f t+! t0rb0l!n-! .in!ti- !n!r :16;, ba!* n t+! a#! /l0#!tri- #!a0r!#!nt *ata4

T+!r!, 2! b!r/!* n!ati/! t0rb0l!n-! "r*0-tin ini*! t+! ti" /rt!3, a 2!ll a l f t0rb0l!n-! !n!r *0! t t+!

t0rb0l!n-! *iff0in4 Mr!/!r, t+!! t2 l! 2!r! lar!l -#"!nat!* b t0rb0l!n-! -n/!-tin4 Nt! t+at t+!!r!"rt!* 70antiti! * nt *!"!n* n #all -al! t0rb0l!n-! #tin, an* t+!r!fr! t+! ar! li.!l t b! -l! t t+!ir tr0!

/al0!4

In t+! afr!#!ntin!* t#ra"+i- PIV #!a0r!#!nt, 2! "ri#aril f-0!* n btainin 70antitati/!l a--0rat! r!0lt,

an* t+!r!fr! 2! .!"t t+! t+i-.n! f t+! #!a0r!#!nt /l0#! nl D mm4 In t+! "r!!nt t0*, +2!/!r, t+! f-0 i t

+a/! a !n!ral 0n*!rtan*in f t+! /!rall fl2 fi!l* an* lar! fl2 tr0-t0r! ini*! t+! #i3!r4 T+!r!fr!, 2! "!rfr#!*

"+a!%l-.!* t#ra"+i- PIV #!a0r!#!nt in $( mmt+i-. /l0#!, at f0r an0lar "itin f t+! i#"!ll!r bla*!4 )!,

n-! aain, 0!* t+! a#! HR%1(( i#"!ll!r :1$; a t+! aitatr, an* .!"t t+! !ff!-ti/! fl2 *#ain al#t a#! a t+at int+! "r!/i0 #!a0r!#!nt :1&, 16;4 Aft!r -#binin r!0lt fr# all t+! f0r #!a0r!#!nt, 2! -0l* 0--!f0ll btain

*itrib0tin f #!an /!l-it an* #! t0rb0l!n-! tatiti- ini*! t+! !ntir! 1'( 2a.! r!in t+at fll2 t+! l!a*inbla*!, a 2!ll a *!t!-t!* lar! /rti-!4 Sin-! all t+! t+r!! bla*! f t+! i#"!ll!r ar! i*!nti-al, t+! *itrib0tin 20l* b!

a#! !/!n in t+! 2a.! r!in f t+! t+!r t2 bla*!4


4/18

T+! r!#ainin f t+i "a"!r i rani!* a fll24 @irt, 2!

2ill *!-rib! t+! fl2 !#!tr an* t+! !3"!ri#!ntal

#!t+*l in !-tin ' an* , r!"!-ti/!l4 In !-tin $, 2!

2ill *i-0 a #!t+*l t+at 2! a*"t!* t #t+ all t+!

fl2 70antiti! r!"rt!* in t+! "r!!nt t0*4 In t+i !-tin, 2!2ill al *!-rib! a "r-!*0r! t -#bin! t+! f0r

#!a0r!#!nt r!0lt4 In !-tin 5, 2! 20l* "r!!nt #!a0r!*/rti-al tr0-t0r! an* #! tatiti-al 70antiti!, 0-+ a,

.in!ti- !n!r f t+! #!an fl2, t0rb0l!n-! .in!ti- !n!r, an*

t0rb0l!n-! *ii"atin rat!4 In t+i !-tin, 2! 2ill al

70antitati/!l -#"ar! t+! t#ra"+i- PIV r!0lt 2it+ t!r!

PIV #!a0r!#!nt r!0lt, in r*!r t a! 70antitati/!

a--0ra- f t+! fr#!r4 @inall, 2! 2ill *ra2 -n-l0in in!-tin &4

1.1. Nond!"ens!on#$!%#&!on

In t+i "a"!r, all "+i-al 70antiti! ar! "r!!nt!* in nn%

*i#!ninal fr#4 T+! "atial *i#!nin, t+! #!an /!l-it

an* t+! /!l-it fl0-t0atin -#"n!nt, an* t+! .in!ti- !n!r

f t+! #!an fl2 an* t+at f t+! t0rb0l!n-! ar! nn%*i#!ninali!* 2it+ r!"!-t t t+! i#"!ll!r *ia#!t!r =D>, t+! bla*! ti" /!l-it =DK'>, an* 70ar! f t+! bla*! ti"

/!l-it =%D%K$>, r!"!-ti/!l4 Si#ilarl, t+! !-n* in/ariant Qf t+! #!an /!l-it ra*i!nt t!nr an* t+! t0rb0l!n-!*ii"atin rat! ar! nr#ali!* 2it+ r!"!-t t $K'an* D'K, r!"!-ti/!l4

)! 20l* in*i-at! *i#!ninal fr# f a "+i-al 70antit b "0ttin it ini*! -0rl bra-!, li.! F4

'. S(STEM DETAILS

T+! !ff!-ti/! fl2 *#ain r!!#bl! a 70ar!%+a"!* -lin*ri-al tan. fill!* 2it+ 2at!r, 2it+ t+! rtatin HR%1(( i#"!ll!r#0nt!* n a t+in, r0n* +aft an* "la-!* aln t+! -!ntral a3i f t+! tan.4 T+i 70ar!%+a"!* fl2 *#ain i r!ali!* b

in!rtin a la +0tt!r in a #r! -#"l!3 !#!tr, a -+!#ati-all +2n in an i#!tri- /i!2 in @i41, a 2!ll a in

*!tail!* *iara# in @i4'4 A +2n in t+! fi0r!, t+! riinal !#!tr i a r!-tan0lar -lin*!r =nt a 70ar!>4Mr!/!r, a "ra#i*%+a"!*, +ll2 la "ri# i atta-+!* t n! f t+! f0r /!rti-al 0rfa-! f t+! tan., in r*!r t

r!ali! a *itrtin%fr!! /i!2 f t+! fl2 fi!l* ini*! t+! fl2 *#ain4 T+! "ri# 0rfa-! t+at i r*inaril 0""!* t b!

"r!!nt at t+! "ri#%tan. int!rfa-! i ab!nt4 @0rt+!r#r!, t+! int!rfa-in la 0rfa-! b!lnin t t+! tan. i al -ar/!*

0t, in r*!r t in0r! fr!! "aa! f t+! 2at!r int t+! "ri# an* t !ail r!#/! tin b0bbl! t+at #!ti#! fr# n it

t+! inn!r 0rfa-!4

T+! bai- tr0-t0r! f t+! afr!#!ntin!* 2at!r "ri# i #a*! b ra"i* "rtt"in, 2it+ f0r bli70! 2in*2 l!ft "!n4

Lat!r, t+in la +!!t ar! ti+tl l0!* t t+!! 2in*24 A 2! 2ill *!-rib! +rtl, t+! f0r -a#!ra t+at 2! 0!* t

/i0ali! t+! fl2 fi!l* ar! !t al#t "!r"!n*i-0lar t t+!! 2in*24 T+i -nfi0ratin r!atl r!*0-!* t+! *itrtin t+at

20l* +a/! ta.!n "la-! if t+! "ri# 2!r! ab!nt an* t+! -a#!ra 2!r! /i!2in t a tan. 0rfa-! bli70!l4

T+! HR%1(( i#"!ll!r, 2+i-+ i "+i-all +2n in @i4, i *ri/!n b an !l!-tri- #tr in t+! -l-.2i! *ir!-tin =2+!n

/i!2!* fr# t+! t">, 2it+ t+! an0lar "!!* f 15(RPM=i4!4 154D rad/s>4 T+! *ia#!t!r f t+! i#"!ll!r,D, i !70al t6( mm, an* it i a#! a t+at 0!* in 0r "r!/i0 t0*i! :1, 15, 1&, 1, 16;4 All t+! #!a0r!#!nt ar! "!rfr#!* at t+!

