TFAWS06–1036

Xiao-Yen J. Wang

Glenn Research Center, Cleveland, Ohio

Conjugate Heat Transfer Analyses on the

Manifold for Ramjet Fuel Injectors

NASA/TM—2006-214455

November 2006
NASA STI Program . . . in Profile

Since its founding, NASA has been dedicated to the

advancement of aeronautics and space science. The

NASA Scientific and Technical Information (STI)

program plays a key part in helping NASA maintain

this important role.

The NASA STI Program operates under the auspices

of the Agency Chief Information Officer. It collects,

organizes, provides for archiving, and disseminates

NASA’s STI. The NASA STI program provides access

to the NASA Aeronautics and Space Database and its

public interface, the NASA Technical Reports Server,

thus providing one of the largest collections of

aeronautical and space science STI in the world.

Results are published in both non-NASA channels and

by NASA in the NASA STI Report Series, which

includes the following report types:

• TECHNICAL PUBLICATION. Reports of

completed research or a major significant phase

of research that present the results of NASA

programs and include extensive data or theoretical

analysis. Includes compilations of significant

scientific and technical data and information

deemed to be of continuing reference value.

NASA counterpart of peer-reviewed formal

professional papers but has less stringent

limitations on manuscript length and extent of

graphic presentations.

• TECHNICAL MEMORANDUM. Scientific

and technical findings that are preliminary or

of specialized interest, e.g., quick release

reports, working papers, and bibliographies that

contain minimal annotation. Does not contain

extensive analysis.

• CONTRACTOR REPORT. Scientific and

technical findings by NASA-sponsored

contractors and grantees.

• CONFERENCE PUBLICATION. Collected

papers from scientific and technical

conferences, symposia, seminars, or other

meetings sponsored or cosponsored by NASA.

• SPECIAL PUBLICATION. Scientific,

technical, or historical information from

NASA programs, projects, and missions, often

concerned with subjects having substantial

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific and

technical material pertinent to NASA’s mission.

Specialized services also include creating custom

thesauri, building customized databases, organizing

and publishing research results.

For more information about the NASA STI

program, see the following:

• Access the NASA STI program home page at

http://www.sti.nasa.gov

• E-mail your question via the Internet to

help@sti.nasa.gov

• Fax your question to the NASA STI Help Desk

at 301–621–0134

• Telephone the NASA STI Help Desk at

301–621–0390

• Write to:

 NASA STI Help Desk

 NASA Center for AeroSpace Information

 7121 Standard Drive

 Hanover, MD 21076–1320
National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

Thermal & Fluids Analysis Workshop (TFAWS) 2006

sponsored by the University of Maryland College Park and

NASA Goddard Space Flight Center

College Park, Maryland, August 7–11, 2006

TFAWS06–1036

Xiao-Yen J. Wang

Glenn Research Center, Cleveland, Ohio

Conjugate Heat Transfer Analyses on the

Manifold for Ramjet Fuel Injectors

NASA/TM—2006-214455

November 2006
Acknowledgments

The NASA integrated systems test of an air-breathing rocket (ISTAR) project has supported this work. Xiao-Yen J. Wang

greatly appreciates the support received from Derrick Cheston and helpful guidance from Ananda Himansu.

Furthermore, Xiao-Yen J. Wang is grateful to Robert Buehrle, Thomas Cressman, Thomas Krivanek,

and James Yuko for reviewing this paper.

Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22161

Available electronically at http://gltrs.grc.nasa.gov

Level of Review: This material has been technically reviewed by technical management.

This report is a formal draft or working

paper, intended to solicit comments and

ideas from a technical peer group.
|E1

TVUHX[WYW|fHedZWloHjKed}oH\^]pY}oKcH}\bkzWUW \bkkzXz\boHjK¡¢WYXV\^o1\^]£i<j[Wlj}okzUHW¤Z\^oeg¡¢}]gf]gpl\bkzWYfcH¥Hj6kzXKW \^Z¦^¡

kzUW§Xz\^ZKWYk=¡¢cWl]}egoKWlp|kz}X#\^XKW§¥WYXK¡¢}XKZ%WYf5cHj[egoH	w ̈afHWYj[ed^o©al«¬\­1oHegk[W|Wl]dWYZ%WYoyk®pl}Z¥Hckz\bkzeg}o1\^]° ̄1cHegf

