Experimental Investigation of High Frequency Combustion Instability In
!"#$
%&'# (' ") *' +" , ,- +.#'/ ' 01,(2 , "2 ) 1 #1,+' 0%1+' 1$#,+' ,03' + '
! " # $ % &%
, '
, ' !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
,-- + #' !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! *
,- "2)' !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! %
), "#1!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! %
2 #"0 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! %
'0)"#" , ,-,# + ") 1 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! %*
03 ,4)'$+'(' " $$ 0)" ('#!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! %*
5! #,$ 0 , !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 5
6! "03+#, $!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 7 % & ' ( % % )*$ $ + % ( '!$ $ * , % ( & '!$ $ *$ - % ( % '!$ $ . % ( ( /0 $ 1 % ( + " $ & % + 234 $ $ && % + & && % + % '!33 &% % + ( $ &% % 5 $ &+ % & " $ 0 & % % !$ $ & % ( &, % + 6 $ &, % 5 &, % , 5 &- % , & 5 &- % , % ! &. % , ( # &1 % , + 5 %&
7! '#" #' #*'1 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 68 ( & / $&1-% %- ( % / &1-%&11 (, ( ( $ (, ( + ) 7 +& ( + & 84 9 +& ( + % ) 9 +
( &
9! ,(2 ,#$'*'),&(' !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!:7 + & 3$ 9 ( + & & 9 ( + & % 5)5 + & ( /5 6 - + & + " 1 + & " 1 + & , , + % 89 $ , + % & 2$ , + % % ,& + % ( /0 ,% + ( 5$ ,( + ( & 5$&: $ 5)5 ,( + ( % 5$%:) ,+ + ( ( 5$(:3 ;<; , + ( + 5$+:) ;<; ,, + ( 5$ :9 ;<; ,. + ( , 5$ ,1 + + 89 :;< - + + & ;< $ 9 - + + % 5 -& + + ( " 0 -% + + + 0 -( + + # - + + , 2$ -, + + - 3 -,
:! %&'# (' ") '0. / ' !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!;5 & $ .& & & .& & % $ .& & ( 9 .% & + .% & ! .+ % # ! . ( 2$ ., ( & 2 = ., ( % 9 $ .. ( ( 2 = 9$ $ .. + 5 $ & %: 9 .. + & $&> .1 + % $%> 9$ 1 + ( $(>93 $ 1% 5 $ ( +:3 $9 1 & $+>93 1, % $ >93 $ 1- , 5 $ :3 $9 & & , & $,>993 & & , % $->93 $ & & - $ & %
, & 7 & ( , % $ & , ( : && , + 3 &&+ , + & $ &&+ , + % '9 ! &&- , + ( 3 $ &&. , 5 $ &%& , , /0$ &%+ , - &%.
8! )"('#' &, ' !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 56> - & )9 $ &%1 - % 7 &(& - ( 7 $ &( - + # 2 = $ &(- - # $ 3 &+& - , # $ 3 &+, - - " $ $ &+1 - . &
;! %1+' 0,#'#' &, '!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 5:7 . & )93 & ( . % 23 & . ( # $ 3 &,& . + / &,+ . &- . , &-(
>! , 0) , !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 58:
5=! ),,3!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 588
55! '-'#' 0' !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 58>
&&' $ % ! 4 #' , " ,# '+(' $' + $1 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 5;> & 9 &.1 % / 9 &1& ( 0 &1+ + ? &11 &11
&&' $ %! $ (' , !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 6=5 ; & 5 9 % &
&&' $ %! ,$ - '$ '0, $"#1 ,??)'!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 6=: 5 & )@@ %
5 % # @@ % ,
&&' $ %! ,-"# 0)' #' ) +-#,( . 4,#3!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!6=> # & % 1 # % 5 $ $ % 1
,-- + #'
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
,- "2)'
&:$ $ $ *$ . %: $ $ $ $ && (:5 $ $ 3 &( +: ! ;< -% :;< 0 $ -( ,:7 ! ;< 9 9 @@ &&+ -: $ $ ;< 3 &&1 .:/0$ $ &(& 1:/0$ 9 9 $ & & : G $ $ $ $ '23 $ 3 $ &-%
), "#1
8 '23 '!3 ! ) 9 $ CF
5 3 * ;*9
$ $ 3
5 + )$
# 8% 8
$ 5 3 2% 23 7 ! " $
C1 . F% 5 $
G % G
G8% G - #
G23 G 3 ) 3 $
" ) $ " ) 3 23 44 3 % # 2 = $ $ $ $ " 6 3 " $ ' % / 44 4$ $ 0 ' % 5 AQ!RB
'8% '! $ &"'( ;*C 57# 5 $ 7# 58) 8 ) 5 A7 B )*# 5 $ $ $ #') G $ 5 # $A'23B 7 7 AB /)" ) / ! A7 B A3 B@@ 28) 8 $ ' A7 B 23A3 B 8 8 $ + A3 B@@ , 34 3 4 3 - @4 3
2 #"0
! "# $ # % & ' #% & #% &' #
' ! # & ' # ' ! # ( ' )*+, & ' #% & ' )*+, & #
( & Q./+R & ' )*+, # 1 & )+2" && #% ./+ ! & )*+, #./+& 3454& # + ' & ,64/ 74/#( ' & #( 88 && #%& & ' 9 #
./+& & ' & ' #& :4; ' & ' ' # 1 ' & Q R #)+2 #< ' )+2 & & # % ./+& ! #
'0)"#" , ,-,# + ") 1
$ & & & & & & #$ $ & & & = ( & ' & #
$ & = ' > ( ?65@#
$ & = R & = #
A #+
A ,4?,
03 ,4)'$+'(' " $$ 0)" ('#
1 $ & (* . B C) &#% & & #( BD & ( & ! #
$ B ./ #
1 ./+ $& D / ! B + # % C?4C,6& CF CG C B ( C & # D% @ % 1 & #% < > % #
$& & & ' 9 < . + > D8 C 8 A C J 1B #$ $ #
% CJ D < & & ' & C L
1$& / < #
& 1 &&&# ## "#% & #
% 1 ' #( & & #% 1 & & " #
5!
! " & # % ! & & & & #
> ! # > ! # = & # #+& & #
$ & ! ' #$ & ' 88# < & #( & ! & #
%' ' & # ( & & ' #% & #
% ' & +1 D ( > B G B " $ #%B $
3$ ! 34 * % /
! < ! # % + D #% Q @R #
( & & & @ +1 #% & & #% & & #
> & & #) & & ' * +1 #1 & & & #
% & ! && & #% F#> 3 & & & Q./+R# > 7 & ./+#( ./+ 5# ./+ : & ' @#1 6#
3$ ! 34 *
6!
% ' 9 # B & & #1 #
6!5 " 0.*'. 0)'
( R # % Q R & ' #1 1 ,#?#
! #( & & & & & # % & & & & #
C & & #
% &# % #% #
3$ ! 34 * + ; *
# #
A NOTE: These figures/tables/images have been removed to comply with copyright regulations. They are included in the print copy of the thesis held by the University of Adelaide Library.
7 % &: '")>A B A $ % &%BC $ A8 % -BC @A $ % &%BC # /6A;% -B
6!6 ,03' &#,& ) ,
#. # %
?" , ,
&, ' & 88 #
% & ' # 1 & 88# % #( & #. # > & 88#
3$ ! 34 * ; *
% 9 # . & # ! "# QR & #+ & #( & #+ 9& #1 ,#, & #1 # % & & & #
'! 3
A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.
'!$ $ * * *
7 % %: !C *$ $ A/ : 9 $ % B
> R ' #( ! # ! QR # & ! Q R . " #%! ( 7 1 ,#F #
3$ ! 34 * , ; *
" A B
$$ '")
* 7 '") A6 % B
7 $ $ *
7 % (: $A #< % -B
6!7 / $&#,&'))" #,03' ' + '
& # % #M & ' #
! ' #% & 1 ,#3#% & ' R #( ' #( # +& & & & & # ' ' & # % &
3$ ! 34 * ; * -
# % 88 #
7 % +: $ ! *A D; @% &C$ .B
6!7!5 / $&#,&'))" #,03' ' + '&'#-,#(" 0'
# # " & #%
O 4 ," 4 O 4
& & N.8,44?#,@"#1 & &
# F" 4
+ # % ?
3$ ! 34 * . ; *
& & # #
. #. & ' & #1 C B ! ( ! C & 333@ 333@4J + NG?667#?,5"# #
&:$ $ $ *$
$ * $ $ $=
'! $ $ % M+ $ $ &1 M%- %( M(. '! $ $ &. M%(( =6 A D; @% &B
6!7!6 / $&#,&'))"
% " # ! % #> # $ & & # + & Q R#( #> #
) J,)," 74 74 8& 8 =BC+" & & ( 74 "# % & # + & (A ?4 ( C # J,), & 8 CC+" #
% )*+,"#% #$ & M ( 7 # = )*+, A , M M$J>$ (7C! C ! "#
3$ ! 34 * ; * 1
( & ? ?" #% & 1 ? M #
6!7!7 @'0 ,# 1&'
% & ' # % ' ' #M ' & #
' & 1 ,#7# % & ' & ' & # C ' ' ' & ' #$ ## " ## "#
7 % : ! *0 $A D; @% &C$ %-+B
3$ ! 34 * & ; *
> ' 1 ,#5 ' # > ' && & ' & & ' & # ' & )*+, )"& D+,"#% & ' )' #1 )*+, ' #
Copper faceplate LOx (cross-section) H2 H2 LOx post
LOx post outlet flush with faceplate Neighbouring (no recess) elements
7 % ,:0 4%ABA#* &1-%C$ (, BC $ 3 0 9 A B
6!7!9 #,&'))"
% " # )*+, # % , # % )*+, # < #
% #% & #% & #! & & & #% #B & #(
3$ ! 34 *
> ,445" & # #
" #$
" "
% & ' ( )*' % + ))& ! ,- #*. / 0 1' #2* ( ,- #21 , ,- #3* 4 32*1 - M 6 6 6 ++ $ " 1 1 7 8 + #'' 9 ,- : , 6
0 1' : 70+ 1'9 1' 1' + 7/#!&9 + 7;<=!9
6!9 %1+' .1$#,+' &#,&'))" 0,(2 " ,
( )*+, ' & ! #
6!9!5 1$#,+' - ')
+ & & &%,# $ & & # & 8 & #
< ,4#3/ # + & & #1 & & # D & & #% #
< ' #> &
! #
88 & Q R#% ' & @4/,,4/#% D+," ' #
6!9!6 / $,%1+' ,% $ '#
) & #)& & ? ( %A % $ & M , & > ( 7# B #
( )" & 64/# $ & # #( & # + & )& #+& & ) #
) ' #$ ' ?44 / ' #
6!9!7 &'#0# 0")0, $ ,
$ ,#, & # % # 1 ,#: #% 88 & #1 & #( & & #% & #
( & )*+, #% %F# )*+, & F4 ,44# $ & ' )*+, #
! )
% # .$ - 7 8 + #'' 6 ))9
" )$ >
- ( !
> 6 $)*# 1& 1* ? )# *. ?
> 6 )*# 1' &) # *)
$ & # % 8 #( & Q R 1 ,#@ & #% # J # + ?676" 1 ,#@#% & ' #
Superheated vapour Short time Supercritical after injection fluid Critical temperature Gaseous Critical point phase
Liquid Compressible phase liquid Intial injection state of LOx
Critical pressure
% # 2$ - @ 6 A 7 *2#9
!
$ )*+, ' #$ ) ' & & & #% & ) ) & # % & O P' 1 ,#@#
( ' #) ' )*+,# % & & ' # 1 && & #( #% & 1 ,#6#$ & & C N ,443"# 1 ' F#F#
A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.
# $!%&' () * $++,!-.!
6!: ,(2 , 0."(2'#&#,0' '
. )*+,# 88#. & ' #% #
!" /
6!:!5 #,&'))" @'0 ,
( ' & & , 5 & ?4 F4* #% & 4#7 , ?4 # $' & & ' 8#
% ' & ?44/ ' & ?44#< ' & ?73#76/ 74#3# + )' & # % ' ,#3#F#
6!:!6 ,( " , ,-) / $&#,&'))"
1 ' ' Q R# ' & Q R # . ' ' & # 1 & & # & & & # % & 8 ' ' & ?4?7 +' N ?6:,#:3"#
A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.
# $!+&' 0 () *1 %%2,!2.!
1' & & ' Q R #> 8 & '
!" 2
#1 ,#?4 ' & ' # 1 ' #% & & & & & #
6!:!7 '0, $"#1" ,( " ,
% ) ' & & # & +, &#B D #,444" #
= & #%> > "1 & D #,444"#
6!:!9 "&,# " ,
1 & #( #+& & # % & #
M & & #( & )*+,' # & +, &# % #
6!:!: ,(2 ,
> & & & #( ! ),*+, ?) $NC,44,"#1 ' 8 ' #1 8 &
!" 3
)# % 8 & ) & & &# % , / $C ,44,""# % & & ' / ?) #
$ ' & #! & 8 & CN ,4439) ,445"#B ' ?44; )*+, #
6!< ,(2 , "2 ) 1
> #% #% & #
+ & #) #% & #
< #$ #
6!
% # $ & #> Q R& & 7; N.8,44?"#< 7; & Q R 1 ,#??# ) & # & #
!" -
# $!&1 4 ( * 5$++,!6%.!
$ # & 1 1" Q R & ' & # & ?4 344+8#$ 1 $1" 344 ?444+8 #M & & ' #+1 +1" & & Q R ?444+8#+1 #
6!
+ #%& 88 ' & #% && & " #
% +1 9 # & & & 1 ,#?,#% & #%' 88 #% # 1 ,#?, & ?%" ,%" ? " #$ & " & & #% & & #% & & 1 ,#?,# 1 #
!" %
Acoustic pressure Acoustic pressure node / Injector with dozens Combustion Nozzle antinodes velocity antinode to hundreds of chamber throat (green line) injection elements Acoustic gas motion (white arrows)
Traditional liquid propellant rocket (a) First longitudinal (1L) mode engine thrust chamber configuration
First tangential (1T) mode Second tangential (2T) mode First radial (1R) mode
(b) Examples of transverse modes, with acoustic gas motion transverse to the direction of injection
Maximum acoustic pressure is at the injection plane
(c) Nature of 1T mode Standing 1T mode Rotating 1T mode
# $!$&' !
% # ( & #$ ?4 & N.8,44?"#( ?%1 ,#?, ' #% ?% ' 9 ' & ' # +1 & # ?444 #$ +1 #
6!
$ & & 9 " # ?@:@9?637"
!"
& # & & & " "#( & # % & > #$ & 8# %
, O 4# 3" 4
# ( & # 1 & & & #+ & & #
1 ' #> & & #$ & > & # <' +1 &#) A ,&3344+8+1 1 & & )' & + N ?667"# $ & ) & 1 & +1 + N+ ?667"#
% +1 & ' # % +1 & ' # & ' #$ M # & +1 +'N ?6:," #+& & & #
1&' )*+, & #
!" #
& & +1 ' # & # ( ?6:?" & & # ( & # & & & #! +1 > ?67," & & # 1 / ) & ,445" #) & & +1 # D +1 & #% # < C ?654" & # ?667"#) & & +' N ?6:,"# % & & #1 #
(& +1 F#
6!
# & 1$1" # +& 1 $1 +1" & #
1 $1 & # ( ' & 1 #) & # 1 & # ( # D $1
!"
& & N .8,44?"#
B +1 & #B & # +1 & 88 # B M +C 54 & 88 .8 ,44?"#+&G ?6:," & 88 #
( .N+'?6:,9) ?6:,"#% & & #! & #(& #
! # + && # & +1 & +' ?6:,"# B 8 8 & # $' $ & ' # +&' 8 & # > % & +1 # >' $ ' # ) # # $ #
!" $
J88 J88 # # %88 #
# +& # . & #
+1 #% ' ' & +1 & #%( 5 +1 & # % & 7@ ( & +1 # ( & ?3 ' +1 # 1 ,#?F & ' #% ' #M #% 7@ ' & C NB ?6:,"#
% !#$&' ( ( ) *" )+, #-./!#0.1!
B 1 ? M & & +1 #( ,444 ) N S ?66F"# $' & # +& & & #=
!" 2
& & 1 ? #( C ? &+1 & %8>ND&?65@"#
( & #1 D $ ( ?657 ?6:," & & & & #% +1 #1 # J ! #
+ & #% & # $ & # ( & & & #%> $ ( > $(" =## 1N/?66:"#B & #$ & ?4; # % & & # % & & & #
( & & # ( # > & # $' #C ' #C & & #% #1 ' ' & & & 88 & # D ?65,"> # ?654" & #+& & #
1 &
!" 0
#+& # + #1 ' & GNS,445"# ' !" # ,4??"# < #
$ +1 & & # +& & +1 #% & +1 ! #
!"