2at!r t!#"!rat0r! f 16C4 T+! -rr!"n*in R!nl* n0#b!r Re D'K' 56$((4 In r*!r t #ini#i! b0bbl!fr#atin in t+! fl2, t+! 2at!r i *!a!rat!* b!fr! fillin int t+! fl2 tan.4 It i *n! b firt +!atin it 0ntil ( &, an*

t+!n l!ttin it nat0rall -l *2n 0ntil 16&, 2+il! #an0all tirrin t+! -lin 2at!r n +0rl bai4

)! -arri!* 0t t+! "+a!%l-.!* #!a0r!#!nt in (4$$$D =$( mm> t+i-. /l0#!, f0r ti#!, 2+i-+ -rr!"n*!* t f0r

*iff!r!nt an0lar "itin f t+! i#"!ll!r bla*!, a -+!#ati-all +2n in @i44 T+! #!a0r!#!nt r!in it!lf i fi3!*

in "a-!, a a""r3i#at!l #ar.!* bt+ in @i4' an* $4 T+! fi0r! al +2 t+! ri+t +an*!* Cart!ian -r*inat! t!#

=X(, Y(,Z(> in 2+i-+ t+! #!a0r!#!nt r!0lt ar! btain!*4


5/18

an i#"!ll!r bla*! 2!r! !"arat!* b (4 T+! f0r 0--!i/!

2a.! r!in -rr!"n*in t t+! f0r #!a0r!#!nt ar!

r!f!rr!* a M1, M', M, an* M$, r!"!-ti/!l, an*

a""r3i#at!l #ar.!* in @i44 T+!! f0r #!a0r!#!nt

r!0lt, 2+!n -#bin!* t!t+!r =a 2! *!-rib! +rtl, in!-tin $>, all2!* 0 t btain t+! #!an /!l-it an*

t0rb0l!n-! tatiti- in t+! !ntir! 1'(

an0lar 2a.!%r!in t+atfll2!* t+! l!a*in i#"!ll!r bla*!4 Sin-! t+! i#"!ll!r bla*!

ar! i*!nti-al, t+! #!an fl2 an* t0rb0l!n-! tatiti-

*itrib0tin 20l* "!ri*i-all r!"!at !/!n in t+! 2a.! r!in

f t+! t+!r t2 bla*!4 T+!r!fr!, !ff!-ti/!l, t+! "r!!nt t0*

all2 0 t 0n*!rtan* t+! t0rb0l!n-! "r"!rti! f t+! fl2 in

t+! 2+l! &("a-! 0rr0n*in t+! rtatin i#"!ll!r4

O0r "r!/i0 t0*i! +2!* t+at t+! t0rb0l!n-! l!/!l in t+!

r!in ra*iall fart+!r fr# t+! #ar.!* #!a0r!#!nt r!in i

n!liibl! :1&,1,16;, a 2!ll a t+! fl2 /!l-it t+!r! i /!r

l28 t+!r!fr!, 2! !3-l0*!* t+at r!in fr# t+!

#!a0r!#!nt4

In a**itin t t+! afr!#!ntin!* t#ra"+i- PIV#!a0r!#!nt, 2! al "!rfr#!* a "+a!%l-.!* t!r! PIV

#!a0r!#!nt 2it+ t+! "itin f t+! bla*! a#! a t+at in t+!firt #!a0r!#!nt =M1>, in r*!r t a! 70antitati/! a--0ra-

f t+! t#ra"+i- PIV r!0lt b -#"arin t+!# 2it+ t+!

t!r! PIV r!0lt4 In t+! t!r! PIV #!a0r!#!nt, t+!

t+i-.n! f t+! la!r li+t +!!t 2a r!*0-!* t (4(D =

mm>, ##!tri-all, an* n0#b!r f t+! !!*in "arti-l! 2a

a*!70at!l in-r!a!* =in r*!r t btain +i+%fi*!lit r!0lt>,

2+il! all t+!r !3"!ri#!ntal "ara#!t!r 2!r! .!"t !3a-tl a#!

a t+! in t+! t#ra"+i- PIV #!a0r!#!nt4 In t+! i#a!anali, 2! 0!* t+! "arti-l! i#a! a-70ir!* b t+! -a#!ra 1

an* ' =!! @i4'>4

,. E-PERIMENTAL METHODOLOG(

T+! /!rall !3"!ri#!ntal !t0" -nit f =1> t+!

afr!#!ntin!* fl2 !#!tr, ='> "+!ri-al Nln "arti-l! fa/!ra! *ia#!t!r '( 'm, in r*!r t !!* t+! fl2, => f0r

Et+!rn!t%-nn!-t!* CC< -a#!ra, in r*!r t a-70ir! "arti-l!

i#a!, =$> a *0bl!%"0l! N*9YAG la!r 2it+ '(( m(/)u*sef

t+! #a3i#0# !n!r 0t"0t, =5> an "ti-al t!# t+at !3"an*

an* -n/!rt t+! !#itt!* r0n* la!r b!a# int a r!-tan0lar

la!r b!a# f -r%!-tin (4$$$D(4D =$(( mm'>, 2it+

it /!rti-al #i**l! "lan! "ain t+r0+ t+! -!ntral a3i f t+!

rtatin i#"!ll!r =fr t+! t!r! PIV #!a0r!#!nt, t+! la!rb!a# -r%!-tin 2a (4(D(4D =( mm'>> =&> a

*iital ti#!%*!la !n!ratr, =D> a "r!-i!, la!r%ba!*, "+a!%n-+rniatin #!-+ani# =*!tail!* !l!2+!r! :16;>, 2+i-+

all2!* 0 t a-70ir! t+! "arti-l! i#a! "r!-i!l at t+!

*!ir!* an0lar "itin f t+! i#"!ll!r bla*!, an* => a

-#"0t!r t n-+rni! t+! !l!-trni- !70i"#!nt an* t tr! t+! a-70ir!* "arti-l! i#a!4

In r*!r t r!*0-! t+! la!r%"2!r r!70ir!#!nt =2+i-+ i al2a a #att!r f -n-!rn in t#ra"+i- PIV !3"!ri#!nt>, 2!

0!* a "air f "lan! #irrr t r!fl!-t t+! !#!rin r!-tan0lar la!r b!a# ba-. int t+! fl2 *#ain4 )! a*0t!* anl!

)!*+re , An 0"i*!%*2n i#a! f t+! "it-+!*

i#"!ll!r HR%1(( :1$;, 2+i-+ i 0!* a t+! aitatr4

)!*+re ' S-+!#ati- *iara# f t+! fl2 *#ain9 t"an* frnt /i!24 All t+! "atial *i#!nin ar!

nr#ali!* 2it+ r!"!-t t t+! i#"!ll!r *ia#!t!r,D4


6/18

an* "itin f t+! #irrr a""r"riat!l, 0-+ t+at t+! r!fl!-t!* b!a# alin "arall!l an* ri+t ab/! t+! in-#in b!a#,

2+il! "r!!r/in it r!-tan0lar +a"! =a -+!#ati-all +2n in @i41>4 Mr!/!r, *0! t t+! * 70alit f t+! la

0!* t #a.! t+! fl2 tan. an* * 70alit #irrr, t+! "2!r f t+! r!fl!-t!* la!r b!a# i al#t a#! a t+at f t+!

in-#in b!a#4

T+! f0r CC< -a#!ra t+at 2! 0!* t a-70ir! t+! "arti-l! i#a! ar! al -+!#ati-all +2n in @i4'4 T+! -a#!ra ar!

arran!* at t+! f0r !n* f t+! )*us+a"! =J> an* l.in at t+! #!a0r!#!nt r!in t+r0+ t+! f0r 2in*2 f t+!2at!r "ri#4 T+! nr#al a3i f t+! )*us+a"! ="arall!l t t+! Z(a3i> a""r3i#at!l "a! t+r0+ t+! -!nt!r f t+!