fi<o1\^ZedpYj±¬w ̈a32 ́§j[^¡`kμ\^X[Wb&TVUHW	 ̄1:­1WY]dfb¡=kzUHW.UH^k¡¢cHWl]±¶}·6 ̧^ ́3 ̄H°egoH1k[UHX[^cH}Uk[UHW¤Z%\^oHe£¡¢}]df

edjj[edZocH]~\bk[Wlf»\^oHf:kzUHW1⁄4 ̈\^]g]	k[WlZ¥WYXz\bk[cHX[W1⁄2b¡Mk[UHW1⁄2Z%\^oHe£¡¢}]dfPedjpY}Z¥HckzWYf=3⁄4TVUHW¿}2Ào@cHZWlX[egp \^]

X[WYj[cH]£kzjV^¡#k[UHW¡¢cHWl]kzWlZ¥WlXz\kzcHXKW5\^X[W5pY}Z¥1\^X[WYfegk[UkzUH}jKW5}Ákz\^edoHWYfÂcHj[egoHÃ\23\^o1\b]gi<j[egj ̈Á1\^jKWlf

}oÄWlZ¥HedXKedpl\^]WYÅ@c1\bkzeg}oHjYÆ\^oHfkzUHW|ij[UHWlf1⁄2\Ã}<f\b}X[WYWlZWloyk &TVUHWMo@cHZ%WYX[egp \^]=XKWljKcH]gk[j.XKWY{^W \^]gWlf

kzUH\bkegkVkz\^Ç^WYj¤\^XK}cHoHf1⁄4}ÈyÈÉj[WYpl}ofHj.k[%XKW \^pqUkzUWMWYÅ@cHed]gedÁHXKedcHZÊUHWlXKWMk[UHW5¡¢cHWl]=k[WlZ¥WYXz\bk[cHX[WU1\bj

fHXK}¥H¥Wlf1⁄4\^Á^ck.}Ë.aÌ¡¢XK}ZÍk[UHWedoH]gWYkVk[Ãk[UHWW|egkb¡k[UHWZ\^oeg¡¢}]gf=

Î QÏYNG®Ð
Ñ D¢GN

s¤j ̈¥H\^XKk^¡
\Ér	shsÒ ̄Hed}Uyk ̈fWlZ}oHjKk[Xz\bk[ed}o%¥HX[°KWlpYkkzÉ\bf{b\^oHplW	kzUHWj6kq\bk[W¤^¡®k[UHW5\^X6kegoX[<pqÇ^W|k

Á1\^jKWlfÓpY}ZÉÁHegoHWlfPpYi<pl]gWÌ±Fv	mVwVwV ́Ã¥HX[^¥HcH]djKed}oÔfHW|{}Wl]g}¥HZWloykk[UHX[}c}U»XKedj[ÇÌXKWlfHcpYkzeg}oÓW|ÕB}X6kzjedo

{}^]g{<edoH}XK}cHoHfÁ1\^jKWlf1⁄2W)¥WlXKedZWloykzjYB\?¡¢cH]g]£μjKp \^]gW5fHedXKWlp|k¤pY}oHoHWYpYkpY}ZÉÁHcjKkz^X	XKedÖ±¬2wVw ̈v	 ́j6kzcHfi

\^j¤egoHegk[e~\bk[Wlf=TVUHedj.W|¥WlX[egZ%WYoyk¤WYj[j[WYoykze~\b]d]gifcH¥H]degp \bk[WljVkzUWopl^oHfHegk[ed}oj.b¡§\%XKWl}WYoHWlX[\bkze£{}WY]gi¡¢cHWl]

pl<}]gWlfUyi<¥WYX[jK}oHedpÂX[\^ZKWYk)_j[plX[\^ZKWYkÉWYoH}egoHW ̄1Í¥1\bkzUÌb¡UHW \bkÉj[edoÇ×pl^oHjKk[X[cHp|kzed^okz1⁄2jKedZÉcH]d\bkzW

kzUWÃ\^pYk[c1\^]§pl^oHfHegk[ed}oj¤kzUHW?WYoH}egoHWÉ^cH]df¿ÁW?}¥WYXz\bk[WlfØ\bkÁyixcHjKedoHÄ\¡F\^pYed]gegkμi¡¢cHWl]§UW \bk[WlXloTVUHW