7!
> +1 & #+ #% #
% #% +1 ' )*+, #! & ?6:,?667 #% & +1 #1 #
7!5 *' +" , & ,5>86
#1 & & ?674 #% +1 ' #
> ! & ?634 # % ?674 & # & & & # & #
> ?67?" +1 # >
!" 3 4
#% & & # = # $ # > ?67," & ' & & 9 QR Q R#% Q R& & & & # % & & " > N > ?67F"# >R ?675 ?6:," ?67? & &Q R#% & & +1 & # . & > D+' ?654" & +1 # >+' ?65," #% & & &1 F#? #% & C ' 88 ## " >?6:,"#
A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.
% $!#&' ( *' /" )+, #-5/!$531!
' & C ?674 #C ?677" & ' & ' #( 1 F#, ' C & ' & & #C ' ' #C ' # 1 & & # > C R &
!" 4 -
& & & #
A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library. "7* (1
% $!&8 )* 1 *9#-00/!0.1!
( +' ?6:," && & ?67, (' D ! # % & # & . > ?677" & +1 && # 1 & # ! " ' & 88#. & & 88 & & & ' # & & & #
( , BQ R & +'N ?6:,"#M & #
!" $ 4
?67@ ?6:? #6?" & # ( & & & &#% & #
. ?67@" +1 )*+, # M ' & & & #% #( & +1 & )*+,& & & ' & & & # % ' )*+, & +1 #. ' 9 & #
+ ?657" +1 #+ 9 )+2" >+2" # % & F#3 5#6 ?4#F# $ & & ' & ' * # ? ??44+8& #1 && 4#, )+2>+2 & & ?4#F & & # % & & & #$ & )+2 O)+2 & & #P +& #% & + . > ?655" #% & & 4#F 4#3 & #
. & +1 & & # $ ?674 & #( +1 # . ?675" ?65?"
!" 4 $#
?6:," & ' #
<C ?654" & +1 # % #( #% # < C & & #1 8 #
% &?673?657 & ?6:," # +& & & #
%( ?654 & = # ! & #+ J(( & & #
+ ?6579?657" ' & & # +R & ' & #1 & +1 & # = & Q R ' & ' #+ +1 F744 7444+8 ' # B ' & ' # )' 1 F#F# & & #
% ' + # ( ' * # % & # +& & ' J, & #
!" $ 4
% $!$&: ) *" #-50 /!#1!
% & * & + & + N < ?6559 ?655"# % ' # $ & #( & & #% R & & & & & #
% & #$ & #% + < ?655" & #% & # $ & & & ! 3 ,#5#F" # & #% T
B 7"
!" 4 $$
& " # & & +1 #$ +< ?655" # % T
, O 4 # 5" B , ,C S D T OD T 4 E U
) #1 F#3 # $ & & # 1& # ( + < ?655" & # % & # +& ?6:?" & & #
% $!2&, *" +; #-55/!31!
!" $2 4
( )*+, & & #( 1 F#7 & ## "#% )*+, ' +1 #+& & & # < & & & #
% $!0&, *" +; #-55 /!#.1!
$ ?654 A ?653"B ?657" B ?6:," & ' )*+, ' #! & )*+, ' & & +1 & # & ' &#B +, & ' # &' +, #) ' & #( 1 ?65:" & & +, ' +1 ' 1 #
% & #%' & & #1 & ?654 A , (#$ A , &' #B ' & +1 # . & +, & +
!" 4 $0
N + ?667"# % & +, +1 +, #
A , & +, ' 9 ' # $ ) & & ' # & &+, " & %8>ND&?65@"#% +, & #
$ ?654 < J((R & > ' )*+, "# $ <R #< > ?655" & ' 5#7 5#7# + ' ? & # % & && ' 1 # #<1 C ?65@" 88 8" # B ' " # $ ' # > ' & # > & ' & # <C ?656" ' ' & && #$' #
<R & # +& & ' # % & ' + N ?667"#< & # 1 & < ) % ,447 J # ,446" & +1 & #
( & ?6:, J(( ?63 +' #. & +1 # B 8 & # %
!" $5 4
& & +'N ?6:,"#
+' ?6:," & & !U! " # % & & & & # & & & &+1 & & & & #J & & & & #
7!6 *' +" , -#,(5>86 ,5>>:
1 & & J(( ?63& ! #B C!" ?6:4 & & ?6:4 +1 & # % ?6@4 4," ! (3 & M SN( ?667"#% ! +1 & & & #% ( ( & # J +1 ( 7 M7?4 #< +1 & )*+, ( +C:*+C:. M *M , & & &+,' &F474/ N ?6@6"#%( ! ?6@4 & ( " "& =#
$ ' &# & ' # $ & # > & & # % & & #
( & =?667 S( ?667"#% & J(( ?63& & ?6:,#
7!7 +.&#' #'#' '"#0.
+ 9 ?654 & #< ?65F ?6:," & &'
!" 4 $.
! & " ' #
= & & # $ & & & # ! & ' #
?676 & ' # 1 9& 8 #+ 8 & # ?676" & # . ?65:" & & & !?*F " & #
J& .8 & ?6:?" ' # ( ' >)," & ' J," & ' # % & & & #< J, >), & J&.8 & ' >), #! ' ' & # $ & ' & #
(' ?654 + & )*+, # ) ' & ' # + ?65: B ?6:," # > & !U! & !V! # $ & # ' & #( (' R & & +1 & B ?6:,"# % ' #
!" $3 4
%)J! ( QC R @ B = =## ' # % & )*+, )*>+3 # ) )+2 >+2 & >( # & & > # ?66@9,44F9,445"C # ?66@"S ,44?" D # ,443"# ( & # & & #
& C # ,4??" !" )*>+3 & & C # )*+, &# ) ,445" J =## )*+, #) ! BJ" ' #1 )+,#
$ ?664 =##(1 (1 "% = D ( > B " ' # C' & ) & # ,445"# $ ' ' & ) & ?666") &C ,44,"> # ,44F"#% & ' #< & & ' & ' ' #
% ' #D& # ?663" D& C ?663 C N % ?665" & ' #% & ' C!"# $ & & # ) & # ?666" ' # % & & C ,443" ' #
( (1 ' & & J*DJ," ' "#C& B & ' )*+,' # C % ?665" )*+, '
!" 4 $-
& #& 1 F#5 C # ?665" & & & & # &  F#: & # ( # C ,443" & ' # ) & & & #
A Near-injector region showing the flame (upper) and flowfield (lower) NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.
First 30 mm of the chamber with flame (upper) and flowfield (lower)
% $!5&% ( ) ( 4:<"20 * 9 !#--51!
!"
x = 0 x = 60 mm
A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.
# $!%&' ( ( ) * )* ) + !,--.*!
) ?665C% ' #> & & & # % ' & & # & ' # +& & & +, #
<& # ,445" = & #" ' )*+, #% #W,, 74 ' ' # $ ##<& # # & #& & * & # (& < # # <& & & #% ' S N ( ?667"#
1 <& # ,445" & B C% ?665"#$ & ' & # $ <& # & ' #
!"
# ,44:"> # ,44F" )*+, + < ?655"< # ?655" # B )*+, ' & # %& ' & ' #> & & & #% & & # ( & ' & & #. ' & & #
( +1 +1 #
7!9 '0' "2 ) 1#' '"#0.
% +1 S( ?667#C & & > ,445" & ' #( B ,44:" & ' =#% & & ' #
! +1 & ' & ' # > ( 1 (1 " = = D $ % =## B D J > >J " J ( )J! ("> 1 A ( ! ( A(Y("A#% & ' ' & #
7!9!5 , #'"0 +-),4
(1 ' # > % ,44, > # ,44F" & ' # 1 & 1 F#@ & ' &
! " #
& & & & #% ' & & & #$ & & ' #
> B % ,44F" J,*DJ,"' #$ &1 F#6 ' &# % ' B N> ,445"# & + ?657" ' & #. B > & ' # % # < & # B > ,44:" & & #
$ % $ % $ % $ % $ & & $ '!() * & & +# , , -+# ./ ! #00'1 !23!
! " '
$ '!2) * & & , +#4-+# ./ ! #00'1 !#53!
( & ' # 1 F#?4 & # ' #
# ,445" B > R ,445 >1B #$ # & & # ! & ' #
$ B > ,445" # ,445" ' & " # + # % & B > #% & /) & ,445" # & #% +1 # >
! "
)*+, #
$ '!0) / & , 1 1 .6 7 / #0051 !83!
. # ,446" ' & #% ' #( & ' & & ' #< ' & ' & #% ' & > # ,44F"#% & 1 #% & Q R & & & & #. # +1 '
! " 8
#
7!9!6 '"0 +-),4
< ) & ,44F" )*+, +1 #B & & & # % ' & & #
& # ,443"& ' B Q >R ./>"#= ' !$ ,4; ! & # ' 1 ? " +1" & #+& & & # 1 F#?? & R QM R & && # )' ,443 ,44:" # ( )*+, . ?66F"& 56"& ? ,4"# % & #
A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.
$ '!) 9 . ! #00 1 !3!
$ B & :@44+8#% & & ' #,443"#/ + > ,447" C!' #%
! " 5
& & +, & ) ' # % & / +8 +1 # $ & ) "& & F6; ' #% & :344+8 :@44+8 B #1 & ' C! B / + > ' & # + ,446" ./> )*>+3)+2 & & #% ' ' ' & & ' & & & ' & /+ > #
( & = C# D # ,445" & ' #%' & ),*+, & ' # $ & & M & & && &# D # & % # % & & # & ' ,44 ?744+8"#$ D BNS ,44:" & & & & #% % D # #
( A < F#?" & @4# ( & < & +, & 95,/ ) 74/ & J #,44@"#%& & & <R # B ' ' ) #% ) ' & O P 9 &' & & ' # /& # ,4?4" )*>+3 & # J # ,4??"
! " :
) & & ) #% & ' / # ,4??" >R # ( & ) & & <R #( J # ' & < # & ' & & +1 #
B > ,445" > ,446" ' # ! # & & C #B > & +, ' ) # 1 & & #< O PJ # & #
( 1 ! > >J & ' # ( & ' & & & C $' > C$>" C )J! (# $ )*+,& #,44F" )*>+3" #,445" &' & # $ C$> & & 1 F#?,"# ' && # % C$> ' ' #% C$> & )*>+3 54 " 6& )*+, "#( S> ) & ,44:") & # ,44@"# ( )*+, )*>+3 ' < ' #$ )*+, )*>+3# = )*+, & )J! ( & #
# ,443" +1 C$># ! ' ' &
! " (
& ?% # % ' ' #% & ' #$ & ' #
*
;
< <
$ '!#) * %"= . 3 >*/1 & . 3 & . 3 ; .? #0051 !:(3!
= +1 # % & & 1 F#?F &' & )*>+3#% #% # ?:"& C # ,445"# ( & & 3; ! " & ' # $ & &' && # C #,445" & & & #% & & & #
! " 2
A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.
$ '!') / .1 &3 & .> ! #0051 !'3!
> D ( > B " +1 )*+, # / ) & ,445" B & > > > >"#%> > +1 )*+, 3#?#, "#% & & ' & # + )+2" & #/ ) & & & #% & & R ,#5#F#
( = =## C # ,447" & & +,)," # % ' #( ' & & #,4459S #,44@9S #,446"# Y # ,4??"& ' #% & #+8 ( C ,4??" # % & #
< & # % Q R &
! " 80
& #(Q R & CN ( ,4??"# ( & ' & 1 F#?3# B & & & & < J N ( ,4??" ' # < ' & #
$ '! ) @ A & & .<1 + 7 B #01 !'3!
( & ' ! D$ % =## < & 7 +8 ?% #%?% & # & ' & . #,44@"#% & #( & ?%' & #,44@"#!& > > B # & )*>+3 ?% #$ & ?% # ! & # % & & D N ) & ,4??"# 1 ?% +1 #
! " 8
7!: (("#1
B +1 #% & +1 # = ! T& +1 9 9 & &[. +1 #
< & & ' ' & & ' #( & ' ' & +1 #. & ' )*+, #Q+ R # $ & & )*+, ' # % & #
+ ' )*+, & # M +, & # ( & && #% # < & ,444 & # & #B & & #
( & #% & #
! "
9!
. & & +1 & & )*+, #= & ' ' )*+, & # C & & ' * #1 & & #(& & #% & ' ' #
1 && #1& & & & && #1 & 3#3#
9!5 %&'# (' ")0,(2 ,##'* '4
9!5!5 ,# 0"),*'#* '4
! & #B & # #
?674 # 1 . > ?677" +1 && #% C ?675" ?% & && & 1 3#?#
! " 8 /
< +1 # # # + & & & & # & & &' # + & # A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.
$ !) ; .; 7 > 2853!
# 1 + ?657" ' & # % & #< & B > F#3#?" & #. ?66F" ? )*+, #% & ? #< & #
) 88 #( && 88#( 88' #% & & #< # % & #B ' #
% 88 & # 1 ?6@:"& # % 88 & &#%' & ' ? "
! " / 88
& ' & # J 88 & #. && & 1 3#, # B & # C 88 > > > >" >J B C $' > C$>" M + ( C M+(C" )J! ( >J # ! & & +1 & & & #
A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.
$ !#) < & CC . 7 $ 2(:1 !#3!
9!5!6
,44, $ ! $ +!" C > ,447" B / 1 N ) &,44:9 ,4??" > > > >"#%> >& & D 1 & ' +1 #% & 1 ?666" & #%> > 1 3#F & ,44 34#( + & #% ,44 ?%" 3 +8& & )*+,#( + 88 & ' ' # % ' ?*?4 #) & 5 && && # % )+2
! " 85 /
& & #% & #
A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.
$ !') /?/ "$ .D1 $ 7 % & #00:1 !'3!
1 +1 &' 88#C Q 88R ?% #M 88 & & #( 7; *! C7;" )*+, #% 88 ' ' & #% & ' ' 1 3#3 # % ?% ' #
A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.
$ ! ) @ 6? & CC (0 .3 20 .3 .D1 $ 7 % & #00:1 !'3!
( 1 3#3 & 88 #% 88
! " / 8:
& ?% #( & ' ' ' # & 88#
% > > ?4 ' & & & # 1 ' 64 88#% & & #
9!5!7 " $
% C $' > C$>" +1 C )J! ( ,445"#% ' C$> & & ?: 1 3#7# ( 88 & & > >#% &#= & & # ! ?% # <& & ' )+2 & )+2 #< C$> :7 & )*+, # ,443" 6#
# C$>#. &
? , ? , :" , , ,
& - # . C * - "
? , & # @" , ,
F C$> & )*+, &C34A* #% &
! " 8( /
" $ 6"
& " #% $C3#7CA*F# . # #
% ! +1 # % ! W54 & W5 >!(, & D C. ?663" & $C ,#:, *F" 6#::5A* #/" F7F3/" W 63CA*F# ! +1 & 74; ! & &C4#7 F4&?47 ",*^ ,#:, *F" ?7@7* ",_W4#:CA*F ?; #% #
?% & ' # % & ?#:M,#4 '" # ( ' & ' C$> #% & 8 8 & & #% & & #
$ !8) * >*/ & , .1 31 , .3 . ? #0053!
%M+( C M+(C" C$># 88 M+(C & 88 ' #. 88 88 M+(C ,4; ! # % & C$>& &
! " / 82
& )*+, #,44F"#) & C #,44@"#
$ !5) * >*/ & 9"B> .3 .> ! #00(31 ; .3 .? #0051 !# 53!