#!a0r!#!nt /l0#!4 T+! anl! t+at t+! lin! f i+t f t+! t" an* t+! btt# /i!2in -a#!ra #a.! 2it+ !a-+ t+!r i

ab0t 5(4 T+! a#! i tr0! !/!n fr t+! l!ft an* t+! ri+t -a#!ra4 T+! S-+!i#"fl0 -n*itin, in r*!r t +ar"l /i0ali!

t+! ill0#inat!* /l0#!, i a-+i!/!* b 0in tilt%+ift l!n! f f-al l!nt+ !70al t $5 mm4 T+! i! f t+! a-70ir!*

"arti-l! i#a! i !70al t 1&((1'(()+!e*s4

In r*!r t #ini#i! r!fl!-tin fr# t+! inn!r 0rfa-! f t+! fl2 tan., 2+i-+ -an *!t!rirat! t+! 70alit f t+! a-70ir!*

"arti-l! i#a! inifi-antl b #a.in t+!ir ba-.r0n* bri+t!r, 2! -/!r!* t+r!! inn!r 0rfa-! f t+! fl2 *#ain 2it+*ar., nn%r!fl!-ti/!, -##!r-iall a/ailabl! t+in "a"!r +!!t, 2+i-+ 2!r! !"!-iall *!in!* t 2it+tan* in 2at!r fr

ln ti#!4 T+! la +0tt!r 2a l!ft 0n-/!r!*, t+at t+! fl2 -an b! /i0ali!* b t+! -a#!ra4 T+! a-70ir!* "arti-l!i#a! +a/! *ar. ba-.r0n*4 T+! bri+tn! f t+! !!*in "arti-l! i al#t a#! in bt+ t+! l2!r an* t+! 0""!r +al/!

f t+! i#a!, -nfir#in t+at t+! "2!r f t+! r!fl!-t!* la!r b!a# i al#t !70al t t+at f t+! in-#in b!a#4

Si#0ltan!0l, +2!/!r, 2! *i* b!r/! a bl0rr!* b0t -l!arl r!-niabl! b0n*ar t+at *i/i*! t+! t2 +al/! f t+!

i#a!4 )! *i* nt b!r/! an nti-!abl! !ff!-t f t+i b0n*ar n t+! btain!* /!l-it fi!l*4

In !a-+ f t+! f0r t#ra"+i- PIV #!a0r!#!nt, a ttal f ((($ "air f t+! "arti-l! i#a! ar! a-70ir!*, 2+i-+

20l* i!l* ((( t+r!!%*i#!ninal intantan!0 /!l-it fi!l*4 T+! ti#! int!r/al b!t2!!n t+! t2 i#a! f a "air i 5((

's4 B!fr! analin t+! "arti-l! i#a!, 2! tri!* t r!#/! an 0n2ant!* bri+tn! in t+!ir ba-.r0n* t+at #i+t b!"r!!nt, b 0btra-tin #ini#0# int!nit f t+! i#a!4 @r t+i "0r"!, 2! 0!* an O"!n S0r-! "rra# -all!* I#a!

:'1;4 )! anal!* t+!! i#a! 0in a !lf%*!/!l"!* GPU "rra# 2ritt!n in t+! CU, r!"!-ti/!l4 T+! /!rla" rati f t2 -n!-0ti/! int!rratin /l0#! i .!"t

!70al t 5(?, 2+i-+ i!l* t+! intantan!0 /!l-it /!-tr !"arat!* b (4(11D=1 mm>4 T+! /l0#! !ar-+ *itan-!,

2+!n -al-0latin t+! t+r!!%*i#!ninal -r%-rr!latin fr# t+! r!-ntr0-t!* /l0#!, i .!"t !70al t 6 v,!e*sin !a-+

"atial *ir!-tin, 2+i-+ i f0n* t b! 0ffi-i!ntl lar!4 O0r anali "rra# ta.! ab0t '$ m+-utest i!l* n! t+r!!%

*i#!ninal intantan!0 /!l-it fi!l* n a G!@ORCE GTQ TITAN GPU an* ab0t '( m+-utesn a G!@ORCE GTQ

)!*+re S-+!#ati- *iara# =t" /i!2> +2in *iff!r!nt "itin f t+! i#"!ll!r bla*! r!lati/! t t+! #!a0r!#!nt

r!in M1t M$4 Nt! t+at t+! bla*! "itin in t+! fift+ *iara# =#ar.!* a M=1>> i a#! a t+at in t+! firt *iara#

=#ar.!* a M1>4 T+! bla*! tra""!* in t+! #!a0r!#!nt r!in M1i t+! l!a*in bla*!4


7/18

6( GPU =bt+ b NVI, fr t+!

#!a0r!#!nt M1

f t+! t#ra"+i- PIV !3"!ri#!nt4 T+! int!rratin 2in*2 i! in t+! t!r! PIV anali i .!"t!70al t (4(D(4(D = mm'>4 Sin-! t+! t+i-.n! f t+! ill0#inat!* /l0#! +!!t i (4(D = mm> in t+! t!r!

PIV !3"!ri#!nt, it r!0lt -an b! r!liabl -#"ar!* 2it+ t+! t#ra"+i- PIV r!0lt4 )! btain!* a ttal f (((

intantan!0 /!l-it /!-tr fr !a-+ f t+!! t2 -a!4 )+!n -al-0latin -r%-rr!latin -!ffi-i!nt, 2! !t t+!

/!rla" rati !70al t &D?, in r*!r t btain t+! /!l-it /!-tr !"arat!* b 1 mm4

,.1. C#"er# C#$!/r#&!on

T+! -alibratin i "!rfr#!* 2it+ a *ar. -arbn "lat! f i! 6565 mm', 2+i-+ +a 2+it! -ir-0lar "t "rint!* n

it4 T+! *ia#!t!r f t+! -ir-0lar "t ar! (4$ mm, !3-!"t t+! -!ntral "t 2+! *ia#!t!r i 1mm, 2+i-+ i 0!* "ri#aril

fr r!f!r!n-! "0r"!4 T+! -!nt!r f t+! "t ar! !"arat!* b '46 mm4 T+! "atial a--0ra- f t+!! "t i b!tt!r t+an

1('m4 I#a! f t+! -alibratin "lat! ar! a-70ir!* aft!r #/in it t $1 *iff!r!nt#(l-atin, fr# F#( '( mmt F#

J'( mm, at t+! -ntant int!r/al f 1 mm4 Anali f t+! -alibratin i#a! +2!* t+at t+! -alibratin !rrr at *iff!r!nt

"itin f t+! "rint!* "t ar! *itrib0t!* in t+! ran! ('45)+!e*s4 H!r!, 2! 20l* li.! t !#"+ai! t+! i#"rtan-! f

t+!)*us=J> arran!#!nt f 0r -a#!ra, 2+i-+ i!l*!* n!arl%-ir-0lar i#a! f t+! -alibratin "t4 A nt!* !arli!r:1&,16;, 2+!n t+! -a#!ra 2!r! "la-!* at t+! !n* f t+! 1r,ss+a"! =>, int!a*, t+! i#a! f t+! -alibratin "t

b!-a#! !lli"ti-al, 2+i-+, in t0rn, 0btantiall in-r!a!* t+! -alibratin !rrr4

Sin-! t+! afr!#!ntin!* -alibratin !rrr i lar!r t+an t+! r!-##!n*!* li#it f (4$)+!e*s:'';, 2! intr*0-!* a "!-ial

"r-!*0r! in 0r /l0#! r!-ntr0-tin "rra# t a*!70at!l +an*l! lar! -alibratin !rrr4 Cn-!"t0all, t+i "r-!*0r!

firt btain an int!r"latin f0n-tin ba!* n t+! -alibratin !rrr *itrib0tin fr# all t+! -alibratin "t, fr !a-+

-a#!ra, t+at t+! -alibratin !rrr at an "int -an b! !ti#at!* r!liabl, !/!n if it *! nt li! n t+! -!nt!r f a

-alibratin "t4 Aft!r2ar*, t+! r!-ntr0-tin "rra# 0! t+!! f0r int!r"latin f0n-tin t a*0t !a-+ "i3!l f t+!

a-70ir!* "arti-l! i#a!, t+at t+! tra-!r "arti-l! -an b! r!-ntr0-t!* 2it+ +i+ fi*!lit4 In "ra-ti-!, t+! int!r"latin i

-arri!* 0t n0#!ri-all, b 0in a t+r!!%*i#!ninal -0bi- B%"lin! -*!, 2+i-+ i !#b!**!* in t+! GPU "rra# t+at 2!0!* fr t+! i#a! anali4

@r t+! t!r! PIV !3"!ri#!nt, 2! 0!* t+! a#! -alibratin i#a!, b0t nl t+! 2+i-+ 2! a-70ir!* at t+! l-atin F#( ' mm, 1 mm, (, J1 mm, an* J' mm4

,.'. Re"o0#$ o S2+r!o+s Ve$o3!&y Ve3&ors

t+! lin! #ar.!* a Bla*!%1, Bla*!%', an* Bla*!% a""r3i#at!l r!"r!!nt t+!