}¥WlX[\bkzeg}o¿^¡k[UHW%WYoH}egoHW\bkkzUHW]dWlXMXz\^ZKWYkjK¥WYWlfHjM ̈\^j1^¡ ̈ÇbWYi¿ego@k[WlXKWljKkMkzkzUW%}¥WlX[\bkzeg}o¿^¡

kzUW1⁄4{}WYUHedpY]dWbÒÙμoÓ^X[fHWYXk[pl}XKX[WYpYkz]£iÚZ\kzpqU»k[UHWljKW1⁄2pl}ofHegk[ed}oHj\ØfHWYkz\^ed]gWlfPk[UHWlXKZ\b]	\bo1\^]gi<jKedj}o

kzUW5cH¥HjKk[X[Wl\^ZÍ¡¢cHWY]BfHWY]de£{}WlX6ipY}Z%¥}oHWYoykzj±¢Z\boHeg¡¢}]gfÆ ́ ̈\bjVX[WlÅ@cHegX[WYf=&sÛ¥HX[WY]degZ%ego1\^XKiÃfWlj[eg}oÂ^¡#kzUW

Z%\^oHeg¡¢^]df¿]d<p \bk[WlfcH¥HjKk[X[Wl\^ZÜ^¡ ̈kzUW%¡¢cHWY]egoKWlp|kz}XMedoØkzUHW%Xz\^ZKWYk1WloH^edoHW%edjMj[Ç^W|kzpqUHWYfÚedoaedHx}

TVUHWÂZ%\^oHe£¡¢}]dfpl}oHjKedj6kzj?^¡}oWÂpYi<]degoHfHX[egp \^]ÝUH}XKedÞY}oykq\^]&kzcHÁWegk[UÚ\^oÌ}ck[WlXÉfe~\^ZWYk[WlXob¡1^ßÈ1⁄2ego

\^oHf1⁄4¡¢}cHX	{^WlX6kzedpl\^]
pYi<]degoHfHX[egp \^]=k[cHÁWlj¤e£kzU1⁄2}ckzWlX	fHe~\bZ%W|kzWlXKj	b¡&Èß%edo=.TVUHW1Z\^oeg¡¢}]gf1⁄4egj	Z%\^fHWM^¡

ÙμoHpY}oHWl]
àyá^UH}jKW¥HX[}¥WlX6kzegWlj.\bk.â}È}È^Ë.aÔ\^XKW

ã6ä åæÌç Èè£°á} ̧?mkzc1_b]dÁHZ?-vé êæÔç ÈèßÈ^È}}}àÃmk[cÆ_¡`kKj6μvé ëæPç Èèß^ÈyÉ]dÁHZ_bedo@ì ±6 ́

UHWYX[W ã-äåæ éqêæ \^oHfëæ \^X[W.kzUHWjK¥WYple£­1pUHWl\bk <kzUHWYX[Z%\^]pY}oHfHcpYkze£{<egkμi}\^oHffWloHjKegkμi}X[WljK¥WYpYk[eg{}WY]gi^

TVUHW?¡¢cHWY]§WloykzWYX[jM\bk5kzUW^¥WYoØWYoHfØ^¡&kzUHWÃUH}XKedÞY}oykq\^]
kzcHÁW\^oHfx ̄1j5kzUHXK}cH}UxkzUWÃ¡¢^cHX{}WYXKkzegp \^]