9!5!9 ' 1)*" " " ' *'# 1#'0 " + )"#0,(2 ,#
( = =## +1 & F#3#,# $ 88 +1 # ( & # & ) ' # % & & C # ,445"# % & +1 #1 & ' #
M ' 88 & & & # $ ' & 88 & # % & & & #
9!5!: #$ ' *'# 1#'0 " + )"#0,(2 ,#
( F#3#, = =## & ' ?% #,44@"#% #% & #+& #1 & 1 #1
! " 50 /
#C & ' )*+, & & #
9!5!< (("#1
. & & & & ' & T %88 & #$ & #C Q & R & # $ +1 # = & # ( & & ' ' #% & & # C & # % & # $' ' & ' #
9!6 '40,(2 ,# &'0 - 0" ,
% &+1 & ' ' & 3#?# & & & #( B & & #( ' & ' #
9!6!5 &'#" +0, $ ,
) ' ' &
! " / 5
74#3"& #) & & # 1 # ,44:" B > ,44:" ?4 & ' # > 347454& & #
% #1 )*+, W3#7 # W 3#7 :#, 3 5 #! & & ' ' #% &WF ,& & #
& & &?5 +8#= & ' & & # = + < ?655" #> > > ,44 & 8 ?%& # ) & )*+, & & ?744* & #% ?% 3 +8& & & # & > >#
$ # & ?44 344* & #
( ' ' # & #
9!6!6 ' -"0 ) 1
% & +,' @ B # % D( > B " + D $ # % ! < ! Q @R & )*+, ! #% )+, # & @ * )?#7 * +,& F54#% ?7 & & : & & # B
! " 5# /
& ?54 & 74 * # #
% # @ +, ,@4 F44/ ?44/ 74/# & & +, ' & & F#?"#< +, & D+,"#< +, & +," ' #% D+, +, "$a74/& & #
! & & ' # & & #
% @ & &+1 #
9!6!7 @'0 ,#
%' & & ' #>' & )*+, # & ) ,#5#3" & #% ' & #( & & & & ' & ' #
% ' & ' ' & # $ & ' & ' " & 1 3#:# % Q R ' & ' & & #$ & Q R ' ' C$>&' & # & ' & & & & ' & #
! " / 5'
% ' ' # % & & ' ' 4 37 1 3#:#
° 0 Oscillating transverse acoustic gas motion (acoustic velocity) 45°
View of central jet
$ !:) @ , !
9!7 , 0'& ")$' +
1& & #% & & & # 3#3#
9!7!5 , 0'& 5A +.&#' #'
$ & > > ' #1 3#@ #+& & ' > >& ' & ' # 1 & ' & & ' # % & ' 88# % & & #
Exciter wheel
Secondary nozzle Ø 200 mm Penta-injector CRC chamber configuration
Main nozzle
$ !( " /?/ . 3!
! "
% > > #% & 88 #( > > & #
9!7!6 , 0'& 6A'0 " + )"#0."(2'#
( C$> 3#?#F & # % ' & & 1 3#6# & C$>& ' #% #
Exciter wheel
Secondary nozzle
Penta-injector Main nozzle
Rectangular combustion chamber
# !$%& ' (!
% ' & & & ' & C$>#+& 88 #% 88 C$>1 3#?4#
# !)*%# +, -- '& .**/!01(!
!"
( & & # 8 ' ' # < 8 & > >#
9!7!7 , 0'& 7A%0 " , '+(' -,#
B & @ #% &+1 & & & & # B & +1 & & ' 88 #
% ./. 1 3#??& &+1 & #./+ ' ' # ( & ./. & 88 & 1 3#?,# +& & #./. 74 ?% ?@ +8 3 +8#
A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.
# $!%%& '(' ) ! *++, !-.!
! "
Exciter wheel BKB penta-injector Secondary nozzle Ø 50 mm
BKB thrust chamber Excitation segment (combustion chamber and nozzle)
# $!%*& '(' / ) .!
9!7!9 , 0'& 9A +#' , " ,# '+(' -,#
( ./.& 3 +8?%& # %Q R 1 3#?F & > > & ' ./.# ' > >#
exciter wheel
secondary nozzle
Ø 200 mm Ø 50 mm BKB penta-injector
Ring resonator BKB thrust chamber segment (combustion chamber and nozzle)
# $!%-& '(' / ) .!
( & ./.& #% & (JS ??#4 (JS $ ,4??" & & # ( # & & & # = W ( " T
! "
,. 4 # ?4" ,
( & " " b T
, . 4bb ??" ,
&2*+4- #
1 # +& # % > ,447" > > & #
1 & #% & & J(( D Q> ! & ( R >!(," DNC.?663"#1 & ! W54 W 5 >!(, " WF7F3/ .W?F#F?* "W?#?3 0W?7@7* #
1 3#?3 & & #% & #%?% > > & & 88#%? ?77:+8 & ' #% & ' ? F 1 3#?3"& @@F4+8#% 3 +8 #
& & #) & && & ' && && & ' #
! " #
Pressure node is offset
Pressure antinode at injector
1L ~ 1557 Hz 1T sigma ~ 4668 Hz 1T pi ~ 4770 Hz 1R3L ~ 8830 Hz
$ %!&%' ( )*) !
9!7!: , 0'& :A 4 #' , " ,# '+(' -,#
$ & Q & R % " 1 3#?7#%% & ./. # % 88& & #
Exciter wheel
Secondary nozzle BKB penta-injector
Ø 50 mm
BKB thrust chamber (combustion chamber and nozzle) Twin resonator segment (TRS)
$ %!&+' ,- . /!
(JS& & & #% & FB #$ & ' # % (JS
! "
?7@7* &1 3#?5 "#% ? 8 & & 8 " 1 3#?5 ' & ' # % , 8? " ' #% , 8, ' & ' & ' , 8? &#
Secondary nozzle Velocity Pressure Pressure antinode antinode antinode
Main nozzle
1Lzz ~ 2600 Hz 2L 1Lx ~ 4300 Hz2Lzx 2L ~ 5700 Hz
# $!%& '( !
% & 3 +8 +1 # % # ( ' & ? 8 , 8? & #
1 88 & &&& 8 #
9!7!< , 0'& ')'0 ,
1 & & #1& & (( & % 3#F#,"#(& & # % & & ' #
! "
9!9 '4#'0 " + )"#0,(2 ,#A
< % & # % 3#F#, +1 3#?#F"# % & & & @ #% & ' ' #
9!9!5 0, 0'& ,*'#* '4
%& & Q +RQ./+R9Q./R D&Q. R Q+R B @ # $ 1 3#?: ./+ C$> 3#?#F"# ( ' &' ' #( 88 & " # & & ' 88 #1& 88 Q &R & 88 > ># < 88 & & QR #<& & ' # % && #(& ' ' #% 88 & & & #< & & #
Exciter wheel
Secondary nozzle Optical access window
Main nozzle
Primary injector
Window cooling injection slots
Secondary H2 injection array
# $!%&'(" !
!"
9!9!6 ,(2 , 0."(2'#"0, 0
% ./+ 1 3#?@#B ' (.#% 9 WF47& W74 (W,44& & ' #
Secondary nozzle
Optical access window
Primary injection elements (penta-injector) Main nozzle
Window cooling
50 mm
injection slots 200 mm
100 mm
Secondary H2 injection array
50 mm 305 mm
# $!%& ' ()" !
% ./+ & #1 & 88 ' #% & &#%
, , , C S C S C S - " D T D T D ( T ?," ( , D T D T D T E U E U E ( U
?*, & W^" *."" _ ( & ( # 1 ./+& ! W54 W5 # % W4#36& ' 5 & && +, ' 3#3#3"#1 >!(, " W ::3 / . W F#443 * "W?#F@ 0W?:?,* #% & ./+ % 3# % & ! ?4" &1 3#?6#
! "
% & ? " ?%" & ? ?%" & ? 5 +8# % ./+# % ? ' & #. ?%? ?% ' & Q R ' ' #%?%? ?% & #$ & ? ?%? ?% > >& ' 88 #% > > ,44 & ./+ ?% 3 +8 #% F47 ? ?%#1 && 8 & 8 & #
#$%# &'"!
( ) , - * +",-
* .) . / / 0/ * .# / / . $0/ * .).# . / . 1..2 ) / / 12/$
* , .) / . / .3./
200 mm
305 mm 50 mm 1L 1T 1L1T 2T 1Ly
* $!.4%5 #$!
9!9!7 # ("#1 @'0 ,#
./+ ' & ' ' " 1 3#,4#< & && ' +,' & ' ' #% ' ' # ' & #
$' 8 & ' #%7 ./+#% ) ' ' &
!"
& #. # # & & #% ) & # % ' ) +, &' # % & 1 91W,#5' 1a?#: ,#4' #% & ' & C$>#
/0 7 !- /0 #. # 7 &!2
# * 7 $!
# 7 -!4 !3
%4! %3!% # 5 # 7 &!-- 3&!2 +
+
# $!%&' ()" * + !
, -' ()" + !
.+ , ()" +
/0 + %M2 !-
"% -M3& -!4
"% 5 # &!-M3!& &!--
+ 3!M%!& %!2 .+ + 3!3M3! 3!2
/0 + " 3&M& 6 M& 6
"% + " 34&M2& 6 3&&M$&& 6 0 $!$M!% %M2
.+ % 7 " 6 " 8M3 2M3&&
9 7 -"% 6 -"% 3&M%& %M--
9!9!9 '0, $"#1 @'0 ,
( ./+ ' #D ' & & ' #% +,'
! " $
& #% & +, ' #
8 & ' & & 3#F#," & ' # $ ./+ & & ' & & & & & ' #% 1 3#,?#
; << =>
"% +
* +
? 5 + #5 5 +
.
;
#5 5 +
# $!%3' .+ 5 + : 5 !
( +,' # < ' & & & & #( & & 8 " 8 & #% & # % +,' & 8 +, #
! " -
9!9!: "+ , 0
./+ & && #
B ' # % && !22 3 !22 4# % & #B ' 9 ) ! "+, ! " +, !$ "#% ' & # &1 3#,,#
% 8 # ( / >. 1 3#,,#( & # ?44 +8 & 34 +8#
' # ' #
% & ' ' # > & 88 && ? # % & & && & #
( & #
PCCdyn1 PCCdyn3 PCCdyn6
PIHdyn Secondary H2 manifold: Kistler 6052C PCCdyn1...6 Kistler 6043A60
LOx manifold: PIOdyn PCB M112A05
Primary H manifold: PIFdyn 2 PCCdyn5 PCB M112A05 PCCdyn2 PCCdyn4
# $!%%' ; ()"!
! " &% 8i qrryr
9!9!< & 0")"00'
<& & ' # %&& 8 & & #% & & & & )+2" & F4:#
% && 74 & & ' # % ?44 & & & & ' 8&&#B && & #% && & & & # 8 && && ./+ &1 3#,F#
% && & 8 8 #$' +, ' && #% & &&+, ' +,' #
Pvphyhpprvq Q vh vwrp 9vq
Avt r#!")Pvphyhpprvqhqqvq
9!9!8 %0 " , 1 '(
% ./+ > > C$>88 #< & > > B & #% & 88 & #! > > & 88 & ,4??"#% ./+ &
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv 8i qrryr &&
' & 88 & #
! 88 #% 88 ./+& & & & & ' & & & 8 #% 88'1& > > & 88 88 '.9
1 '' . ?4 # ?F"
% & #% 88& # ( 88 ?% #$ ?% & & ' # % & ./+ 88 & & ?% # % 88 & 1 B! &1 3#,3#% & ?, 88 :4#
Iqhyyvr Trpqh yr 8yrhpi qrsyrpv ! Trpqh yr yrtu& psvt hv Uqr yrtu" qhyyvr
2#"#$C 2#!'#C 2# %'C
Avt r#!#)Hqhyhhyv ryuvturvsyrprsrpqh yryrtuur Uqr p rUur r vphyqrphypyhvr rpqprqvAyrQ9@vthqrrqs & !Uur vh hqrpqh yrrvvruhrirrphyrqs qvrvhyv
! ' & 88 ' #% +1 ?% & ,#5#,"# % 88 & ' & ' ' #
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv &' 8i qrryr
% +, ' 3#3#3" & 88#% & 88 #% & # % #! 5 +8 ? ?%? ?% # &1 3#,7#
% #D DJ," # ( & &1 3#,5#J & & #( 88#
< 88 & & QR #
@pvhvr Tr
8ivpuhir Hhvyr @pvr urry
Avt r#!$)Qut husurrpvhvrvhyyrq7FC
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv 8i qrryr &(
Avt r#!%)Uurrpvhvr7FCvuuvtvhyyrq
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv
:!
% & & D ( > B " $ & + D# % & ./+ @ B #
% & & & & #
:!5 ' ,&'#" ,
:!5!5 ' -"0 ) 1
% & ./+ & ! % 1 > Q @R & ' #% @ 1 7#? & >J! B !(B ( J!>C( +8 ,444"#
% & & # & #% C>>" & & # 1 @ & 3#,#,#
:!5!6 ' 0"(&" +
1 & & ./+ & @ # % & & & & # % &
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv '! @r vrhyrpuvr
& #% && & # C #
Avt r$ )@ rhUrAhpvyvQ's p trvp pxrrtvr rrh pu
:!5!7 "#$4"#' '+#" ,
% ./+ & 1 7#,# % 1 7#?"# % ./+ #% ./+ @ && D+,' #% & &D+, & 88 #
:!5!9 ' #
) @ # ) # % ,4 & & & # % B5@ ?44 & # 1 7#F & ./+ B5@#% & & & & ' #$ ./+ & & # & #( 76 & ' #
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv @r vrhyrpuvr '"
Trpqh yr ruhvr
@pvhvr
Uu s hr
GPyyvr Hhvyr
8yvthr yur
T s hrs Q hri r BC!yr
Avt r$!7FCvrt hvvuurQ'rshpvyv
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv '# @r vrhyrpuvr
Avt r$")Qut husurrpryyq vth7FCr hxrs ur9%'p yivyqvt
:!5!: ' '/ ' 0'
% C>> # & & #
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv @r vrhyrpuvr '$
& & # % & #$ & & & && & # B & #
% & & # 1 & # & # % & Q R & & & #
:!6 "+ , 0 " $$" ""0/ ,
% & ./+ # & & & && && # % @ & # ( ./+ & C>> #( C>> #
% ./+ & & & ? +8# % & /?#7/ &,FF53@//4#443/ 53@ ?,:F/#% /,#7/ & ?45 F?F/ /4#4?7d"M,:Fd/&?45/#% @C>> /4#7/ #% # % /4#,; C>> /?;#1& & # M & & C>> #1 # % /F;#
B ' & ?44 +8#B C>> #
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv '% @r vrhyrpuvr
1 8 #(& & & F4 +8# ( & C>> & & 34 +8 #%F4 34 +8 & &4 F4 +8# % ./+#C /4#43#
:!7 & 0")$ "+ , 0
% #D & # ) & & #% && # ( & )+2 & #) C>>#% & C>> # % & C>> & C>> # > & /7) ?44 +8"& /: ?% 3 +8#% & #
:!7!5 B0.'( ) ( ' 0' 0' ("+ +
$ 8 # > )+2" & B N > ,44,"# )+2 ),*+, & T
)f+)+2 ?3"
),f+)+f+,) ?7"
"#% 8 # )+2 & ),*+, & & #1 7#3 & ),*+, )*+, @ #% Q./BR 3, ' '
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv @r vrhyrpuvr '&
#% 1 7#3& ! W@4& W5# $ #% & ),*+, D ?6:3" & C % ?665" ' # % & F47 F?4 )+2 # ( $8 ,444" )+2 & F45#3 F46#, # $ ' & & F47/7 & # % & )+2 #
OH* peaks at 306.4 and 309.2 nm
1.0
Vibrational and rotational bands of H O
2
0.8
0.6
0.4 Relative intensity
0.2
0.0
300 350 400 450 500 550 600 650 700 750 800 850 900 950 1000
Wavelength (nm)
Avt r$#)@vvrp s hGPC!iphyrpi
> )+2 # )+ " & 8 >+ #)+
+,)f),)+ ?5"
)+2 #1 )+2' )*+, & D N < ?6:@" )+2 #$ #> & # % & # % )+ 8 # )+2 #% )+2 & ! #.& ,443" )+2 & # )+2 & & & # % & & " #% # B &
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv '' @r vrhyrpuvr
F#3#, :#?"#$ ! & #
:!7!6 ."$,4+#"&. ("+ +
& & & # & & >>B"#$& & & # $ ! & ' # ( & #
% ' & ! #1 & ' # 1 & & # $ ' ' # % & & Y & #( D@74 & #% & & @74 & Y #
:!7!7 B0.'( ) ( ' 0' 0'#'0,#$ +4 .&., ,( ) &) '#
C " )+2 & # % C>> # C & ?44 +8 & C>> 34 +8 #< )+2 #% & ?5 @ >>B #% C & )+2 & )+2 & & #
:!9 "(&" + 5" $6A ")."#$4"#' ' +
% ./+ & & & & #% &&& ./+ #1 & #
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv @r vrhyrpuvr '(
:!9!5 ' 1&'5C0)'" 0, - + #" ,
$ ./+ & & )D+, D+, & "$a,64/ 3#,#,"# % & 1 7#7 & && 88 # % QR & 88& & #% & 88 &#
9rpqh yr
9vq Hhvyr
Avt r$$)7FCpsvt hvs rr 0pyrhpsvt hv
% & &#%' & ! W347454& W,35#% &1 7#5 & & ! W34 W, 3 5#% & & #J Wf?7 "& #% ./+ & & & & #
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv ( @r vrhyrpuvr
8 70 350 600
60 550
300
T
H
6
50
500
P
cc ROF 40 250
450
4
30
400
200 Pressure (bar)
20
350 Injection temperature (K) temperature Injection Oxidiser/fuel ratio ratio Oxidiser/fuel 2
10 150
T
O
300
PCCdyn2 Combustion chamber wall temperature (K)
0
0 100 250
0 2 4 6 8 1012141618202224262830323436
Time (s)
Avt r$%)@hyrrrrprs rr 0htrq
:!9!6 ' 1&'6C0)'" 0, - + #" , 4 .,& 0
%QR & & && && & 1 7#:# ( && & && #%&& & & && #
Pvphyvq Wh uvryq
Avt r$&)7FCpsvt hvs rr!0pyrhpsvt hvvuvp
) & 1 7#@# % & ?44 < & & & && & #% ./+ & && # (
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv @r vrhyrpuvr (
& & 8 #% =D?? >>B 1(%>(C?4,3 >$& @ # ( 1(%>(C ( Y , & )+2#% & && #()+2 & # > & F#7M ,) & #
Long-pass filter
High-speed camera for shadowgraph imaging
Xenon lamp
OH*-pass filter
High-speed intensified camera for OH* imaging
Avt r$')Dvvhyvphyrs phhvt hq!