/!rti-al "lan! t+at "a t+r0+ t+! rtatin a3i an*, r!"!-ti/!l, *i/i*! t+! 2i*t+ f t+! t+r!! bla*! int t2 +al/! an*


8/18

='> Bla*!%1 r!"r!!nt t+! #i**l! lin! f t+! l!a*in bla*!4

N!3t, 2! !3tra-t!* t+! r!0lt in t+! an0lar r!in #ar.!*

a R1R$, fr# t+! #!a0r!#!nt r!in M1M$, r!"!-ti/!l4

T+! an0lar !3t!nt f !a-+ f t+!! an0lar r!in i ( 4

T+!r!fr!, alt!t+!r, 2! +a/! r!0lt in t+! !ntir! 1'( f t+!2a.! r!in t+at fll2 Bla*!%14

In !n!ral, 2+!n a "+i-al 70antit i rtat!* ab0t #!

a3i, it #anit0*! ar! alt!r!*4 Sin-! t+! rtat!* r!0lt ar!

!70i/al!nt t a if t+! ar! "r!!nt!* in a fra#! f r!f!r!n-!

t+at i rtat!* b t+! a#! anl! in t+! ""it! *ir!-tin =t

t+! t%b!%rtat!* r!0lt>, t+! alt!r!* #anit0*! -an b!

btain!* b analti-all r!"r!!ntin t+! fl2 70antit in t+!""it!l rtat!* r!f!r!n-! fra#! in t!r# f #! fl2

70antiti! in t+! riinal r!f!r!n-! fra#!4 In "!-ial -a!

2+!r! t+! t%b!%rtat!* fl2 70antit i an in/ariant r if it

r!"r!!nt a -n!r/atin la2, 0-+ a, rat! f -+an! f

!n!r f a 0btan-!, it /al0! r!#ain 0nalt!r!* !/!n in t+!

rtat!* r!f!r!n-! fra#!8 i4!4 /al0! f 0-+ a fl2 70antit

*! r!70ir! an alt!ratin, *!"it! it rtatin4 In t+! "r!!nt

t0*, 2! 2ill "r!!nt *itrib0tin f t+! tatiti-al 70antiti!Q, E, TKE, an* , in t+! !ntir! 2a.! r!in8 2+!r! =1> t+!

70antit Q i an in/ariant =it i t+! !-n* in/ariant f t+!#!an /!l-it ra*i!nt t!nr>8 ='> TKE i an in/ariant,

b!-a0! TKE (45 tra-! f t+! R!nl* +!ar tr!

#atri3 =t+! tra-! i t+! t+ir* in/ariant f t+! R!nl* +!ar

tr! #atri3>8 =>E in!ti- !n!r f t+! fl2 TKE, an* t+!r!fr! it i al an in/ariant8 an* =$> t+! 70antit i t+!

rat! at 2+i-+ t+! t0rb0l!n-! .in!ti- !n!r i "+i-all *ii"at!* t t+! int!rnal !n!r f t+! fl0i*, an* t+!r!fr! it /al0!

20l* al r!#ain 0naff!-t!* fr# t+! rtatin, i#ilar t t+! t+!r t+r!! 70antiti! Q, E, an* TKE4 Eff!-ti/!l, 2! -an

-#bin! t+!! fl2 70antiti! fr# t+! *iff!r!nt #!a0r!#!nt #!r!l b -+anin t+! "atial l-atin f t+! *ata "int,

a fll29

!n!2#(in2J!(-2

"n!2"(#n!2#(-2!(in2

2+!r! =!n!2,"n!2,#n!2> an* =!(,"(,#(> r!"r!!nt t+! n!2 an* t+! riinal "atial l-atin, an* 2i t+! anl! f t+! rtatin =a

#!ntin!* b!fr!, fr t+! r!0lt fr# t+! #!a0r!#!nt M1, M', M, an* M$, 2 1(, 1&(, 16(, an* ''(, r!"!-ti/!l>4

In t+i t0*, 2! 2ill "r!!nt t+! -#bin!* r!0lt in t+! !ntir! 1'(r!in a a 2+l! =2it+0t !"arat!l !#"+aiin n

t+! f0r an0lar r!in>4 In r*!r t #a.! !/i*!nt t+at t+! "r!!nt!* r!0lt ar! aft!r t+! rtatin, 2! 2ill 0! a n!2 ri+t

+an*!* Cart!ian -r*inat! t!# =Xn!2, Yn!2,Zn!2> in t+! "lt4 T+i n!2 -r*inat! t!# "!rf!-tl -in-i*! 2it+ t+!

riinal -r*inat! t!# =X(, Y(,Z(>4 On t+! t+!r +an*, 2! 2ill .!!" 0in t+! riinal -r*inat! t!# =X(, Y(,Z(> in

"lt f t+! 0nrtat!* r!0lt4

In #! -a!, 2! 2ill al "r!!nt li-!* -nt0r "lt, in r*!r t +2 int!rnal *itrib0tin f t+! fl2 70antiti!4 T+!

li-in in *n! b /!rti-al "lan! "ain t+r0+ t+! Y(A3i4 T+!! /!rti-al "lan! ar! !"arat!* b a -ntant anl! !70alt !it+!r 1(r 5=*!"!n*in n t+! "lt>4 )+!n t+! anl! f t+! !"aratin i 1( , t+! /!rti-al "lan! at =1> t+! an0lar

*itan-! (, 1(, an* '(fr# t+! l!a*in bla*! b!ln t t+! r!in R1=!! @i45>8 ='> t+! an0lar *itan-! (, $(, an*

5(b!ln t t+! r!in R'8 an* n4 Si#ilarl, 2+!n t+! !"aratin anl! i 5, t+! /!rti-al "lan! at =1> t+! an0lar

*itan-! (, 5, 1(, 15, '(, an* '5b!ln t t+! r!in R18 ='> at t+! an0lar *itan-! (, 5, $(, $5, 5(, an* 55

b!ln t t+! r!in R'8 an* n4 H!r!, 2! 20l* li.! t !#"+ai! t+at, *!"it! "r!!ntin t+! li-!* r!0lt in t+! ra*ial

"lan! =2+i-+ ar! t+! /!rti-al "lan! "ain t+r0+ t+! a3i f t+! rtatin>, t+! r!0lt it!lf ar! in t+! Cart!ian

-r*inat! t!# =Xn!2, Yn!2,Zn!2>4

)!*+re 5 S-+!#ati- *iara# f rtat!* #!a0r!#!nt

/l0#! in t+! n!2 -r*inat! t!# =Xn!2, Yn!2,Zn!2>4T+! -r*inat! t!# =X, Y,Z>, 2+i-+ i +2n in t+!l!ft%t" -rn!r f t+! *iara#, i 0!* =t+r0+0t t+i

t0*> t +2 nl ri!ntatin f t+! -r*inat! t!#

in 0!4


9/18

.'. S"oo&6!n*

Sin-! t+! 2at!r i a -ntin00 #!*i0#, "lt f all t+! tatiti-al fl2 70antiti! ar! !3"!-t!* t b! r!anabl #t+4

H2!/!r, t+! #!a0r!* tatiti-al r!0lt * /ar abr0"tl, a !/i*!nt fr# @i4&=a>, 2+i-+ +2 "lt f t+! t0rb0l!n-!

.in!ti- !n!r =TE> btain!* fr# t+! #!a0r!#!nt M14 S0-+ abr0"t -+an! in t+! "lt li.!l r!0lt fr# "r!!n-! f

ni! in t+! #!a0r! intantan!0 /!l-it fi!l*, a 2!ll a al *0! t i#"!rf!-t r!#/al f "0ri0 /!l-it /!-tr

fr# t+! r!0lt4 T+!r!fr!, 0-+ abr0"t -+an! +0l* #! #t+!* 0t, in r*!r t #a.! t+! r!0lt r!!#bl! t+! tr0!

/ariatin in a b!tt!r 2a4 In t+! "r!!nt t0*, 2! #t+!* 0t all t+! tatiti-al r!0lt b #!an f a "atial, t+r!!%*i#!ninal Sa/it.%Gla filt!r4 @r t+i "0r"!, 2! 0!* a i#"lifi!* a""ra-+ r!-!ntl "r"!* b S+!.+ar :'$;4

E!ntiall, a Sa/it.%Gla filt!r firt btain a l!at%70ar! "ln#ial /!r a -+!n *ata "at-+, an* t+!n !t t+! *ata

/al0! at a "atial "int =ini*! t+! "at-+> !70al t t+! /al0! f t+! l!at%70ar! "ln#ial at t+at "int4 K' $> *ata "int 2+i-+ li! -l!r t t+! b0n*ar !70al t t+!ir l-al /al0!4 T+! #t+!*

TKE "lt =-rr!"n*in t t+! riinal TKE"lt in @i4&=a>> i +2n in @i4&=b>4 A !/i*!nt fr# t+! fi0r!, t+!

#t+!* "lt a""!ar #0-+ b!tt!r, 2it+ !ail r!-niabl! *itrib0tin "att!rn4

5. RESULTS AND DICUSSION

At firt, 2! "r!!nt t+! #!an /!l-it fi!l* -rr!"n*in t t+! #!a0r!#!nt M 1, in @i4D=a>, in fi/! *iff!r!ntZ"lan!, int+! riinal -r*inat! t!# =X(, Y(,Z(>4 T+! =U, V> /!l-it -#"n!nt ar! +2 b #!an f /!l-it /!-tr, 2+!r!a

t+! 0t f t+! "lan! /!l-it -#"n!nt, W, i +2n b -nt0r -lr4 T+i #!an /!l-it fi!l* an* t+! t0rb0l!n-! .in!ti-

!n!r "lt in @i4&=b>, t!t+!r, +2 t+at t+! fl2 i a-ti/! nl in t+! ri+t +alf f t+! "lt, 2+!r!a t+! l!ft +alf n!it+!r

+a an inifi-ant #!an /!l-it nr an t0rb0l!n-!4 )! b!r/!* i#ilar *itrib0tin !/!n in 0r "r!/i0 t0*i!

:1,15,1&,1,16;4 T+! fi0r! f0rt+!r -nfir# t+at t+! i#"!ll!r "0+! t+! fl2 in t+! *2n2ar* *ir!-tin 2it+ lar!

/!l-it, 2+i-+ al -n/!-t t+! t0rb0l!n-! "r*0-!* at t+! bla*!%2at!r int!rfa-! in t+! *2n2ar* *ir!-tin, 2+i-+, in

t0rn, #a.! t+! t0rb0l!n-! l!/!l b!l2 t+! rtatin i#"!ll!r lar!r t+an t+!r r!in in t+! fl2 *#ain4 In t+! #( ( "lan!

f t+! #!an%/!l-it "lt, 2! -an -l!arl b!r/! a -ir-0lar "t f +i+l n!ati/! W, ab0t t+! l-atin =!(,"(,#(> =(45,

)!*+re 7 T0rb0l!n-! .in!ti- !n!r "lt 8#9b!fr! an* 8/9aft!r #t+in 0in Sa/it.%Gla filt!r, -rr!"n*in tt+! #!a0r!#!nt M1=in t+! riinal -r*inat! t!#>4

8#98/9


10/18

(4(, (>, fll2!* b a""!aran-! f a /rt!3 in t+! fll2in "lan! #( (41 an*#( (4'4 T+i /rt!3 i ft!n r!f!rr!* a

ti"%/rt!34 T+! +i+l n!ati/! Wr!in in t+!#( ( "lan! in*i-at! "r!!n-! f a "rtin f t+! l!a*in bla*! ab0t t+at

l-atin4 @i4&=b> al 0!t t+! "r!!n-! f t+! bla*! ab0t t+! #( ( "lan!, a 2! -an -l!arl b!r/! an !lnat!*

r!in f lar! TKEin t+at "lan!, in*i-atin "r*0-tin f t+! t0rb0l!n-! n t+! bla*!%2at!r int!rfa-! =a t+! bla*! -0t

t+r0+ t+! 2at!r>4 In t+! 2a.! r!in, t+i t0rb0l!n-! ra*0all *iff0!, a it i -n/!-t!* *2n2ar* b t+! #!an fl24 In

fa-t, "r!!n-! f t+! bla*! -an al b! b!r/!* in t+! #( (41 "lan! f t+! TKE"lt, a t+! "rtin f t+! 0"2ar* t2it!*

bla*! #a.! t+! TKE#anit0*! +i+ at t+! 0""!r !*! f "lt4 T+!r! i n !lnat!* r!in f lar! TKEin t+!#( (4'"lan!, in*i-atin t+at t+! bla*! "rtin in t+at "lan! fall ab/! 0r #!a0r!#!nt /l0#!4

T+!r! i ant+!r r!in f lar! TKE in t+!#( (41 an* t+! #( (4' "lan! at li+tl *2n2ar* l-atin t+an t+!

!lnat!* r!in f lar! TKEin t+!#( ( an* t+!#( (41 "lan!4 T+! TKE#anit0*! in t+i r!in i #all!r t+an t+at

+2n in t+! #( "lan!, a 2!ll a t+! #!an /!l-it fi!l* *! nt +2 !3it!n-! f an /rt!3 t+!r! =!! @i4D=b>>4

Mr!/!r, t+i r!in i at a #all!r *itan-! fr# t+! a3i f t+! rtatin4 All t+!! b!r/atin 0!t t+at t+i +i+

t0rb0l!n-! r!in i li.!l -r!at!* at #! inn!r, fr2ar* "rtin f t+! 0"2ar* t2it!* #/in bla*! an*, 0b!70!ntl,

-n/!-t!* *2n2ar* t it -0rr!nt l-atin, fat, b t+! /!rti-al -#"n!nt f t+! #!an fl24

5.1. Vor&!3#$ S&r+3&+res

T+! !3it!n-! f t+! ti"%/rt!3 i in t+! fl2 i +2n b t+! Q-rit!rin :'5;, 2+!r! Qi t+! !-n* in/ariant f t+! #!an

/!l-it ra*i!nt t!nr4 Mat+!#ati-all, Q 1

2UiXj

UjXi

. In t+! "r!!nt t0*, Sa/it.%Gla *iff!r!ntiatr ar! 0!* t

-al-0lat! t+! #!an /!l-it *!ri/ati/!4 T+! r!in 2+!r! Q 1 i tr!at!* a t+! r!in 2+!r! a /rt!3 t0b! !3it4 I*!all,QW ( r!"r!!nt a /rt!3, b0t +!r! Q 1 i -+!n, int!a*, t *i-ar* n!liibl 2!a. /rti-!4 T+! QX 1 r!in i#itt!* fr# t+! "lt, fr -larit "0r"!4 T+! t" /i!2 f t+! t+r!!%*i#!ninal -lr -nt0r f Qi +2n in @i44 @r

b!tt!r /i0aliatin, an i#!tri- /i!2 f t+! Q"lt i +2n in @i46=a>4 A !/i*!nt fr# t+!! "lt, 2! -0l* 0--!f0ll

-a"t0r! t+! ti"%/rt!34 H2!/!r, i#0ltan!0l, 2! -an al b!r/! t+at t+! fr2ar* r!in f t+! /rt!3 t0b! i li-!*

0t, in*i-atin t+at 0r #!a0r!#!nt r!in M1li! li+tl b!l2 0""!r "rtin f t+! ti" f t+! rtatin bla*!4 T+! li-!*

0t r!in al in*i-at! t+at t+i /rt!3 t0b! a""r3i#at!l -in-i*! 2it+ t+! ra*iall 0t!r "rtin f t+! !lnat!* TKE

r!in in t+!#( ( "lan! f @i4&=b>4 A t+! ti"%/rt!3 i -n/!-t!* *2n2ar* in t+! 2a.! r!in, it tart fallin 2!ll

2it+in t+! fll2in #!a0r!#!nt r!in M', M, an* M$4

)!*+re 8#9 M!an /!l-it "lt -rr!"n*in t t+!#!a0r!#!nt M1=in t+! riinal -r*inat! t!#>4 T+!