% & & && & # % & #1 7#6 & #
8 70 350 600
Period 1 Period 2 Period 3
P
cc
60 550
T 300
H
6
50
500 ROF 40 250
450
4
30
400
200 Pressure (bar)
20
350 Oxidiser/fuel ratio ratio Oxidiser/fuel 2 Injection temperature (K)
10 150
T
O
300
PCCdyn2 Combustion chamber wall temperature (K)
0
0 100 250
0 2 4 6 8 1012141618202224262830323436
Time (s)
Avt r$()@hyrrrrprs rr!0htrqvuvp
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv
& &)+2 ' #( ! #+ #% & & # B ) ' ' & 9 & #! 34 &1 7#?4# & & #
" # $%& ' ( )% ' *+ ,( ' *-+ ,
:!9!7 ' 1&'7C4 .'%0 " , " $,& 0
$ & & 1 7#??# ' & +, & # % #) & #
% # $ & & &' ' & & &# = & & & & & # & & 88 & & #
( && & & 1 7#?,#% QR && ' &# % & && 88 && &#% & #% & 88 & & & #
! .
% 88 & & # < & & & & #% & & & #( & ' ' #1 7#?F & #
) & &1 7#?F#< ?7 & && # % & 9?%? ?% , ?%# % 4#7 !22 +"& & # % & +1 #
( & & )*+, 6 & +, ' #
" # $$&/0! .1'
! )
2 ' 34 5
6 ' 2 ' 7 ' 88
" # $& '
60 7 600
1L 1T 1L1T 2L 2L1T
6 6 550
50
5 500
P 40
cc ROF
4 4 450
30
3 400 Pressure (bar)
20
2 2 350 Oxidiser/fuel ratio ratio Oxidiser/fuel
10 Excitation frequency (kHz)
1 300
PCCdyn2
0 Combustion chamber wall temperature (K)
0 0 250
0 1 2 3 4 5 6 7 8 9 10
Time (s)
" # $.& .1 '
% ,#B # % & & W 4#7 #% && & ?444 " & )+2& ?,744 &+1 #
% & & ,#( & & 744< & D557JB 4#,7" & ' # %&
! #
& 1 7#?3# B & ' # J & & #
<)+2 # B )+2 & # ! )+2 &1 7#?7#( )+2 > :#
" # $)& ' .( #% ' *-+ ,( -% ' *-+ ,
BKH optical window
Injection
+,2 +,$9
" # $#& '2!: .( *;)+,( $9 *;# .+,
:!: "(&" + 7" $9A'%0 " , " $,& 0 4 ."(2 ' .1$#,+'
% & ' ' & # +& ' ) 1 7#?5#% & #
% #% # ' & & "+, &)+2&
! (% @r vrhyrpuvr
# ( & )*+, ), #
Urpryyv vtvqr
7 rqGP Ahpryhrqhhtr
Avt r$ %)Wvqrs hrq vtrrprshvy rhq ryvtuh qh rqhhtr
:!:!5 ' 1&'9C4 .'%0 " ,
1& && & #% & & 88 ' DJ, ' #% QR && 88# % & DJ, & & 88 & &
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv @r vrhyrpuvr (&
& #( &1 7#?:#
8 70 7 600
1L 1T 1L1T
60 6 550
P
6 cc
50
5 500 ROF 40
4 450
4
30
3 400 Pressure (bar)
20
2 350 Oxidiser/fuel ratio ratio Oxidiser/fuel
2 Excitation frequency (kHz)
10
1 300
PCCdyn2 Combustion chamber wall temperature (K)
0
0 0 250
0 2 4 6 8 101214161820222426283032343638
Time (s)
Avt r$ &)@hyrrrrprs rr#0p yyrqrpvhv h
:!:!6 ' 1&':C4 .'%0 " , " $,& 0
1& && & #% & 1 7#?@& 1 7#?6#
Long-pass filter
High-speed camera for shadowgraph imaging
Dichoric mirror
Xenon lamp
Photomultipliers OH*-pass filter High-speed intensified camera for OH* imaging
Avt r$ ')Hqvsvrqvphyr
% & & & ?444< & ) # ( D @74 # ! & 1 7#,4 & & 9
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv
# J 34 1 7#,4& & &&&#( & > @#
( & 1(%>(C (7 & & && ,4444 9 #% )+2& #( 37 & &&#% & & 64 )+2 #% & & & & " & #
&
& '!(
& ' ) *
" # $%&
!
+,-. /0!1
+,2. /0!1
" # 1.% * -. * 0!1+,/ 2. * 0!1+,
< & # % )+2 & ,3444 9 & ? , # & ? ?%? ?%#( & 1 7#,?#J & ? ?% #
8 70 7 600
1L 1T
60 6 550
P
6 cc
50
5 500 ROF
40
4 450
4
30
3 400 Pressure (bar)
20 Oxidiser/fuel ratio ratio Oxidiser/fuel
2 350 Excitation frequency (kHz) 2
10
1 300
PCCdyn2 Combustion chamber wall temperature (K)
0
0 0 250
0 5 10 15 20 25 30 35
Time (s)
" # 1$% #)*
! $..
$ & ?% #( && & # % & )+2 ?% 1 7#,,#% ?% & ' & & & &&#( )+2 > :#
+,' +,$3
" # 11%4 *'!( " # 1$ +, $3 +,
%& C " & )+2 & #% C & & && & &&#% C & & )+2 & & # ( ' & 1 7#,F#
" # 15%
! $.$
:!< "(&" + :A'%0 " , " $,& 0 4 .0#1,+' 0.1$#,+'
% & & +, & 74 /" ' # % ' +, ' #B & &+,#( 88 & #
:!
( & & +, ' +, & +, "& & #% & & & # ( 88 & & & # ??#>#?#
:!
% & 7 3 7#7#," # & & # $ 1 7#,3 & & D+, #< ) ' 54 #J & 1 7#,3& & #
% C & && ?4 #% & & & && 1 7#,7#
+,-. /6!1+,2. /6!1
" # 1-% * -. * 6!1+,/ 2. * 6!1+,
! $.1
12±1 mm Ø ~ 10 mm
10±1 mm
PM2
PM1
" # 1#% 7
:!8 (("#1,-"0. '*'$,&'#" +0, $ ,
) &./+ && ' ' #./+ & 93454 "& W5&D+, & +,# % & & )+2 # 1 7#,5 ./+#
Clean configuration with GH
2
Excitation and optics with GH
2
Excitation and optics with LH
2 (bar)
cc 60 P
50
40 Combustion chamber Combustion pressure,
2 4 6
Ratio of oxidiser-to-fuel, ROF
" # 12%8 9:!
!
$ & ./+ & & # . ./+ & & # % ./+ & & & & #% & ./+ ) D+, +, #% && && #C ' & #1& & 88 #
! > > & #) & # ,44@" & > > & & & 88 #% & & # ( # ,44@" & # $ & #( ./+ & ' & #
% & 1 ! 1!" (JS# % 1! ./+ ' & #B #C
! $.- 8
# 1 +, & 74 ' #% 1 5#?#1 & & #1 & 744+8& & @ % 1 # $ & & & +1 #
!1 A >>/ ? ? >>+ ,
6'B A ?
4 ?
" A ?
@ * A
+,"
>> *
8 >>
+,; +Q R /* >>,
" 2 $%" 9:!* +, + * >>,/ +, +* >>,
! 8 $.#
% & 1 F4 & & # ( ,#,#% & & ./+ . W4#43 #% (JS& #C Q R& 8& 5 +8 & # % & 7 ?4" 8 7#% QR &1 5#?#
(& #W4 & 88 & #( & #! & & #
% 88 & !6W " ?"*, 88 C > ?6::"# % # % 88 88 # % 88 & #
1 ./+ ##& 88#(? 54 & D+,#% & < < ?65:" & +1%:4 && +8 N ,44,"# % & , ."T
C , S ?4. D T ?:" D , T E ! U
! #% ! & #1 5#, & !22 + ,4 +8# ( F4:F5?35?,,6,+8 #$ !$ 1 5#, & +, # % 1! & # ( & )+, ' # C 1! !$ #%1! 5?+8 ,;" ?>"
! $.2 8
+,' #% 1! & & +, # % 1! ,; !$ #% & & +,' #
-30
-40
-50
-60
-70
-80 Powerdensity (dB/Hz)
-90
-100
-110
01234567891011121314151617181920
Frequency (kHz) +,& C + ,
-30
1C 2C 3C 4C 5C 6C 7C
-40
1R
-50
1C1R
2C1R
-60 3C1R
-70
-80 Power density (dB/Hz) density Power
-90
-100
-110
01234567891011121314151617181920
Frequency (kHz)
+,& C + !1 A ,
" 2 1%& C +,/ +, * * "
B ?> & ?> # % 1! !$ ,> F> #" ? , #" ?>? ,>? #"# % & & 1! 1 5#F#( ?4?44+8 & 1!#
! 8 $.7
" +$D, !1 A
$D 5D $E 5D$E
" 2 5% " !1
% ? ?%? ?% # 1 5#3 & & !22 + 1 5#, & %3 3#3#, 1! #( ' 1! 1 5#3 Q R#
1 ,344+8 # $ !$ 1 5#," !22 + # $ & ,344 +8 !22 + & & & #
> 1! & ? #1 ' 88 # $ & 88# % & ? QR ? #% ? ?%, &# % 1!& ? #$ #% ' 1! #
! $. 8
-65
FE model
-70
Theory 1L 1T 1L1T
2L
-75
1L 1T 1L1T
2L
-80
-85
-90
-95 Power Density (dB/Hz) Density Power
-100
-105
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5
Frequency (kHz) +,& C * "
-65
1L 1T 1L1T Selected
2L -70
Sensor artefact
-75
-80
-85
-90
-95 Power density (dB/Hz) density Power
- 100
- 105
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5
Frequency (kHz) +,& C&DD 1*
" 2 -%& C * " +,/ * Q R+,
% !22 3 !22 4 & & # 1 5#7 ? ?%? ?% & 1! #% & & # D #1 ? !22 3 + & & !22 7 4#!22 8 9 & 8 # #1 !22 3:+ ? & 1 5#7# % # % " & # # ,446" C$> & & #%1! ./+ # +& !22 3 :4 # %
! 8 $.
"# % & !22 + ? ?% !22 4 ? ?%#% & !22 8 9 ? #
0.12 PCCdyn1 PCCdyn3 PCCdyn5
0.00 Pressure (bar)Pressure
-0.12
74.6520 74.6522 74.6524
Time (s)
(a) 1L mode PCCdyn2 PCCdyn4 PCCdyn6 0.06
0.00 Pressure (bar) Pressure
-0.06
74.1610 74.1612 74.1614
Time (s)
(b) 1T mode
0.04
0.00 Pressure (bar) Pressure
-0.04
74.8924 74.8926 74.8928
Time (s)
(c) 1L1T mode
" 2 #%; $6 51..!>+,/$3 -57.!>+,/ $6$3 #57.!>+,
B & 1! # % 1! >!( # % $ 6" 6" & $ 6W6:#3;#$ & $ 6W 6 * 60 <2&=>W * 0 N.8,44?"#% & ' 1!
!
# % $ 6 1 5#5 & #
-65
1L 1T 1L1T
Selected
2L -70
FE model 1L 1T 1L1T
2L
FE model - correct ed -75
1L 1T 1L1T c*
2L
-80
-85
-90
-95 Power density (dB/Hz) density Power
-100
-105
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5
Frequency (kHz)
# $!$%& ' ( # ) !
$ & & & #1 # % & 1! #B 1! #
% ?> +, ' ? & # % ?> & +, #C & & ?637"#( & & ?> & #% & "#
$ +, & #. & ?> & +, 1 5#:#% & 1! #% & 1 5#:# 1! & F44 +8 ?> & ? #
!"
Baffle plates Secondary H2 injection manifold
Acoustic gas motion
Manifold supply inlet
Three-dimensional internal volume geometry for FE model
# $!*%' "+ ! ( # ( !
% & ./+ #% !22 3!$ 54 & D+, &1 5#@ 1 5#@#%!$ & 1 5#," 1 5#@ # +, 1! & !$ 1 5#@ & # % ?> & & & #% & ,>, F>, #"# % +, !22 3"1 5#@1 5#@ & # J !22 3 !22 + & +,#% & & +, # $ +, ./+ & ./+ #
$ ' ./+& +, & # $ )+,' ' #+ + ?667" & A , ' & +1 & & # ( ?654 ) #% # % #$ ./+ & # % & ' #) ?% & & ' # $ & ' * ' +1 #
!"
& & # & ' # D) & ,4??" ?% # $ F#?" + D& ?656"&& #$ ' & & +1 #
( ./+& & # ( & # B 1! #
!" #
-30
1C 2C 3C 4C 5C 6C 7C -40
1R
-50
1C1R
2C1R
-60
3C1R
-70
-80
-90 Power density (dB/Hz) Powerdensity
-100
-110
01234567891011121314151617181920
Frequency (kHz)
$ % " $ % & $' (!%)
-30
1C 2C 3C 4C 6C 7C 8C
5C 2C2 3C2 1R 7C2 -40
1C1R
-50 2C1R
3C1R 4C1R
-60
-70
-80
-90 Power density (dB/Hz) density Power
-100
-110
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Frequency (kHz)
$% " $ % & )& '
-30
1C 2C 3C 4C 6C 7C 8C
5C 2C2 3C2 1R 7C2 -40
1C1R
-50 2C1R
3C1R 4C1R
-60
-70
-80
-90 Power density (dB/Hz) density Power
-100
-110
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Frequency (kHz) $%* $ %
-80
1L 1T 1L1T
2L
Selected
-90
-100 Power Density (dB/Hz) Density Power
-110
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0
Frequency (kHz) $ %* $ % &
' (!+,- & " .$ %/ 0 & $ %)$%/ 0 & ) $) % / 0 !
!" 1
% ./+& 88 & & & # 1 88 # > ?% & 88 #$ 1 5#6#$ & & 54 & D+,9& & 88 & M## &"#%5 1! $ 6 & 1 5#6#%1! :7+8 ?% ?46+8 ? ?% & #> 1! 1 5#?4 & ?% ' 88#% & & #
-60 4 (,' 56"& Clean configuration & 33 !
-70 Secondary nozzle added
-80 * 33
-90
$
-100 ((+7 ((87 Power density (dB/Hz) density Power
-110 9 #8:"3 #:"3
2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
Frequency (kHz) 4 1#:;"3 18:"3 ' (!2,/& 94 :(;1"3 :12:"3 & & 33 !
!; ;!; <!; $ % $%& 33
' (!;,' 4 .$ %& ) $%& 33 !
!" :
0.9 PCCdyn1 PCCdyn3 PCCdyn5
0.0 Pressure(bar)
-0.9
23.7398 23.7400 23.7402
Time (s)
(a) 1L mode PCCdyn2 PCCdyn4 PCCdyn6 3.5
0.0 Pressure (bar)Pressure
-3.5
29.9952 29.9954 29.9956
Time (s)
(b) 1T mode
5.5
0.0 Pressure (bar) Pressure
-5.5
36.0121 36.0123 36.0125
Time (s)
(c) 1L1T mode
' (!,= & 9 $ %)4 $%) 94$%!
< ? ?%? ?% !22 3 4 #) & 1! 1!& 88 #% &1 5#?? & ,@44+8 8 ,344+8#J & 1! # 1 ?% !22 3 & & &&!22 + !22 3a @7; !22 +" 88 &#$ 3#3#: ?% & ?,#
!"
<& & #% 1 11% " & # % & +&& & #
1 5#?, & !22 + 3 7#7#?"9 & # % & @444+8 ?444 5444+8 W f?4 f34 9 ?55#:+8* # % ?% ? ?% & & #%? & & 88 & # 1 5#?F 1 5#?,& 4 34444+8#) 1 5#?F#% ( ># $ #) & #$ & & & ? ?%? ?% #
Excitation frequency 1L1T mode
1T mode
1L mode
Sensor artefact
# !$% & ' ( ))) )))"*!
!"
Excitation overtones
Excitation of chamber modes by excitation signal overtones
1L1T 1T 1L
# $!%& # $!'( ) *+(+++ ",( ) !
1 Wf4#4 f?#7 & 1"Q R @4 ?44+8 #% ?4; ! & . ?65F" ' # > ?% F644 3,44+8 ? ?% 7?44 7744+8 #$ & # 1 & #) & & @4?44+8& #% ) & & @4+8 34 ?44+8 54 #= 9 34 74+8 # J & & #( & & # & 1 & & # ) & & ?44
! " -
& && # % 1 5#?3#J # % & QR & #
Non-linear coupling with 100 Hz chugging 1L1T
1T
Non-linear coupling with 50 Hz chugging 1L
Transition period free of LF chugging instability Transition 100 Hz chugging period 100 Hz 50 Hz 50 Hz
# $!*& $+ .# !
C ./+ && #( !22 + & # 1 & ,@44+8 & & ' ,344+8#( C ' && ?44 #1 C , # ?44 # % #% 1 5#?7
34& D+, #
! " /
6 6000
Selected 100 ms samples
1L1T
5
PCCdyn2 raw signal 1T 5500
acoustic pressure amplitude, p' 4
5000
1L
3
4500
2
1 4000
0
3500 Pressure (bar) Pressure
-1 Excitation frequency (Hz)
3000
-2
2500
-3
-4 2000
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
Time (s)
# $!0& 1 .( 2 .2 ! 2 3 4! 2 3 4 !
%: # % && & +, #% & ?>
+, 5#,"# M & & & +,#% ./+ & #> > $( ,#5#3" & 7; ?4; " ! #% ./+ & " &4#,;4#F;#$ > $( 7; # ) & #
2 & 56" !
( 7
8 +!'M+!%
8 ( ) +!%M!%
. !*M!/
2 $!0M-!%
.2 -!*M/!0
) ? ?#6;& # B ?% ? ?% &5#76#7;& #% & ./+ +1 # $ ? ?%
! " '+
?%#( ?% ? ?% & & #
% #% 9
=! 2 . ?@"
&=. 88 & ' #% 0 88 & & & 88 & 88 88 T
C ?? S 2D T # ?6" 0 D T E . . === 1 U
% & #
( & ?% % :& & ! W3F#7 +,# ( 0WF#67 & 0?! W6#?;#C & 4#,M4#F;# B ! ?6#( ?% 3F#7 & !22 + # % ?%
WF#3@/4#43 ?! W@#4;# % & & " 6#?;#
$ 88 & #% & 88 & & > > #>& ./+ & #
) & #1 & # % 88 88 & # % ' #1 & # # ,446" & C$> # B ./+ & #
! " '
1 ./+ & & #1 5#?5 & !22 + F 7#3#F"9 & #B ?% ? ?% 1 5#?5# % ,#:; ?34+8" 7#7;5,/#(& 1 7#?F#% & & 6 65; 6@; & /?#6;"#% ?%#
Increase of 1L1T mode frequency during 1T-mode excitation Excitation frequency
First overtone of
secondary H2 mode 1L1T mode
1T mode 1C mode of
secondary H2 1L mode
Sensor artefact (water cooling) LF chugging
(Nonlinear coupling of excitation frequency
with secondary H 2 mode)
# $!$& ) !
( 1 5#?5 & & & & F?44+8# % & +,& F?44+8#> & & +, # ! +,
! "
1 5#?F& & #
( & 1 5#?5 ?% # % #! & ?%1 5#?: 54 & &D+, ' #$ & 1 5#?: #$ 1 5#?: #% # ) & #1& & #% & #
6 5000
Resonance modes
1L1T
5
PCCdyn2 raw signal
4500 1T
acoustic pressure amplitude, p' 4
1L
3
4000
2
1 3500
0 Pressure (bar)
3000
-1 Excitation frequency (Hz)
-2
2500
-3
-4 2000
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
Time (s)
# $% & #'" ( $
10 6000
Resonance mode
1T 1L1T
8 PCCdyn2 raw signal
5500
acoustic pressure amplitude, p'
6
5000
1L
4
4500
2
4000
0 Pressure (bar)
-2 3500 Excitation frequency (Hz)
-4
3000
-6
2500
15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
Time (s)
#$" #)* & '"$
+ )!,-. / & & # $0 )* & '"#$!
!" 1
% & &+,' #( & +, & 1 5#?@# 1 & ?% & # +& & D+, 1 5#?7 # D+, ? #% & ?% # ( 344+8 ?% & #% 1 5#?@& @F#F+8* & & & ?55#5+8* #
+ )!2- & / 3/ 4* & 3"!
. & & D+, +, & ' #$ & &+, ' & > F# 1 +, < > ?655" )*+, " &5#7#1 & 1 5#?@ & & ?4#:# <R
!" 4
+, &&+1 #% > # ?65@"
! ? " # ,4" "$ ! ,7#? $ '
= 1 5#?@ "$ "W?,/ & +,' "$W:7/#
> "$ " ! ,4" ' ! " ' !$ & # C ' ?% & #
1 ' & Wf?3#5 f?7#? 34 +, 1 5#?6#% # % ' #% ' 9:; ! +,F?; ),7; +,#% ' 1 5#,4 Wf,4 f,4#7 #. & ' & ?% #
. # ,446" & ' & ' #% ' & ' & -+" ' ' # % ' ./+ ?% 3#3#:" #= ?% !22 + ' & #$ ./+ ' &# +,' & #
% . # & ./+ # % ' +, 3#7 ?5#4 & D+,?#7 5#5& +,#! ?% ' & ?#35/4#43#< & ' + & +, & 4#3, ,:; -$$ # ! ? ./+ ' #?
!" 5
?#47/4#43#( ' &' ./+ #
-30
1L 1T 1L1T 2L1T
Combustion chamber 2L
-40
1st excitation overtone
-50
-60
-70
-80
-90
-100
-40
H manifold
2
LOx manifold -50
Power density (dB/Hz) density Power Secondary H manifold
2
-60
-70
-80
-90
-100
-110
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Frequency (kHz)
+ )!6-% ( / 4* & 3" + )!2!
-30
1L 1T 1L1T 2L1T
Combustion chamber 2L
-40
-50 Excitation frequency 1st excitation overtone
-60
-70
-80
-90
-100
-40
H manifold
2
LOx manifold -50
Power density (dB/Hz) density Power Secondary H manifold
2
-60
-70
-80
-90
-100
-110
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Frequency (kHz)
+ )!*-% ( 4* & 3" + )!2!
!" )
( ' & ) A(Y( F#3#,"# ( ./+ ) - W *, & W7:5* - W?563+8# ) 1 5#,4 ?744+8 & # % ) ?% 1 5#?6# % +,' & -$W $*,$& $W:53* -$W3@F7+8# ( +, &# % ' 1 5#?61 5#,4#
%1!& & ' #% +,' ) ' 1 5#,?#% ' # % & 74F+8 +, 1 5#,?" ,64+8 ) 1 5#,?" #% +,' ) & 3?,@+8?:6@+8 1 5#,?1 5#,?" #% #
% ) && 1!# ) & & # % & 1 5#,? 1 5#,? #% 1 5#,? 1 5#,? +, ) # % 1 5#?61 5#,4#
( +,1 5#,?& 7, ./+ ' 1! # % & ' #
!" ,
(a) First bulk mode of H 2 manifold ~ 503 Hz (b) First bulk mode of LOx manifold ~ 290 Hz
(c) First longitudinal mode of H 2 injector ~ 4218 Hz (d) First longitudinal mode of LOx injector ~ 1798 Hz
(e) First transverse mode of H 2 manifold ~ 9294 Hz (f) First transverse mode of LOx manifold ~ 7320 Hz
+ )!-+ " ( # $ 37 ( # $!
!"
% ' & #. 88 ' #J & ' # & && & ' # % & & ' #
% ./+#(& ' & #( & & & # +& ' & &#% +, ./+ ' +1 #
! ./+ 88 & & +1 #( & ' 1 # & ? ? ' ' ?%& ' # & 1 +1 & & & #
( & ?% # % #% & & +, & #% & &+,' #$' & #
!"#
8!
$ # )+2" & )+2 # ?%? #
% # % #( & #% 3454 #
8!5 '* '4,--)"('#' &, ' $ '
! & F#3#,3#?#( & # & ./+ #
% C$> & 88 ?%" 3#?#F"# ,445" C$> & )*>+3 54 & & # $ #%C$> ' & & #% ?% )+2 & # & & # ,44@"# C$>& )*+, # ,44F" 6 ,# ! & #%M+(C C$>& &
!"# $% &
88 88 & & C # ,44@" #
%> > & 88 3#?#,"# / # ,44:" ) & / ,446" ,44 )*+, ?% #% )+2 & # % & #( / & & #( ,4??"& )*>+3 > > & # 88 & ' & #
( & ' )*>+3 & 88 & C ,445" = 3#?#3"# % ' 88 & # C # ,445" && ' & & #
( = & " ?% & D>>" 3#?#7"#< Q R ' & && # # ,4??" Q R D>> #+ & >+2 & # ! & Q R #$ & #
./+ )*+, ' ! # + & )+2 # % )+2 # % # ) & Q R +," D+," & #
!"# & $
8!6 )"(' # 0 #'
$ & 34 54 D+," Q R +," & W 5# $' %@# & 34 +, 54D+, #% ( .# % #( )+2 & 54 & D+, . &1 :#?#) &# < & 4#@ 4#F; ! ?#, ?#3;#$ & #% )+21 :#? & 8 & )+2 #$ ' & #% ' #$ ?4 ,4 &' )+2 & )+, #%& ' & #( ?4 ,4& ' #% # % & #$ &1 :#? ' # % & ) ' # % ' && ?44"& & & ' # & ) & > @#
' ()* "
+% +% +% ,% ,% ,%
' -#.#.#-#-#.# / /
0 1 2 +%"3 +$"4 +"4 ,%"+ 45"5 ,%" 6 ,"+ ,"% ,"% ,"% ,"% ,"%
& * $ 172 % 34 4% , ,
8 * $ 172 $% $ , $ 4 , 9 : 1; 2 + $+ $ $ +% )* % ++", %"3 ,"% $4" $4" ,"$ 6 3"+ "5 " ," ,"$ "
!"# $ &
coaxial injection BKH window width: 100 mm element LOx
H2
line of 50 mm sight
window combustion chamber cross-section showing the Central jet combustion 5-element injector raw OH* image chamber wall window chamfer resolution: 224x112 pixels 128#<
combustion emission (near-infrared)
line of sight
LOx core of central jet raw shadowgraph image window chamfer resolution: 890x445 pixels 1 2! :
& 3"() 8#< = : 12= : 1 2= "
% )+2 1 :#? # = )+2 & # % & ' #( )+2 7 & 1 :#,#1 #% & & & #% 1 :#,# % # # % & ,7& ' #% & ' # ( & & ?4;" 88 & & && & #( 1 :#F& (. 34 & +,#> . 1 :#F" ' & ( 1 :#F" (#( &
!"#
' .#$ 74& #% & & #
#$ % #$&"'
(!)*+ % #$ &"' #$ ,- %.")!
#$/-01") 2#$/-01") 3
(!*+ &"' /-01") 2#$0 /-01") 3#$!
% )+2 & ?% 1 :#3#% 7 ,4 ?% # % & W3#37/4#43 ?! W:#3;#$ &1 :#3 )' & &&#% 1 :#3 # % & && ) & 9 && 74"#( & #
intact core
acoustic velocity
#$ % #$&"'
(!/*+ % #$ &"' #$ + %45(!/6!
!" "# Ayhr rr
Line of sight
Cross-section Cross-section Intensity hPss rhpr/2 !*
Line of sight
Cross-section Cross-section Intensity i Uqr rhpr/2'*
Avt r&$)Q wrprqp rpvsursyhrs ur#ih rvuGC!phr6
Line of sight
Cross-section Cross-section Intensity
hPss rhpr/2&*
Line of sight
Cross-section Cross-section Intensity
i Uqr rhpr/2%*
Avt r&%)Q wrprqp rpvsursyhrs ur#ih rvuGC!phr7
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv
% ?% & 1 :#71 :#5& 34 & +, ( . # ( & )+2 F4& ' (77 & .# % Q R # $ )+2 # < & & & & 1 :#71 :#5#B (1 :#7 & & & & ) ' # % ' #=?% 1 :#7 & #% # % # & ' # 1 .1 :#5 ' ' ?% #$ & (# 1 & & ' 1 :#5# > 8 & # % 1 :#5# # ,443" ,445" C$> ?% F#3#,"# % & #$./+ & ' 6#, ?: C$>" #
8!7 )"('$ &)"0'('
! ?% ' # %
? # ,?"
1 ! #1 ?! W6; #154 & D+, W?:F?* ""W?#F@ " & & >!(," & D C. ?663"# % W??F* # % ?% ' ' & +,' #
!"# $
)+2& # ( ?% & &&#( & &&# 1 & #% & @ ,75 ")+2 & " #% #( & #1 #1 :#: & # . & )+2 &#
1. 2. 3.
Displacement Selected tracking point
%"%& '""( ) ")*+#,' *( ' * *( * "
% # 1 & &
" ,,"
& ! ,?# )+2 & ./+ # ,3 ? ?% #% 1 :#@# % & #B # ( # 1 & & # B ?% & #
!"#
Test time (s) Test time (s)
30.061815 30.062115 30.062415 30.062715 14.883448 14.883748 14.884048 14.884348
8 8
measured flame displacement
estimated acoustic particle displacement
4 4
0 0
-4 -4 V e rtica l p o sitio n (m m ) V e rtica l p o sitio n (m m )
-8 -8
2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24
Frame number Frame number
$%&' ()#* $ %&' (+#*
Test time (s) Test time (s)
24.832033 24.832333 24.832633 24.832933 13.204330 13.204630 13.204930 13.205230
8 8
4 4
0 0
-4 -4 Vertical position (mm) position Vertical (mm) position Vertical
-8 -8
2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24
Frame number Frame number
$%,' ()#*$ %,' (+#*
"-./ "
8!9 1 "( 0B'( , #' &, '
% )+2 & #( & )+2 #% &1 :#6 34 +, .& #1 & ?,744 ?4 #% & & #% 9 ,:44+8 7344+8 #% # % #B ,:74 +8 Wf3#: & ? 5,74 +8 Wf?4 # % 1 5#?5 5#7"#( J )+2 5,74+8#% && 5,74+8 Wf3#3 4+8 Wf@#F & #
% )+2 & )+2 # % ? F?44+8 ?%
!"# -
3444 +8 ?% #$ ? ' & ?% & ' #$ ?% Wf7#, f7#3 3744 +8# % ?% ,% #%,% && ? #( #
Alias Excitation frequency first overtone (alias) First artefact overtone 2T mode response? Excitation Excitation or velocity response? frequency frequency (alias) Alias 1T mode response
Alias Alias 1L mode response Primary artefact frequency
Alias Alias LF chugging during 1T-mode excitation Alias
"0.! 1#2 &' (+#*3 4"
1 & ,3444 #% 3 # ?% 34 54 & D+, &1 :#?41 :#?? #%)+2 & ?% #% & ' && &#J &3454 # ( 54 54#
!"#
3rd artefact overtone Alias Excitation frequency first overtone 2 nd artefact overtone Alias Excitation frequency 1T mode response Excitation overtone response 1st artefact overtone Alias
LF chugging Primary artefact frequency
$" %&! '#( )% *+#,"
4th artefact Excitation frequency overtone first overtone Alias
3rd artefact overtone Alias Excitation overtone response obscured by artefact overtone 2nd artefact overtone Excitation frequency Alias 1T mode response obscured by artefact overtone 1st artefact overtone
(little LF chugging Alias in this test) Primary artefact frequency
$" &! '#( -% *+#,"
!"# # Ayhr rr
C " )+2 # C 3454 & D+, &1 :#?,1 :#?F #% C # ? ?%? ?% #1 C && & C #( ? #% ? #
% C ? & # C ?44 ? & ./+ #% C !22 +"& & & ?44+8 ? #( & #< /?4) ??#@ ? "8 & #% C )+2 #
Excitation frequency overtones
1T mode overtone response
1L1T mode response
1T mode response
Natural 1L mode 1L mode response response
Avt r& !)Trp t hsuyvyvr vthyh#ih vuBC!