=U, V> -#"n!nt ar! r!"r!!nt!* b /!-tr, 2+!r!a t+!

W-#"n!nt i r!"r!!nt!* b -lr -nt0r4

)!*+re 8/9 T0rb0l!n!- .in!ti- !n!r =TKE> "lt-rr!"n*in t t+! #!a0r!#!nt M1=in t+! riinal

-r*inat! t!#>4 T+! =U, V> /!l-it -#"n!nt ar!

r!"r!!nt!* b /!-tr4


11/18

T+! Q"lt =!! @i4 an* 6=a>> al +2 t+! "r!!n-! f a !-n*ar /rt!3 lin 0n*!r t+! "ri#ar /rt!34 T+i

!-n*ar /rt!3 i al a ti"%/rt!3, b0t -r!at!* b t+! "r!-!*in bla*!4 It tr!nt+ +a inifi-antl fa*!* 0t 2it+ ti#!an* it +a b!-#! t+i-.!r4 T+! "lt al +2 t+! "r!!n-! f an inn!r /rt!3, 2+i-+ i li.!l -r!at!* b inn!r "rtin f

)!*+re ; T" /i!2 f t+! -#bin!* Q"lt, in t+! =Xn!2, Yn!2,Zn!2> -r*inat! t!#4 T+! "lt -l!arl +2 "r!!n-! f

t+! ti" /rti-! an* t+! inn!r /rt!34 A""r3i#at! "itin f t+! i#"!ll!r bla*! =!"arat!* b 1'(> ar! al +2n4Bla*!%1 i t+! l!a*in bla*!4 @r -larit "0r"!, t+! QX 1 r!in ar! #itt!* fr# t+! "lt4

)!*+re


12/18

t+! bla*!4 @0rt+!r#r!, t+!r! i n !/i*!n-! t+at t+i inn!r /rt!3 fall i##!*iat!l aft!r t+! l!a*in bla*!, in*i-atin t+at it

-#! int !3it!n-! nl #! ti#! aft!r t+! bla*! +a "a!*4

T+! li-!* /i!2 f t+! Q"lt in @i46=a> i "ltt!* in @i46=b>, in r*!r t +2 int!rnal /ariatin f Qini*! t+! /rt!3

t0b!4 @r t+! a#! r!an, li-!* /i!2 -rr!"n*in t t2 t+!r i#!tri- /i!2 f t+! a#! Q"lt ar! "r!!nt!* in@i41(=a> an* =b>4 T+! li-! ar! an0larl !"arat!* b 5, in all t+!! "lt4 A !3"!-t!*, t+! Q#anit0*! ra*0all

in-r!a! a 2! #/! t2ar* t+! -r! f t+! t0b!, in*i-atin in-r!ain tr!nt+ f t+! /rt!3, a !3"!-t!*4 Alt+0+ nt

a""ar!nt in t+! "lt, t+! #anit0*! f Qb!-#! a lar! a 1&( in t+! -r! r!in4 On t+! t+!r +an*, t+! #anit0*! f

t+! /rt!3 ra*0all *!-r!a! an* t+! i! in-r!a! 2+!n 2! #/! t2ar* t+! tail f t+! /rt!3 t0b!, in*i-atin t+at t+!

/rt!3 *iff0! 2it+ ti#!4 T+! li-!* Q"lt al +2 t+at t+! tr!nt+ f t+! !-n*ar ti"%/rt!3 /ar /!r l2l a 2!

#/! t2ar* it tail4

5.'. Ener*y o &6e Me#n )$ow

T2 li-!* "lt f t+! !n!rEf t+! #!an fl2 i "r!!nt!* in @i411=a> an* =b>4 T+! li-! ar! an0larl !"arat!* b1(4 Mat+!#ati-all,E =U'J V'J W'>K', 2+!r! #t+!* /al0! ar! 0!* fr t+! #!an /!l-it -#"n!nt4 T+! "lt

-l!arl +2 t+at, aft!r t+! bla*! -0t t+r0+ t+! 2at!r, #anit0*! f t+! #!an /!l-it r!*0-! fat in t+! 2a.! r!in4

T+! r!in f /!r lar!E, in t+! 'n*an* t+! r*li-! fr# t+! l!a*in bla*!, +2 t+! l-atin 2+!r! #! "rtin f

t+! bla*! i "r!!nt4 T+! "lt al -nfir# t+at Ei inifi-antl lar! in t+! r!in b!l2 t+! rtatin i#"!ll!r, b0t

n!liibl! in t+! r!in ra*iall 0ti*! =t+i r!in, 2+i-+ i i*!ntifi!* bEX (4(1, i #itt!* fr# t+! "lt>4

It 20l* b! !/i*!nt fr# 0"-#in "lt f t+! in*i/i*0al /!l-it -#"n!nt in !-tin 54$ =!! @i41> t+at, *ir!-tl

b!l2 t+! i#"!ll!r, t+! U-#"n!nt f t+! fl2 /!l-it i t+! lar!t, 2+!r!a #anit0*! f t+! t+!r t2 -#"n!nt,Van* W, b!-#! inifi-ant nl at *2n2ar* l-atin4 In fa-t, t+! U"lt -ntit0t! a r!in f f0r *itin0i+abl!

+rintal la!r 2it+ alt!rnatin /!l-it *ir!-tin4 In t+! t" la!r, t+! U i "iti/!, t+!n it b!-#! n!ati/!, t+!n"iti/!, an* t+!n n!ati/! aain4 T+! V"lt =!! @i41>, n t+! t+!r +an*, i n!ati/! in t+! !ntir! /!rti-al r!in 0n*!r

t+! i#"!ll!r4 T+! W"lt =!! @i41> i n!ati/! in t+! !ntir! #!a0r!#!nt r!in, b0t t+! #anit0*! r!#ain !it+!r

#*!rat! r #all, !3-!"t in t+! /i-init f t+! #/in bla*!4

5.,. T+r/+$en3e K!ne&!3 Ener*y #nd T+r/+$en3e D!ss!2#&!on R#&e

)! -al-0lat!* t+! t0rb0l!n-! .in!ti- !n!r =TKE> fr# #t+!* t0rb0l!n-! int!nit -#"n!nt uRMS, vRMS, an* wRMS, b

0in t+! r!latin+i" TKE= 12

(uRMS2 + v RMS2 + w RMS2 ) . In r*!r t -al-0lat! t+! t0rb0l!n-! *ii"atin rat!, , 2! 0!* a t2 t!"