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv Ayhr rr #
Excitation frequency overtones
1T mode overtone response absent?
1L1T mode response
1T mode response
Natural 1L mode 1L mode response response
Avt r& ")Trp t hsuyvyvr vthyh%ih vuBC!
8!: 1 "( 0#' &, ' , #" *'# ''%0 " ,
+ )+2 & & # )+2 & ?% & #% " & # % #% & ? " " " # % & & ,#5#F" & ! 3"# % ! T
OO 4 # ,F"
$ & )+2 * # %
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv #! Ayhr rr
# %
" " " ,3" ! "
& " #% " & !22 +#( ?% 1 :#?3#J & 88 &#% " && & ! # % " "# %
" " " ,7" "
& "
? " . " ,5"
# ( 1 :#?3#
?% 34& D+, 1 :#?7#1 :#?7 &)+2 "& "#% # 1 :#?7 1 :#?7 #% * )+2 & # % 1 :#?71 :#?7 #( & # < 64 " 64 "#% ?% & # 1 )+2 # % 1 :#?7 # & & # & ?% #
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv Ayhr rr #"
hQrhxhpvp r rhyvqr
iQrhxhpvprypvhyvqr
Avt r& #)Srp prqhpvp r rhqrypvqv vivsur Uqrrqs urphypyhvsShyrvtu vqvpr0hhurvsrhxhpvp r rs Q88q!hhqrh r shppyryhr hurvsrhx rypvhyvqri
% & 1 :#?5# % & :#F &)+2 1 :#?5# 1 :#?5 & #( "#+ & "#% & & #+ & &#$ &
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv ## Ayhr rr
# % & & #
hUvrhr htrq hPCvhtr ,
iUvrhr htrq r rShyrvtuvqr pUvrhr htrqrypvShyrvtuvqr
qUvrhr htrq r ruhr rUvrhr htrqrypvuhr
Avt r& $)Srrsursyhr Uqr rhprph vtvrhr htrqqv vivsur hPCvhtrh ur r rihrqShyrvtuvqriurrypvihrqShyrvtuvqrphpvp r ruhrqhqhpvp rypvuhrr
' < J ( ,4??" # ,4??" ,4??" # C & & #$ & & # % & #
1 #> & #<J ( ,4??" & #( & & #
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv Ayhr rr #$
5.
5.
10.
flame absent
4.
4.
9.
displacement
3.
3.
8.
(a) Example frame sequence 1
(b) Example frame sequence 2
2.
7.
2.
flame present
1.
1.
6.
Figure 7.16: Sequence of raw OH* images (upper row) and band-pass filtered emission distribution (lower row) illustrating how transverse (up and down) convective motion results in artefact signals in band-pass images. example frame sequences are given from excitation of the 1T Two mode at 4350 Hz.
Avt r& %)Trrprs hPCvhtrr hqihqhsvyr rqrvvqv vivyr vyy hvt u hr rhqqprpvrv ryvh rshpvthyvihqhvhtrUrhyrs hr rrprh rtvrs rpvhvsur Uqrh#"$C
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv #% Ayhr rr
8!< 1 "( 0#' &, ' ,), + $ ")'%0 " ,
1 & ? #( ? 1 :#?:# % ?% 1 :#?3 & & ? #> ? #% " 1 :#?@ 8 && ' " & & #% && #
hQrhxhpvp r rhyvqr
iQrhxhpvprypvhyvqr
Avt r& &)Srp prqhpvp r rhqrypvqv vivsur Gqrrqs urphypyhvsShyrvtu vqvpr0hurvsrhxhpvp r rvurvqhhqrh r shppyryhr hurvsrhxrypv hyvqriUurrypvhvqrvyphrqq rhsurvq
> & 54 & D+, 1 :#?@ &
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv Ayhr rr #&
#% &# % & " 1 :#?@#
# % & # %& & # % & & & &&#% & 1 :#?@# & & & #
' & & Q R ($"#%($ " 1 :#?@#% ($ 1 :#?@" @#7/7#5 )+2 #% 1 :#?@ 8#% & & & #% 1 :#?@ 6@#:/7#5 ($ ' & & #
< & )+2 & ? & #% & +< ?655" T
OOOO " " # ,:" OOOO " ,
+ #( & & )+2 T
BB " " ! " = # ,@" , C " S BBD T =E ! U
% ? ( 54 & D+, 1 :#?@" 1 :#?6#) )+2 & #% ($ 1 :#?@ W4#@?/4#?5#
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv #' Ayhr rr
< ./+ #( W4#:@/4#F7& & . 54 & D+,# % 1 :#?6#% & & .# ? 34 #%? 34 #
6 rhsvr r6D
hUvrhr htrq hPCvhtr
iQ r rihrqShyrvtuvqr pWrypvihrqShyrvtuvqr
qQ r ruhrrWrypvuhr
Avt r& ')Srrsursyhr Gqr rhprph vtvrhr htrqqv vivsur hPCvhtrh ur r rihrqShyrvtuvqriurrypvihrqShyrvtuvqrphpvp r ruhrqhqhpvp rypvuhrr
h%ih vuBC!phr6i%ih vuBC!phr7
Avt r& ()Srrshp qv vivs pyvtsPCrvvvuhpvp r rq vt Gqr rhprv rh%ih vuBC!phr6hhq7i
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv Ayhr rr #(
< 8 & #. 88 + < ?655" "W?#F@W 4#@59 # % ./+ 88#+ & 88 & #
% & # ( )+2 #% # & #
8!8 ., ,( ) &) '##' &, '('" #'('
& )+2 # !22 + ?44 & ? #% & ! ,@ # )+2 ./+ # ( 1 :#,4# 8 4#5 ?#?# % & D+, +,#( & ? # % & )+2 1 :#?6 # % " & 54 #
1.5
GH off-resonance PM1
2
GH PM1
2
GH PM2
2
LH PM1
2
1.0
LH PM2 N
2
GH high-speed camera
2
0.5 Response factor
0.0
40 60
Chamber pressure P (bar)
cc
Avt r&!)Srrshp s pyvtsPCrvvvuhpvp r rq vt Gqr rhpr
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv $ Ayhr rr
8!; (("#1
)+2 & & 8 ./+#B ?% & & ' #$ )+2 & ' & # C$># ' ./+ ' C$>#
( ?% # B #
%)+2 )+2 #% )+2 #. 8 ? ' # ?%? & )+2#% )+2 ?% & #$ #
> & ? & #( 4#@ & ? # % & ./+ #< & +1 # $ ?% +1 #
. ./+ & +1 ! # $ ?% +1 ' #( ?% ./+ #% #) + ?657" ' #> ?6:," ?654 # B 1 ? 8 ' ' & ) NS?66F"#
$./+ # # ,443" ,445"
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv Ayhr rr $
& +1 # % ' #1 & # $ )+2 ? ./+ # B @ :) " & )+2 #$ & & & ?% ./+ ? #
1 # ?% & +1 # ,44@" & & ' # ' & O P# & ./+# ( & & & 9 & #% ' ' ' # % & & # # B & #
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv
;!
B & ./+#% #% #+ & & #C ) & & #% & # % & #
;!5 '* '4,-,%1+' 0,#' $ '
% ) ' & #1 & & +1 #J ) & #
$ ' ' #$ ) #<& # ,445"S> ) & ,44:" & )*+,#% & & ' #"#% & & & & )*+,#S & )* & & 3444 "# . & S #,44:"#
1 #% S
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv $# Ptrp r rr
# & & & ?,4+8 & ## J ) & ' < & ' & #1> ?66," O P ' > 8 ?667" + ,444" & #
# ,4?4" )*+, & & # % & & # # ,4444 && #1 & +1 9?444+8#
) ) +1 #% & +1 # % ' ' #! C ?677" & ' & & ' # B > ,445" ' & # J,*DJ,"& )*+,#% & ! W74#3"# % ' ' & & C N % ?6659 C # ?6659 C # ?66@9 > # ,44F" #B > & & # 1 C # $ B & & +1 #. C & & #
+ ?657" ) )*+, & # % ' 9+,& ' & )' #+ & #. & & # ,4??" ' )* & #$ & ) #
+ ' " & )*+, & < # ?655"#C & ?4 + N+ ?667"#$ & B > & C & & & #
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv Ptrp r rr $$
> N % ,44:9 # ,44@" 8 # 8 # ,44@" # & #V7#% && & ,#7; ! # % +1 & 7; ?4; " ! 1N/?66:"#
#,44@9 #,446" ' )* C$>& 3;# # ,443" ' & & )*+, 4#@;# / 1 ) & ,44:"7; & ## > >" & )*+,# J ) & & #
) B > & ' & #% & ./+ & #
;!6 %1+' 0,#' # 0 #'
$ & ! W 34 54 D+," +," & W 5# $' %6# 54D+, & (.>#
Uhiyr()Dwrpvh hrr s rvuuhqt huvhtvt
#ih #ih %ih %ih %ih %ih
Urqrvthv BC!GC!BC!BC!BC!GC! 678
8ivpuhir r r ih "($ #"$ %# $(( %# %! Shvsvqvr sry $( % % % % %
Cq trrr h r $ F !(! &$ !'" !'% !'& %!
Ptrrr h r $ F !( "! !( !$ !" !% Qr ryrrhsy hr t ($ ! "! "! "! #
Ptrvwrpvrypv " '' !# ! ! "
Cq trvwrpvrypv " #&% ' #$ #!" #!! '#! Wrypv hv % $! & "" "$ "$ %" Hrsy hv (& ( $( %" %!
PtrvwrpvSryq 1 "" $ # $ ## $ #! $ # $ ## $
Cq trvwrpvXrir 21 $& $ & $ %& $ $( $ $" $ '( #
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv $% Ptrp r rr
1 &1 @#? & 54D+, (#% ) ' ' &" #% & ) # % +,)" & ) +, & # % #% & & & &#( & & #
% & ' & ) 1 @#?#< ) ' & & ) ' & #% ' & ' #
coaxial injection BKH window width: 100 mm element LOx
H2
line of 50 mm sight
window combustion chamber cross-section showing the LOx core of central jet combustion 5-element injector raw shadowgraph image chamber wall window chamfer resolution: 890x445 pixels hDhhruhqt huvhtr
line of sight
central jet raw OH* image window chamfer resolution: 224x112 pixels iDhhrPCvhtr
Avt r' )@hyrvhhruhqt huvhtrhhqp rqvtvhhrPCrvvvhtruv shyrpy is h%ih rvuBC!
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv
1. 10. 19.
2. 11. 20.
core structure separated
3. 12. 21.
4. 13. 22.
5. 14. 23.
6. 15. 24.
7. 16. 25.
8. 17. 26.
next core structure 9. 18. 27. begins to separate
$ %"&'( ) *+ ,-#&"
!"#
B ) # % & #B ?F*' & ' # & & # % 1 @#, & #
./+ & ' > 8 ?667"# % & ' & 4#7 * B$" U?44 #(./+ #( ./+' # % ' & & #. & ?4 *' & # #% 8 ' & & #% ' 1 @#3 > 8 & ' ./+ 1 @#,#% & ./+ # ) ./+#
A NOTE: These figures/tables/images have been removed to comply with copyright regulations. They are included in the print copy of the thesis held by the University of Adelaide Library.
$ "%&' ( ) *+,,-"
$ ".&( / 0 +( 1) *,,2"34-"
1 ) &&#$ 74;
!"# ,
& ?7 && && #1 &&9 ?44,@#7 )' *'a,@#7"#( B > ,445" J,*DJ,
?, * ' # ,6" # 7#4
1 54D+, ./+ *'W3#@ #$ & B > ' &
,7 * ' # F4" # ,#4
% *'W?:#3 ./+ #% *'W,7#: <& ?66F" 9
33#4 C S ' 44,7#4* D $ T :5#4 B ,,#4 # F?" D T $ E U
% )' < # % < M > D ?666" & ) #%<& & )*+, <& # ,445"# ( & #
$ ' & & # ,4?4" *'W34# # # & # 1 & ' # $ ./+ ' ' & ) #% #<& #
& %68 ' 1 @#7#J & 1 @#7 & & #% 1 @#7 # i ) & & ! W3454#
!"# 54
+-.4 26#3
+ -54 26#3
+ -.4 27#3
+ -54 27#3
$ "&( 0 +.4 - +54 - 2 .4 06#3+-254 06#3+ -2.4 07#3+ -2 54 07#3+ -"
# ,4?4" & 34 54# 1 # % " W?73#76/" 54# #1 & & " D #,444"# 1 @#5 & #. #
!"# 5
& & & & # % & #1 @#: ),*+, C #$ & # % ) ' ! W54#
A NOTE: These figures/tables/images have been removed to comply with copyright regulations. They are included in the print copy of the thesis held by the University of Adelaide Library.
$ "5&( $ "8&! 9 +' 1!344.2"-" +' 1!344.2"-"
;!7 1 "( 0#' &, ' , #" *'# ''%0 " ,
( & #B ?% ' ' & +, ' # % & )+2 & & ?% & :#, 1 @#@ #$ & 1 @#@ ) 1 @#@& a:*'& ' #
$ & &1 @#@ & # ) ?% & & # $ 1 @#6 ) & a?#7*'" & ' #$ F Q&&R & &#$ 3 & F & & & # ( 8 )
!"# 53
& # % & && #J & ) & & > B % ,44F"B > ,445" ,445" + ?657"#$./+ ) ' & ' # ) & #
intact core
acoustic velocity
+- + -:
$ "&: 0 + 0- #; + 0 0- +-2 : 09<8".=+ -"
$ 1 @#6 & & #% & ?% # & +,#% )+2 # $ & +1 # ,44F" & ' & & #$ & # 1 & ? # C # ,445" ' 3#?#3"#$ & &' && # & DJ, & & #% & & & # % DJ, & ./+& & ' & & #
!"#
intact core
acoustic velocity
1.
surrounding gas has 1. shifted downwards with acoustic velocity
2. pocket of LOx gathering on downwind side of core
3.
3.
pocket has torn away from intact LOx core
4.
4.
5.
$ %"&'! ( ) (*#+, +),))) - (./0"12"
' ' # > % ,44F" & F#3#?"#%' .
!"# %# Ptrp r rr
& & ' ' # ./+& &#
A . # ,446" ' #< & # B & & Q R#% && ' &# % & & & & & ' # < . R & ' ' & ' #1. # & F & ' V?4 B$V ?4,#V?"#./+ & & #1 & . R ./+#% ./+ " & "& . # & & #$ & +1 #
;!9 "0 0,#')' + .('" #'('
& & # ( & & #1 #% & & #= & ' & # C & ) #%8 #1 @#?4 ' #
% :7;# C & # > & & # B # 1 & ' #% #% & & #C ' ' /4#7*'#
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv Ptrp r rr %$
LOx core Analysis area (a)
(b)
(c)
Avt r' )Hhw rvurrvhhrqp rqrrpv vr0urivh vhtrp rhrqsyyvt r prvt vuurr rpvsvrqhhyvh rhhurvhpp rpr ryvrihqurprr yvrr yhvqur hvhtrp
8 8
Shadowgraph recording Shadowgraph recording
6 6
Acoustic pressure amplitude, p'
4 4
Raw dynamic pressure signal
2 2
0 0 Pressure(bar) Pressure(bar)
-2 -2
O ff resonance
Off resonance
-4 -4
1T mode excitaiton
1T mode excitation
-6 -6
24 25 26 27 28 29 30 31 32 33 24 25 26 27 28 29 30 31 32 33
Time (s) Time (s) hSrp qvt hr&s iSrp qvt hr!s
Avt r' )6pvp r rvthyhquhqt hu rp qvtq hvs %ih BC!phr6hhqphr8ivu uhqt hu rp qvt hrs&shq!s rrpvry
@r vrhyvrvthvsuvtus rrppivvhivyvvp trvptruq tr pxrrtvr EvTCh qv
> & & ?% #( & 5#3#F9 C ,#% & 1 @#?? 54D+, (>& #< & & & #( ( & :444 ,4444 >#% # 7 & #% F7 ?44 :444 ,4444 # ( #
! &7 &1 @#?,#% > ,4444 " & 1 @#?, & & 3; 1 @#?, & :;#$ & & # ( #.  & #
C*' %6 1 @#?F#% F4; " @;#% *'& & 5;#$ )' & Q R # ( a5; & & # > N%,44:9 #,44@" J,*DJ, ' # ?#, ,F ' ?U#U3# 8 # ,44@" &F4;74; # #$ & # # +& #
% #% 54& D+,#% 1 @#?F a,@#7*'# % 34 & D+, & aF#7; & 54D+, #C 34 & +, & & a:#F; @#,;# % 54 D+, ># C 54 & +, a7#3; & & #% & & &
!" #
#% ? 1 #% & #
% 1 @#?F " # & & #( #% & & && #
100
90
80
70
60 shedding of
core structures
50
40 Frame number Frame
30
20
p'/P = 4.0%
cc
mean = 53 10
Std = 7
0
0 102030405060708090100
Core length (mm) $%& '
100
90
80
70
60
50
40 Frame numberFrame
30
20 p'/P = 7.1%
cc
mean = 26
10
Std = 1.6
0
0 102030405060708090100
Core length (mm) $%"
( )!*+( & , $-- % . - '/"*!0 ' ' ' $%1 $%' !
!" )
Transverse acoustic velocity, u' (m/s)
0 6 13 19 25 31 38 44 50 56 63 69 75 82 88 94 100 107
28
60 bar, GH , test A
2
60 bar, GH , test B
24 2 )
60 bar, GH , test C D
2 / L
20 40 bar, GH
2
60 bar, LH
2
16
40 bar, LH
2
12
8 Normalised intact core length ( length core intact Normalised
4
Trendline for all 60 bar, GH tests
2
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5
Relative acoustic pressure amplitude, p'/P (%) cc
( )!2+3 $4% $4%!
% & #B > ,445" C # % & B > #% B > & B N> ,4459 > N%,44:9 #,44@9 8 #,44@" +1 #$./+ ' # $ ./+ #% # +& +1 #
$ 1 @#?F & *! 8 #+ & )#%&& & ' ' # % 1 @#?3 +, ' 9
, # F," , $$
% & - & )#% +, ' # % +, ) ) #% & & ' #
!" 5
% & D+, & +,1 @#?3 &' +,#% & D+, & ' # $ 34 54 & +, & D+,# +& & +, #
28
60 bar, GH , test A
2
60 bar, GH , test B
2 24 )
60 bar, GH , test C D 2 / L
40 bar, GH 20
2
60 bar, LH
2
16
40 bar, LH
2
12
8 Normalised intact core length ( length core intact Normalised Trendline for tests with GH 4
2
Trendline for tests with LH
2
0
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11
2 2
Ratio of transverse acoustic to H -injection momentum flux, u' / u 2 bulk H H
( )!6+3 $4% "* 7 !
28
60 bar, G H , test A
2
60 bar, G H , test B
2 24 )
60 bar, G H , test C D 2 / L
40 bar, G H 20
2
60 bar, LH
2
16
40 bar, LH
2
12
Trendline for 40 bar, GH test (J = 9.7)
2
Trendline for all 60 bar, GH tests (J ~ 6)
8 2
Trendline for 40 bar, LH test (J = 1.9)
2 Normalised intact core length ( length core intact Normalised
4 Trendline for 60 bar, LH test (J = 1.1)
2
0
1000 10000 100000
Transverse acoustic Weber number, u' D / H O O
( )!,+3 $4% 8 !
( &1 @#?7 < #% <
, $ ' B" FF"
& ) #+ ' +, ) -$#M ) & M> D ?666 #3" & W7#7J* & )
!" #-
34WF#7J* 54#% < D+, +, & +, # 1 3454 #< 34 & D+, +,& 54 #$1 @#?7 #% & # #
;!: '0, $"#1" ,( " ,
& ,#7#F"# B ! & ?, # ?667"#% #+ #$ ' * * D # ,444"# % ' # ( ./+ & # $ :#F & ' #< & & ) & +1 #
( ?% ./+ & # 1 & #% ) # ( & ./+ 8 & C CN% ?6659C #?66@"#% ) # % & ,4??" > > & )*>+3# < ) M> D ?666"#
+ % < BW- D '? W- D'?) # ) ' ./+ 8 # % &#% ) D # % & :#F"#( WF#3@& &
!" #
./+ 34 ?% 3,33+8# % W?45* #
& ) 8 & ./+ 34 #B '8+ & M + ?66@" & '8+WF7 @4) & # +& 8 & 8 8 )*+, & ?663"# D . ?665" '8+ :3) )*+, ?4 #CD ,44@" )*+, ,:#7# % ' C! ' ./+' #% & & & W?, ,?#W4#5F ?#,@#./+' 34 +, ' & CD & # & ,4) 3@)# & & #./+ ' 34 & D+,& #C D# '8+ &. # ,446"D # ,444" & B$#% +,' D+, 8 #( 8,4) +, ,@)& & CD +, #B 8 & . # & & #
M ) !1 ) J $ % ,44,"# % & M # ?666 #3" & ,J* 5J* 34# B - ) ) # + ) 9 D+," ' D)" & & ' & W5#% < & 4#7 #% B? & M # #
B % ?4# ( 4#7 B B? # ( & B # 1 @#?5 1 @#?: & )
!" #*
M # ?666" & # B B ) ./+ %?4#
( ' ' #+&' ' &' & *' & ' 1 @#3"# % & & & #% %?4 ) ) ' #
$ & & #( & & && & & # $ )+2 :#3 ?% & ?% # % & ,% & # $ & ) & #$ ?% 54 1 :#?F# % & ) 54 #
0 -+/ & !
9:" 6- '/"* 6- '&"*
& $)% *) 6)
2 & - $ 4 % 5*- 5
& $34% 6!- 2!
< $ % /"* / =/"* / =
0 $4 $:% *)- 2-- 26** #, 2-- 26**
2 > -4 $ 4 % 2!6 ,, !5 , ,, !5
? )4 $)@!% )! *!, -, 2!5 *!, -,
> A 1 ) #,2* ,2 516,6 *1)# 5
> 8 21 *5 6)2 6# **,2 )*)5 *)6
. 21 41 -!, #!) 6)!* *-! !* #2! *5!# @ = .<* $/ BC 9 556%
!" #2
( )!. ( )!# & 2- $? 1. B/ 555%! $? 1. B/ 555%!
;!< (("#1
+ & & ) ' # 1 ' ' # % ) & ,@#7 *'# % & && #% & #( ' ./+' #i & ' #
% & ' & +1 #( ) ' #% # % ! & # > & ' & ' #$ # 8 )*+, & +,) ' # '
!" #6
& & # & & & # i ) & & 3454 # $ 54 ) ' #
B ?% ) F4; #% # + & & & # C ' &# > & & "# % & & #% & ?% # % #
A & & ./+ #
% ?% ) & ) ./+ # % & ) +1 #$ ) & #
!"
>!
% Q./+R & ' )*+, !" & # ( ' & & #= 88 & & 9 # + 54 & )*+, # ) 34 54 # ) & Q R +," D+," & #
$ & ./+# % ./+ & # ( ' & & ' #% & & ' # % ' +, ' # % & # % & ./+ & ' # ( ./+#
< ./+ & # ( ./+ & +1" & @#F; ?5#5; " ?%"#B ?% 6 & #
1 & D+, +, & # & & )&
!" # .
,@#7*'#% & #%& ' & D+, +,#)+2 && 8& )' #1 ' ' ?4?'& ' #
+ &)+2 ?% ) ' # B ?% F4; #% & # + & #< & ,M7 ?'" ' & & #% ' # )+2 & ) & & ' #< ) & & #
> & & # % & # i ) ' & D+, +, ' # +& ) ' & #1 +, ' D+, +,' & < +, #C & & ) #
)+2 # B & # B ? " 4#@& #. ./+ +1 & # % ) ' & ' #% #! & & ) & +,#% & & #% & & & #
!"
5=!
% & +1 )*+, ! #+& ./+' #
( ./+ #( ' # & # & #1 ' #
% #% )+2 #% & # & & # % & #C & & ) #
% & & &# ) & W5 & ' "$ a 74 ,64/# % ' ./+ ) ' ' # ! ' & & #
$ 5 +,' & # % & ./+ & & # % & ' # ( '
!" #)
' #% ' 88 #
% ./+ # $ 88& #
( ./+& #C & # + # J ' ./+ & #
J ?% ! ' ' #% ./+ & #. ? & & & ?% )' #% & & # % ' & & #$ ' ./+ & & ' #
$ #$ +1 & +1 # % ./+ & +1 #+ & ./+ )' #% & & ./+ ?% # +& & #
J +1 +1 # $ & ' ./+#% #! ./+ # ./+ & & #
!"
55!
(JS$ ,4??"=1F1= 0^> &_ ?F#4(JS$#> (# ( ,4?," ( &3A ,4?,U T**&&&# #*& j*# V# . 1#. A#.#. D#B ># ,446"b. ' b# - . 0 #534#F47 F3,# . #A# 1#<# ?67@"1 -0 :0 : : J(>( C!7@!46 & 1 J ( > ( >)F4 ?67@# .& .#B# &%# ,443" - - 3,($((( C ! ($(( J7 @A ,443# ./#>A## ?677"b b# -0= 1 #,7#?4#7?F 7?@# . )# !# B#+' C#G.#%# ,44@" G - G : H & 35 ($((( C ! ($(( J: ?4A ,44@# . ,44:"I 0 G &@) ,44:U T**&&&##* * * *# V# .1#M#+'B#%# ?6:,"b( b +'B#%# 1#+#J((< B>#F?@ F,,# .# # ?65F"b> b# -0 - #F5#?, ?5# . /#A# ?66F"= 0 ,6 ($((*(C!*(!*(!!A > N! ($((C > ,@ F4 A ?66F# >#+D# # # >#M #+C#D 1# C# . # & B#> (#> # ?66@"b! ' b# -! ! #?3#7#@,5 @F3# >#A C# # >#> <#/ B#J#) &C#D 1# . #M # ,44F" G - 0 7 $ > %J,@ F4) ,44F# >#A C#D# # ># ,445"b b2 1 " 0 #?:@#?5? ?6,#
!" )- A
> .# ,446"= - 0 3: ($(( ( C ($(()17 @A ,446# > .#B B#<#%B# ,44F" - H - 33 ( C N! ($(( J5 6A ,44F# > .#%B#C<#. # A#A# (#) &C# ,44F" D H 0 0 G 7 $ > %J) ,@ F4# > 1# ,447" 0: 0:- - B % $ + = ( C C # >J# 8 #B# ?667"b ' "b G K ( 0 #?55# / /#($((J&S #?46 ?F5# >!#<#.+#!#<A# #M B#<# ?65@" - :: 0 -+LLLL J((%JB 365@ & > J((>)B?65@# > # ?67?"b( $T1 # & & b# -0= 1 #,?#5# ?5F ?:@# > # ?67,"b( $$T & & #+ b# -0= 1 # ,,#?#: ?5# > # ?6:,"b% b +' B#%# 1#+#J((< B>#?:4 ?63# > #># $# ?67F"b+ & b# -0= 1 #,F#7#F4? F?FF,,# > #DA#+'B#%# ?654"b% b=1# #F4#,#?76 ?5@# > #+'B#%# 1#+# ?65,"b% b=1# #F,#F#F55 F:F# > 1#!#># ,445"D . 2 20 -! 1 %) J ( % ) # > #(# ,445"! - 0 -1 & $ > A $,4 ,FJ,445# B B#<#> .# ,445"10: H - : H G - 0 0 33 ($((( C ! ($(( J6 ?,A,445# B B#<#> .# ,44:"bC ' b# -! ! #,F#,#F53 F:3# $8># ,444"b=M)+ b# -!0 'K= !0 #FF#?56: ?:43# B/ ,44:"= &@) ,44:U T**&&&# #* *+*%* ! * M *(*( 4@# V# B J#># ,44,"b> T&b! & 2 1 #,@#?4: ?74# B C# # ,44:"2 K G ($ ( ( < B#># B )#<# ?6:,"b$' b +'B#%# 1#+#J((< B>#FF5 F:F#
!" A )
1G#>J# ?66,"bC ' b= ( 1 #,#?F: ?7F# 1>#!#+C#1# ?65:"' - :0 - 0 0:- J((%JB 3434 & > J((>)A ?65:# 1 # ?666"M"! 0 0- B (*B%* * *66#4F?> J Bb! FC?666# 1 ##/C#B# ?66:"N - - G - - > $ (> C A ?66:# D(#D# ?6:3""0 -- >+ # D(#D#< +#D# ?6:@" :0 3!#> + # D (#Bi#S /#+# ,445": N?N$+ 0: H -: - 33 ($((( C ! ($(( J6 ?,A,445# D (#Bi#S /#+# ,44:"& G -10:2 H 1 ! 3F($((*(C!*(!*(!!A > ($ ( ( > )@ ??A ,44:# D # #. !# ?665"1 20 ( 0 G- 7> 1M ) J Bb ( 1,3 ,: ?665# D& C#. DC# >#/ 8%#CC#CC# ?663"102 H . 0 F4 ($((*(C!*(!*(!!A > $ $,: ,6A ?663# D $#> >#C>#M.#. C# ,444"b$ 8 b= ( 1 # ?4#3:7 7?4# D#C..#A# ?663"2 ! -2 -2 20 & 2 = O!3K= J(( ?F??D > J(( >)?) ?663# D 1#. #M #> <#) &C#M#M# ,443"b>( )Y D+,' b 0 0 K - #,44 + A#+C#SM# C#($((< B># +8 (# ,444"& 0 0 0!P-0 0 F5 ($((*(C!*(!!A > ! ($((+ (?5 ?6A ,444# +'B#%# ?6:,"b+ b +'B#%# 1#+#J((< B>#F4 F3# +'B#%# 1#+# " ?6:," J ( ( < B># +8 C#!#( <#!#C ># # ,4??"2 0 0 3: ($((*(C!*(!*(!!A > N! ($(( B> F?A F( ,4??# +C#1# ?657" - : H 0 0 J((%JB ,:7F & > J((>)C?657# +C#1# ?657" :H 0G : J((%JB ,:,7 & > J((>)C?657# +C#1#D&A#1# ?656"= -0 - H ( J((%JB 7FF6J(( & > >)#
!" )* A
+C#1#< # # ?655"= -- 0 - G ( J((%JB F:36 & > J((>)# +C#1#< # # ?655"= - :$ G ( 0 G G J((%JB F3,3J((>)C?655# +8D# (# # ,44,"1 0' -<'"> 0 G - - -: C $ D +D?71 ,44,# + .# ?657" 0 - 0 - CB 77?5 1% >> BJ&A C?657# + .#. >#> <# ?655" 0 - 0 - CB77,4 1% >> BJ&A C?655# + A#+ A#A# ?667"b$ * b #?56 SM#( <#($(( < B>#F6 :,# + !#(# A# #G.# ?667"b$ b & 2 #?56 SM#( <# ($((< B>#??F ?3,# + A#A# C# ?667"b+ ' b #?56 SM#( <#($((< B># F37 F75# $.#C<# ,44,"b% b # -! ! #?@#,#,3: ,7F# / #/ # A#!# %# ,4?4"(( -0 0 76# B B D + F? ( , ,4?4# /& +#/ /#% %# ,4?4"=2 !0 Q?.0 1 2 35 ($((*(C!*(!*(!!A > N! ($(( J % ,7 ,@A ,4?4# /.# B#+ #B#> #+# ,447"b% & ' b# -! ! #,?#3#:,@ :3,# /.#1G#) &C# ,44:" -?N$+ : 0 37 ($((( C ! ($(( J@ ??A ,44:# /.#) &C# ,445"$ 0 G ( -- ?$+ 0 ?, $ 1&M 8 D ( > B "D D?4 ?3 ,445# / /#BS#$8 J#% +#C %#)%# ,4??"1 - 3: ($((*(C!*(!*(!!A > N! ($((B> F?A F( ,4??# A#>#+ !# ,444"b ' 8 b = G - . 0 ( &#,:7 F4@# A#>#M !#+ !# ?66@"b. 8 & ' ' b# - . 0 #F7:#F7? F:6# #1 # ?6@:"& 1 - ! . ($((*(!*(C!*(!!,FA > ($ ( ( B> ,6A ,A ?6@:# $#(#> .#%B#D# ,44:"' - H : : G - 3F($((*(C!*(!*(!!A > N! ($((> )+@ ??A ,44:#
!" A )2