)!*+re 1= Ant+!r li-!* Q"lt, in t+! =Xn!2, Yn!2,Zn!2> -r*inat! t!#4 T+! li-! ar! an0larl !"arat!* b 54 @r

-larit "0r"!, QX 1 r!in ar! #itt!* fr# t+! "lt4

8#9 8/9


13/18

"r-!*0r!4 @irt, 2! -al-0lat!* it /al0! 0in #t+!* /al0! f t+! nin! t0rb0l!n-! +!ar train -#"n!nt Si,

a--r*in t t+! r!latin+i" (1)= 'Re

+

3

S+3', 2+!r! t+! 0"!r-ri"t =1> r!"r!!nt an int!r#!*iat!, t!#"rar /al0! f 4

)!*+re 11 T2 li-!* /i!2 f t+! "lt +2in .in!ti- !n!r f t+! #!an fl2, in t+! =Xn!2, Yn!2,Zn!2> -r*inat! t!#4

T+! li-! ar! an0larl !"arat!* b 1(4 @r -larit "0r"!, t+!EX (4(1 r!in ar! #itt!* fr# t+! "lt4

8#9 8/9

)!*+re 1' Sli-!* /i!2 f 8#9t0rb0l!n-! .in!ti- !n!r an* 8/9t0rb0l!n-! *ii"atin rat! "lt, in t+! =Xn!2, Yn!2,Zn!2>

-r*inat! t!#4 T+! li-! ar! an0larl !"arat!* b 1(4 @r -larit "0r"!, TKEX (4(' an* X (4' r!in ar!

#itt!* fr# t+! "lt, r!"!-ti/!l4

8#9 8/9


14/18

H!r!, t+! +!ar train -#"n!nt Si, 2+i-+ -an b! i/!n aS+3=1

' ( u+!3

+u3!+)

'

, ar! -al-0lat!* *ir!-tl fr# t+! PIV

#!a0r!#!nt r!0lt =fll2!* b 0b!-tin t+! -al-0lat!* /al0! t t+! Sa/it.%Gla filt!r, in r*!r t btain t+!ir

#t+!* /al0!>4 Nt! t+at, in r*!r t r!liabl -al-0lat! t0rb0l!n-! *ii"atin rat! *ir!-tl fr# an !3"!ri#!ntal *ata,

#all -al! #tin =-#"arabl! t l#r/ -al!> f t+! t0rb0l!n-! #0t b! r!l/!*4 In 0r t#ra"+i- PIV

#!a0r!#!nt, t+! int!rratin /l0#! i! in !70al t ' mm, 2+i-+ #0-+ lar!r t+an t+! l#r/ l!nt+ -al! :1;,

an* t+!r!fr! t+! *ir!-tl -al-0lat!* /al0!, =1>, 20l* b! #0-+ #all!r t+an t+! tr0! /al0! f 4 In r*!r t !ti#at! tr0!/al0! f , 2! a""li!* a 0bri* #*!l =2+i-+ i t+! bai f t+! Lar! E** Si#0latin =LES>> n =1>, in t+! !-n* t!"4

Mat+!#ati-all, t+! #*!l -an b! i/!n a = t

(1) 2+!r!

t

= ( &s )$

ReB (1) +1

1

'

1, &s4 (41D, Z int!rratin

/l0#! i! (4('''D, an* [ (4D(4 )! r!"rt!* *iff!r!nt a"!-t f t+i #*!l !l!2+!r! :1;, in *!tail4

)! "ltt!* li-!* /i!2 f TKEan* in @i41'=a> an* =b>, r!"!-ti/!l4 T+! li-! ar! an0larl !"arat!* b 1(4 )! -anr!a*il b!r/! fr# t+! "lt t+at t+! *itrib0tin "att!rn f TKEan* ar! /!r i#ilar t !a-+%t+!r4 T+! "lt al +2

t+at, initiall, t+! t2 70antiti! ar! lar! ini*! t+! -r! f t+! ti"%/rt!3, b0t t+! ra*0all *!-r!a! in t+! 2a.! r!in, a

t+! /rt!3 *iff0!4 @0rt+!r#r!, t+!! 70antiti! ar! lar! nt nl ini*! t+! "ri#ar /rt!3, b0t al ini*! t+! inn!r

/rt!3 t+at *!/!l"!* at a -l!r *itan-! fr# t+! rtatin a3i4 T+! #anit0*! ini*! t+! !-n*ar /rt!3 ar! #0-+

#all!r t+an t+at in t+! "ri#ar =a 2!ll a t+! inn!r> /rt!3, a !3"!-t!*4

)! -an al b!r/! lar! #anit0*! f t+! t2 t0rb0l!n-! 70antiti! in t+! /!r firt li-!, a 2!ll a in lat f!2 li-! =int+! "lt, t+!! ar! #ar.!* a -n/!-t!* t0rb0l!n-!>4 Sin-! n!it+!r t+! Q"lt =!! @i46 an* 1(> nr t+!E"lt =!!@i411=b>> +2 an !/i*!n-! f a /rt!3 at t+!! l-atin, t+!! lar!%t0rb0l!n-! fl0i* l0#" +a/! li.!l *!-!n*!* fr#

0"4 A 2! al *!-rib!* b!fr!, t+!! fl0i* l0#" ar! -r!at!* b t+! fr2ar* "rtin f t+! #/in bla*! an* -n/!-t!**2n2ar* b t+! #!an fl24

5.. >+#n&!&!0e A33+r#3y o &6e Res+$&s

)! a!!* 70antitati/! a--0ra- f 0r t#ra"+i- PIV r!0lt b -#"arin t+! btain!* #!an /!l-it an* t0rb0l!n-!

int!nit -#"n!nt 2it+ t+! r!0lt btain!* fr# t!r! PIV, in t+! #!a0r!#!nt r!in M 1=!! @i4$>4 @irt, 2! "ltt!*

U, V, an* W-#"n!nt btain!* fr# t+! t2 PIV #!a0r!#!nt in @i414 T+! r!0lt ar! "ltt!* in t+! #( ( "lan!4

Sin-! t+! t!r! PIV r!0lt ar! btain!* in a lar!r r!in, t+! r!in 2+i-+ -rr!"n* t t+! t#ra"+i- PIV#!a0r!#!nt r!in i #ar.!* b a r!-tanl!4 T+! t2 !t f t+! "lt -l!arl +2 r!anabl * ar!!#!nt b!t2!!n

t+! t2 #!a0r!#!nt, in*i-atin t+at t+i-. /l0#! t#ra"+i- PIV #!a0r!#!nt -an b! r!liabl 0!* t btain #!anfl2 fi!l*4 Sin-! t+! Qi al -al-0lat!* fr# #!an /!l-it, t+i ar!!#!nt -nfir# t+! a--0ra- f t+! *!t!-t!* /rti-!

="ltt!* in @i4, 6, an* 1(>4

)! "ltt!* t+! uRMS, vRMS, an* wRMSin @i41$, fr t+! a#! t2 PIV #!a0r!#!nt4 T+!! "lt +2 t+at, alt+0+ t+!

*itrib0tin "att!rn ar! a""r3i#at!l i#ilar in bt+ !t f t+! "lt, t+! ar! inifi-antl *iff!r!nt in 70antitati/! !n!4

T+! *iff!r!n-! i !"!-iall lar! at l-atin f +i+ t0rb0l!n-!, 0!tin t+at t5+1$6v,*ume t#ra"+i- PIV#!a0r!#!nt #a nt b! 0itabl! 2+!r! +i+ 70antitati/! a--0ra- f t0rb0l!n-! tatiti- i *!ir!*, b0t #a till b! 0!*

t 0n*!rtan* t+! fl2 "+!n#!nn in a 70alitati/! !n!4

7. CONCLUSIONS

O0r t#ra"+i- PIV #!a0r!#!nt 0--!f0ll -a"t0r!* t+! ti"%/rti-! "r!!nt in t+! !ntir! 1'(

2a.! r!in t+atfll2 a l!a*in bla*!4 T+! ti"%/rti-! *!t!-t!* 0in t+! Q-rit!rin -nfir#!* t+at t+! /rt!3 ra*0all *iff0! in t+!2a.! r!in, b0t, n!/!rt+!l!, "!rit b!n* t+! fll2in bla*!4 O0r "lt fr t+! !n!r f t+! #!an fl2 r!/!al!* t+at

a ti"%/rt!3 i -r!at!* b ba-.2ar* "rtin f t+! l!a*in bla*!4 T+! fr2ar* "rtin, +2!/!r, -r!at! +i+l t0rb0l!n-!fl0i* l0#", 2+i-+ 70i-.l !t -n/!-t!* *2n2ar* b t+! #!an fl2, l!a*in t a""!aran-! f +i+l t0rb0l!nt "t

b!fr! t+! +!a* f t+! ti" /rt!34 T+! r!0lt f0rt+!r r!/!al!* t+at t+! t0rb0l!n-! .in!ti- !n!r an* t+! t0rb0l!n-!