$#(# 8A#$#> .#%B#D# ,44@"! 2 #1 = 0&-- - !0 " G = 35 ( C N! ($(( J: ?4A ,44@# #A# <# ,44@" ' G 2 33 ($((*(C!*(!*(!!A > N! ($ ( ( + > ,? ,FA ,44@# %#GJ#SM# ,445"' - 0: H 0 33 ($((( C ! ($(( J6 ?,A,445# A#C# #<& #B# #A# ,4?4"$ 0 G ( -Q?N$+ H -- K0:- :- 35 ($((*(C!*(!*(!!A > N! ($((J % ,7 ,@A ,4?4# A# ?@:@"b% b #?@#F?6 F,?# A# ?637""00 - ,!#B J&S # !#+' C# B#. )#G.#%# ,44@"2 - --35 ($((( C ! ($(( J: ?4 A ,44@# A#+)# ,446"b! + )*C >$' > b# -! ! #,7#?#,3 F,# C1#!#># ?6::"b( 88b# -1 #77#,#,,7 ,3F# C <# #<& #B# #A# #YD# M#C ># # ,445"& G - K G 33 ($((( C ! ($(( J6 ?, A,445# C <#C# #<& #B# #A# ,445" 0 3,($((*(C!*(!*(!!A > N ! ($(( > # C<#$.# (#+ =# ?66@"! ( ?N$+ F3 ($((*(C!*(!*(!!A > N! ($((> )?F ?7A ?66@# C<# (#& 8># C# ?665" H 0 0 ?N$+ F,($((*(C!*(!*(!!A > ($(( . M 1 ? FA ?665# C<# (#+#M.#> >#D $#%B#D#<& #B# ?66@" b( 8 b# -! ! #?3#7#@F7 @3,# C<#% +# ?665"b ' * b # -! ! #?,#5#??F: ??3:# C<#)#+# A#A# ,443"b1 b "0 20 K= -. = ' #,44 #G #($((< B># C S#B # #># ,44@" H 00 0 G K ,> $J>( 1,F ,3) ,44@# CC#C#DB# ,44@"b' )Y ' b= ( 1 #?@#@7 65# C >#># ?677"b% ' b# -0= 1 #,7#?4#7,7 7F47F3#
!" )6 A
C/#A# A#>#J J#( <# ,447"& - : H 3? ($((*(C!*(!*(!!A > N ! ($((% (8?4 ?FA ,447# C M#+#B )#<# ?6:,"bB b +'B#%# 1#+#J((< B>#,F ,6# J(( ,44:"=1=:' G H 0 &@) ,44: U T**&&&# #* j * * *?,4j # V# J $ % ,44,"- "0 " ! <&!!>^> &_M :#4=##B > D CB# J $ % ,447""0 0 -- =## B >U T**& # #* * V# J&A#(#.8 & %#(# ?6:?"b. ' b ===# #6#@##?767 ?54,# J S#)%# C#% %#/ /#BS# ,4??"2 0 G 0 H - H 3: ($((*(C!*(!*(!!A > N! ($(( B> # J S#% C#/ &(#C8 /#S #)%# ,44@"$ 0:- G2 Q?$+ H & 33 ($((*(C!*(!*(!! A > N! ($ ( ( + > ,? ,FA ,44@# J S#% +#)%# +#/ &(#$ %# ,446"&-- - - - 0 H 37 ($((*(C!*(!*(!!A > N! ($((B>, 7 ( ,446# ) A#># ,445"bC ' b2 1 " 0 #?:@#,,6 ,7,# ) A#>#SM# ?66F"b> & > $ 1 ?! b# -! ! #6#7#57: 5::# ) A# # ?6:,"b% b +'B#%# 1#+#J((< B>#F,, F,7# ) &C#1G#D#> 1# ,44@"b 1 B > ( > ( b# -! ! #,3#F# 7,3 7FF# ) &C#/.# ,446"b$ & )Y*+, b! ! !0 B #%#.>#+)#A# 1#C#% !B #,3F ,5,# ) &C#CC# ,44,"b ' b= ( 1 #?,#6? ?45# ) &C#J#S.#> 1# ,44@"& G -- (
Q?$+ Q?2$9 - $ > ( 8 $ (> $ # ) &C# (# ?666"b ' b& #,:#36: 745# ) &C# (#/C#C<# ?666" G - +?N$+: H F3 ($((*(C!*(!*(!!A > N! ($(( ( >(,4 ,3A ?666# ) &C# A#A#. #+ A# (#> .#%B# ,445"b$' b2 1 " 0 #?:@#36 ?44#
!" A ),
># ,44@"2' K 0 RISI$R B ( ./ 44? D( > $ + 3A ,44@# B! $# ,44,"!'&8OL3!- ^> &_ B! $# M<(# .# #C>#( <#!# ,4??" - : H G 3: ($((*(C!*(!*(!!A > N! ($(( B> F?A F( ,4??# .# # A#>#! A# #( <#!# ,44@"20 ( -N :2 1 :2 H 1 1 . :& 2 33 ($((*(C!*(!*(!!A > N! ($((+ >%,? ,FA ,44@# B# # ?6@6"- 0 0- 0 0 - (D( B> # 374J(%)( D ( B J 1# #A#D B#># ?65,"2 0 : J((%JB ?346 & > J((>)) ?65,# (#(# ?6:?"2 : G (! >$# J&S # #(# #A# ?663"=G -2 N ? 1 & 2 F4 ($((*(C!*(!*(!!A > ($ ( ( $ $,: ,6A ?663# 1#+# ?6:,"b$' b +'B#%# 1#+#J((< B>#?75 ?76# >#B # 1# #M #># ,443"$ 0 2 = 02 G ! 34 ($((*(C!*(!*(!!A > N! ($((1 1?? ?3A ,443# >#B # #M #># ,44F"& = -$ 0 2 02 G 3 1& M 8 $ > % 1 !>1 F 7A ,44F# 1# ,445"& G - 0 B% R C C > !C,>" >J R!> !> # 1#B # #># ,44@"b! b= = #5,#?#?@ ,:# 1#B # #># ,446"b! b! -02 #F,#,#?55F ?5:4# 1# #B #># ,445"b+ ' b# -! ! #,,#3#:64 :66# 1# #B #># ,445" H K 3,($((*(C!*(!*(!! A > N! ($ ( ( > 6 ?,A ,445# 8A#$# $#(#> .#%B#D# ,44@" 1 :!0 2 #1 = 1 1 = : 2 #' 2 0 33 ($((*(C!*(!*(!!A > N! ($ ( ( + > ,? ,FA ,44@# B#!# ?65:"b) b===# #7#?#?5F ?55#
!" ) A
B#!# ?6:,"b 8 b +'B#%# 1#+#J((< B>#:3 66# %#CS#. C#># ,4??"b ! * b! -02 #FF#?F@F ?F64# D#J(#+C# !# ,44@"b ! ( B > b# -! ! #,3#F#7?5 7,F# <#(# ?6:,"b( T$ b +'B#%# 1#+#J((< B>#?5: ?:4# <#(#B A# #>>#+#. # ?667"b 8 T b #?56 SM#( <#($((< B>#F4: F33# A#># #A# M#( <#!# ,445"& - 0 3,($((*(C!*(!*(!!A > N! ($(( > 6 ?,A ,445# C# ,4??"$ 0 2 -?2$91 & 2 20 B% % = B B %J # C#D#) &C# ,4??"b% b# -! ! #,:#?#?@, ?@6#
A#A# ,44:"$ 0 ?$+ B% C !%= ((# A#A#.C# B#) &C#+)#A#D#C# ,443"$ 0
?$+ - :! 34 ($((*(C!*(!*(!!A > N! ($((1 1?3A ,443#
A#A#D# B#) &C#+)# ,44:"b )*+, b= 1 " 0 #??#F6 3:# B#.# ?676"b% b=1# #,6#@,@ @F7# B#< (#D B#) &C# ,447". 0 - G - 0 - & 0 " 0 " !P! > ( C & # D# #.8)# ,44?" : !#A< J&S # % (#)#C%# ?675" D B ( J & = ! $ ,, ,3( ?677# %8<#(#>!#<#D&%#<# ?65@"bC ?$' B $ b# -1 - #7#F#,@, ,@:# M.#> >#D $# ?666"1 0I : -' F: ($(( ( C ! ($(( J?? ?3A ?666# <A# #1>#!#CA#># ?65@"&-- - 0 - : 0 : J((%JB 3:FF & > J((>)# <A# #CA#># ?656"&-- - H 0 : 0 J((%JB 7F:7 & > J((>)( ?656# <A# # +#>#>!#<# ?655"&-- - H G 0 +L LLL: 0 : J((%JB FF:F & > J(( >)(# < #B# ?65:"b% & T b&&&" = & : #?7#,#:4 :F#
!" A )#
< # #C <# # ?654"&-- - G 0G ( - :- J((%JB ,@: & > J((>)C?654# <C#J J#( <#!# ,4??"2 -Q?2$9 G 3: ($((*(C!*(!*(!!A > N! ($(( B> F?A F( ,4??# <& #B# ?66F"! ( - H - H B % B C! = = (#
<& #B# #1# #A# ,445"Q?N$+ 0 H ( - 3,($((*(C!*(!*(!!A > N ! ($(( > 6 ?,A ,445# < (# B#) &C# ,44F"& G -0 - -- F6 ($((*(C!*(!*(!!A > N! ($(( + ( # YD#+8 C#!#( <#!#C ># # ,4??" G - 0 3: ($((*(C!*(!*(!!A > N! ($((B> F?A F( ,4??# S.#> 1#) &C# ,44:"b( 8 1 )Y*+, )Y*>+3 > b# -! ! #,F#3#:5F ::?# S.#> 1#< #) &C# ,44:"& G - G
?2$9 3F($((*(C!*(!*(!!A > N! ($((> )+@ ??A ,44:# SM#( <# " ?667" ($((< B># S# # #A# ,44?"b! ' * b# -! ! #?:#3 #:@@ :6F# S .#(# ?6@,"b% #?#(! +J J % )b# -!0 20 - ' #??# J#?# S S#>#/#C# A#>#( <#!# ,44@"2 - - G 0 <22>33 ($((*(C!*(!*(!!A > N! ($((+ >%,? ,FA ,44@# S S#>#)b+ # A#>#( <#!# ,446"& 1 -$ 0: 2 2 2 <22>3: ($((*(C!*(!*(!!A > N! ($((# G.#%# ?6:,"b> b +'B#%# 1#+#J((< B>#F?3 F?:# GJ#SM# ,445"b> ' b2 1 " 0 #?:@#?6F ,,:#
!"
&&' $ % ! 4 #' , " ,# '+(' $' + $1
1& % & #% >1B" & & & ' #
!5 4 #' , " ,# '+(' +',(' #1
% & & # % 1 (#?& ' FB & # % % & && ' # +& 88 % #
' 3 DD
9:9
C DD 9:9 7
(
!" 5- < <
.
(
1 (#, & & & #( && % & # % & #% & #% & # % &1 (#F#J & & #
A > *-- ,- D D 9:9 *,1**
. *- A > ,-
2-- 6--
( ' !
!" < < 5
!6 '# ")-),4
( & 88 & # 8 & ' #< & & ' & # % & 1 (#3#
(
% & # 1 & # & & # $ ' ' C% ?665" & :4 & & 74 & # % & ' & ./. W5 #1 & & & 88 ' & & # 1 & 8 & & ' & #
$ >1B"& & & ,44@"#%(JS>1Y??#4 & & & ' & )*+, W 5# % & 54 ' & #% ' & 37 #% &1 (#7#% & & & T
!" 5* < <
>1B> ? > ( & / " >1B> ,
1 ( & %C " >1B> F 1 $ & 344/ %C
( !
>1B > ? & 1 (#5# 8 & ' QR ' & & & #% & #
% & ' > F & # +& & ' & &#
!" < < 52
( & 88 #% 8 1 (#5# +& > , 1 (#: 8 & & #$ > F1 (#@ & & & # . & & & &#
% %?
% %?
( . *!
!" 56 < <
% %?
!7'0, $"#1 @'0 ,
1 (#6 & & > F& #$ ' & & # $ & ' & 88 ' & #
( . 2!
!" < < 5,
% ' & & # 1 ' 9 & & )1 ' 8 ' 8 88 & & & 88 #
) ' % 1 (#?4# & & ' ' & ' & 88#
. 1"* DD
"
"
% ' & &1 (#?? >1B #% 1 (#?, & ' ' & ' #% & #
% ' a?F74* %a,64/ TJ$% J $ %,447"" ?7; " a ?7@4 * )*+, & W5 %aF7F4/M >!(,"#%>1B 1 (#?F & & & & +,#%
!" 5 < <
& & #
( !
8 "* 7 8 "* 7
( 0A 7 !
( 0A ' "* 7 !
!" < < 5#
% ' & #1 & & &1 B!F#4? B! $# ,44,"# % & & & # %& & ' ,64/& ?F74* ?444/ >1B 1 (#?F & ,344 * # ) & ' 1 (#?3#
>1B +, #1 (#?7 & :7;" #
F A(= & &D &*&D *&*&D +,),4
< *"D*2*"D2#*5"D,-2*"D + "*1*5-:12,-4
A(= ,5"D5"D2,6-"D6),"D +,),4
" + "*1---:+*6--4 )2"D 262"D 6-,2"D ,,6,"D
(
!" 5) < <
"* 7 $ ' "* %
/ A ' "* 7
(
( 88 & # % & & 88 WF34* W5 W?7@7* &#! 1 (#?5 & #( & /& # ,4?4"#% % & & ' && #% & & && & #% & #
3*1 =26-4
)2"D )-5"D 2**-"D = 2##5"D ' + =,),4 6#6"D ,6)5"D
(
!" < < 55
!9D" '#0, $' " ,
( )*+, & #% & & & # <& & & & ' #
% & & & % #( 54 & 774 / & & # $ & & #
% & & 1 B!# & & & & #% & 1 (#?: & ' & # + & #
3
A '
8 8 8 8 0 *&*&D
(
!:" -"0 #'-'" 2 ) 1 $1
< % & # & % & % #
% & #% # % & #
!" *-- < <
' #% & #< ' & #
) % & & ./. & ./. ' # % & ' & ./.' & ' # % & ' & #
M & & # % & ./. & % & #
!"
&&' $ %! $ (' ,
!5,(2 ,#$#"4 +
% & & ./+#1 #
1 .#? & ./+ # 1 .#, ' # 1 .#F ' # 1 .#3 & #
( 9!+ ' 9:"!
!" *-* < 9
( 9!*+> 9:"!
!" < 9 *-2
( 9!2+> 9:" 7 !
!" *-6 < 9
( 9!6+& 9:"!
!"
&&' $ %! ,$ - '$ '0, $"#1 ,??)'
!5, $ ,??)'
> #( 1 5#?F # % #$ & #$ ./+ & 88#
% 88 & #1 >#? 88 & & # 1 >#? 88 & # > 88 & & & & & 88 #
round nozzle
100
sinusoid
80
60
40 Nozzle area closure (%) closure area Nozzle
20
0
0 2 4 6 8 10 12
Exciter wheel rotation (degrees) $%$%
( .!+< DD $%1 $%!
!" *- < >
!6, 2)' ' ,??)'
% 9 ? ?%? ?%#$ & & # $ 88& 37#% Q R 88 " 1 >#,#( & 88 & # % & 88 # % %= C & ' & & / #,4?4"# 1 >#, 88 & #
sine-profiled nozzle
100
sinusoid
80
60
40 Nozzle area closure (%) closure area Nozzle
20
0
0 2 4 6 8 10 12
Exciter wheel rotation (degrees) $%$%
( .!*+< DD ' $%1 $%!
1 >#F ./+ & 88 88 & #( # % &#% & 88 88 & #( #! & & 88 #% & & & 88 #
!" < . *-#
-60
(Secondary H mode & overtones) Round secondary nozzle
2
Sine-profiled secondary nozzle
Primary excitation frequency -70
-80
-90 Spectral density (dB/Hz) density Spectral
-100
-110
0 2 4 6 8 101214 161820 222426 2830
Frequency (kHz) $% 1
-60
(Secondary H mode & overtones) Round secondary nozzle
2
Sine-profiled secondary nozzle
Primary excitation frequency -70
-80
-90 Spectral density (dB/Hz) density Spectral
-100
-110
0 2 4 6 8 101214 161820 222426 2830
Frequency (kHz) $%A 1
( .!2+. ' DD ! ' 1 $%1 1 $%!
!"
&&' $ %! ,-"# 0)' #' ) +-#,( . 4,#3
% & & #
!5, # ")"# 0)'
+A##) &C#B.# ,4??"Q1 & )*+, R2&=11 # #,#3?M 36#
+A##) &C#B.# ,4?,"Q( & R! -0 -. 0 & !NK# -= & C,,4?,T?4#??::*46733?44?,3F:7??#
!6, -'#' 0'&"&'#
+A##. #/#) &C#B.#.# ,4?,"2 0G - ?$+- G 3@ ($((*(C!*(!*(!!A > ! ($ ( ( ( DF4A ?( ,4?,#
+A##D8C 8+#>#) &C#B.# ,4?," - H G ,4?,. 1: ?4C,4?,#
+A##) &C#B.# ,4??"= 0 - 0?$+ 3 ! > ( # 3 @A ,4??#
+A##) &C#B.# ,4??"2 ?$ = & 2 ( > %> $ *( NJ&G .J##<#,6J ?B,4??#
+A##) &C#B.# ,4??" = & 2 0?$+! 54 B B D .D,: ,6 ,4??#
!"