*ii"atin rat! "lt =2+!r! t+! latt!r i !ti#at!* 0in a 0bri*%tr! #*!l *!tail!* !l!2+!r! :1;> !3+ibit tri.inl

i#ilar *itrib0tin "att!rn4 )! al b!r/!* "r!!n-! f an inn!r /rt!3, 2+i-+ i inifi-antl 2!a.!r t+an t+! "ri#ar

ti"%/rt!3, li! at a -l!r *itan-! fr# t+! a3i f rtatin, a""!ar lat!, an* lat nl fr a +rt ti#!4 T+i inn!r /rt!3 i

li.!l -r!at!* b ra*iall inn!r "rtin f t+! bla*!4 O0r a!#!nt f 70antitati/! a--0ra- +2!* t+at t5+1$6v,*ume


15/18

)!*+re 1, C#"arin b!t2!!n t+! St!r! PIV =l!ft +an* i*! "lt> an* t+! T#ra"+i- PIV r!0lt =ri+t +an*

i*! "lt>4 T+! #!an /!l-it -#"n!nt U, V, an* W=in t+!#( ( "lan!> ar! "ltt!* in t+! t", #i**l!, an*

btt# r2, r!"!-ti/!l4

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X)

X)

X)

X)

X)

Y)

Y)

Y)

Y)

Y)

Y)

S&ereo PIV To"o*r#26!3 PIV


16/18

)!*+re 1 C#"arin b!t2!!n t+! St!r! PIV =l!ft +an* i*! "lt> an* t+! T#ra"+i- PIV r!0lt =ri+t +an*

i*! "lt>4 T+! t0rb0l!n-! int!nit -#"n!nt uRMS, vRMS, an* wRMS=in t+!#( ( "lan!> ar! "ltt!* in t+! t",

#i**l!, an* btt# r2, r!"!-ti/!l4

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X)

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S&ereo PIV To"o*r#26!3 PIV


17/18

t#ra"+i- PIV #!a0r!#!nt -an b! 0!* t *!-i"+!r lar! -al! tr0-t0r! an* #!an /!l-it *itrib0tin 2it+

r!anabl * 70antitati/! a--0ra-4 S0-+ #!a0r!#!nt -an al b! "!rfr#!* t +a/! a 70alitati/! 0n*!rtan*in f

t0rb0l!n-! tatiti- *itrib0tin, b0t #a nt b! 0itabl! t btain t+!ir 70antitati/!l a--0rat! /al0!4 @r *

70antitati/! a--0ra- f t+! t0rb0l!n-! tatiti-, t+in%/l0#! t#ra"+i- PIV #!a0r!#!nt ar! r!-##!n*!*, a 2!

r!"rt!* !l!2+!r! :16;4

ACKNO?LEDGEMENTS

)! 20l* li.! t r!atl t+an. 7eamte15 8)tr,-+1s &, 9td: fr l!ttin 0 0! t+!ir V*+te6%;; la!r fr t+! "r!!nt

#!a0r!#!nt4 )! al !3t!n* 0r in-!r! t+an. t Mr: Masa5+t, Ta$e#awa\a "t%ra*0at! t0*!nt at Y,$,5ama

""4$5$614

:D; +".ar AR, A0bin , Q0!r!b C, Sa0! NL, B!rtran* an* Rana*! VV Ga%li70i* fl2 !n!rat!* b a "it-+!* bla*! t0rbin!9 PIV

#!a0r!#!nt an* C@< i#0latin In*0trial ] Enin!!rin C+!#itr R!!ar-+ $' ='((> ""4515'4

:; G! CY, )an , G0 QP an* @!n L@ C@< i#0latin an* PIV #!a0r!#!nt f t+! ^2 _!l* !n!rat!* b #*i_!* "it-+!* bla*! t0rbin!i#"!ll!r C+!#i-al Enin!!rin R!!ar-+ an* ""41('D1(&4

:6; Rana*! VV, Taalia Y an* ri+nan H C@< "r!*i-tin f fl2 n!ar i#"!ll!r bla*! in baffl!* tirr!* /!!l9 a!#!nt f -#"0tatinalna"+t a""ra-+ C+!#i-al Enin!!rin C##0ni-atin 16 ='(('> ""4656''4

:1(; Rana*! VV an*

Enin!!rin S-i!n-! &1 ='((&> ""4'D66'(&4

:1';

:1; S+!.+ar C, Ni+in , Ya#an! Y an* H0an St!r!%PIV #!a0r!#!nt f t0rb0l!n-! -+ara-t!riti- in a fl2 #i3!r 0rnal f

Vi0aliatin 15 ='(1'> ""4'6%(4

:1$; HR%1(( i#"!ll!r i #an0fa-t0r!* b Sata.! C+!#i-al E70i"#!nt Li#it!*, a"an4

:15; S+!.+ar C, Ni+in an* I Y St!r!%PIV #!a0r!#!nt f +!ar tr! in a tirr!* fl2 #i3!r 1(t+ Int!rnatinal S#"i0# n Parti-l!I#a! V!l-i#!tr, 4


18/18

:1D; M!r , R!!*!r M@ an* @aan B O"ti#i! #i3in b 0in t+! "r"!r baffl! C+!#i-al Enin!!rin Prr! 61 ='(('> ""4$'$D4

:1; S+!.+ar C, Ta.a+a+i , Mat0naa T an* Ni+in A""li-atin f 0bri* tr! #*!l t /l0#!tri- PIV r!0lt fr !ti#atin ft0rb0l!n-! *ii"atin rat! in a tirr!* #i3!r 11t+ Int!rnatinal Cnf!r!n-! n H!at Tranf!r, @l0i* M!-+ani- an* T+!r#*na#i-, r0!r

Natinal Par., S0t+ Afri-a ='(15> ""4$'D$54

:16; S+!.+ar C, Ta.a+a+i , Mat0naa T an* Ni+in T#ra"+i- PIV #!a0r!#!nt f t0rb0l!n-! !n!r b0*!t !70atin t!r# in a

70ar! +a"!* tirr!* fl2 #i3!r 1D t+Int!rnatinal S#"i0# n A""li-atin f La!r T!-+ni70! t @l0i* M!-+ani-, Libn, Prt0al='(1$>4

:'(; Ta.a+a+i , S+!.+ar- C, #at0naa T an* Ni+in In/!tiatin f rtatin "!!* *!"!n*!n-! f fl2 "r"!rti! b t#ra"+i- PIV#!a0r!#!nt in a tirr!* #i3!r 11t+ Int!rnatinal S#"i0# n Parti-l! I#a! V!l-i#!tr, Santa Barbara, USA ='(15>4

:'1; H#!"a! fr t+!=ma.e("!n 0r-! ft2ar!95tt)>//www:+ma.e3:-et4

:''; S-aran @ T#ra"+i- PIV9 "rin-i"al an* "ra-ti-! M!a0r!#!nt S-i!n-! an* T!-+nl '$ ='(1> (1'((14 ""4'1$'164

:'$; S+!.+ar C On i#"lifi!* a""li-atin f #0lti*i#!ninal Sa/it.%Gla filt!r an* *iff!r!ntiatr t, 0e )u0*+s5ed +-Prr! in A""li!*

Mat+!#ati- in S-i!n-! an* Enin!!rin, Bali, In*n!ia ='(15>4

:'5; H0nt CR, )ra AA an* Min P E**i!, tr!a#, an* -n/!r!n-! n! in t0rb0l!nt fl2 C!nt!r fr T0rb0l!n-! R!!ar-+ R!"rt CTR%

S =16> ""416'(4

:'&; H!r#an GT an* L!nt A It!rati/! r!-ntr0-tin alrit+# C#"0t!r in Bil an* M!*i-in! & =16D&> ""4'D'6$4
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Whole-field flow measurement inside a stirred mixer using Tomographic PIV technique

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