Conjugate Heat Transfer Analyses on the 

Manifold for Ramjet Fuel Injectors 

Xiao-Yen J. Wang 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

NASA/TM—2006-214455 1
kzcÁWYj5ÁW|¡¢}X[W?XKW \^pqUHegoHkzUWÉedoKWYpYk[}XlMÙμo1⁄2kzUHW?pYcHX[XKWloykM\^o1\b]gi<j[egjlBk[UHW?WlÅ@cHeg]dedÁX[edcZ kzWlZ¥WlXz\kzcHXKWÉ^¡

kzUW	¡¢cHWY]=\bkkzUHW	W|egk^¡=kzUWZ\boHeg¡¢}]gf=}kzUW¤WlÅ@cHeg]degÁHX[egcHZ \^]d]ÆkzWYZ%¥WlX[\bkzcHXKW^\^oHfk[UHW¤k[edZWk[ÉX[Wl\^pqU

kzUWÉWlÅ@cHeg]dedÁX[edcZ j6kq\bk[W?\^XKWokzUHW?Z%\^egoÖedoyk[WlX[WYjKk[jl1aÆ^X	¡¢ck[cHX[W?XKWY¡¢WlXKWloHpYW^=k[UHWÉ{}WYXKkzegp \^]
kzcHÁWÉkzUH\bkegj

pl]g}j[WYjKk3k[kzUHW}¥WYo?WloHf?b¡k[UHW ̈UH^X[edÞY}oykq\^]@kzcÁW ̈egj3X[W|¡¢WlXKX[WlfÉk[\^jk[UHW­1XKjKk3k[cHÁWUHed]gWkzUW ̈¡F\^XKk[UHWlj6k

}oHWegjVX[WY¡¢WYX[XKWlfkz%\^j ̈kzUHW5¡¢}cXKkzUkzcÁWb

ÙμoÄk[UHW5¡¢}]d]gedoHH@kzUW?2!\bo1\^]gi<jKedj ̈egjV¥HX[WYj[Wloyk[WlfÖ­1XKjKklHUHedpqUÄedj ̈¡¢}]g]dWlfÂÁyikzUW1^2!\^oH\^]gi<j[egjl

ÙμoÉkzUW52:\^o1\^]£i<j[edjY^kzUW ̈UH}XKedÞl^o@kz\^]k[cHÁWV\^oHfÉk[UHW ̈¡¢}cHX6kzUÉ{}WYXKk[edp \b]kzcÁW}±¢kzUH\bk§X[WY¥HX[WYj[WYo@k[jÝk[UHW}X[j6k

p \bj[W¡¢}XVkzUHW¡¢cHWl]=k[WlZ¥WYXz\bk[cHX[WMfHXK}¥Æ ́V\^X[WpY}oHj[egfHWlXKWlf=Ùk	jKUH}cH]gfÖÁW¥}egoykzWlfÄ}ckk[U1\bkkzUHWMWYÕWlp|k

^¡
kzUHWpY]d}jKWlfÄWloHfÄ^¡
kzUHWUH}XKedÞY}oykq\^]Bk[cHÁWMegjVoH^k.pl^oHj[egfHWlXKWlfÄedoÂkzUHWÃ23⁄4\^o1\b]gi<j[egjl

 Q ÎL	E
 N
E

 D  GN  L"E1N
DG
FÐ

*UHWlok[UHW¤U^k¡¢cHWY]j6kq\^X6kzjÝ ̄1edoHÉegoHj[egfHWkzUHW	Z\^oeg¡¢}]gf=}kzUHW	Z\boHeg¡¢}]gf?ed]d]1ÁW¤UW \bk[WlfÂcH¥Â\boHf

UHWl\bk	eg]d]=k[Xz\^oHj6¡¢WlX.kz%k[UHWÉ\bZÉÁHedWYoyk¤\bedXl®W|k}±ç  ̧^È Ë a3 ́.\^of¿ÁW1k[UHWÉ\bZÉÁHedWYoyk¤\bedX.\^oHfÖk[cHÁW

\^]d]ÆkzWYZ%¥WlX[\bkzcHXKWlj®\^oHf !ÁW¤kzUWedoH]gWYk ̈\^oHfW)e£k ̈kzWYZ%¥WlX[\bkzcX[Wlj^¡®kzUHW	¡¢cHWl]"H\^oHf$#%é&#('lH\boHf

)!ÁWÂkzUHWÂegoHoHWYX?fHe~\^ZWYk[WlXY§}ckzWYX?fHe~\bZ%W|kzWlXYÝ\^oHfÚ]dWYoH^kzUÚ^¡k[UHWÂkzcHÁW^&X[WYj[¥Wlp|kzeg{^Wl]£i}ÌTVUHWedo]dWYk

pl^oHfHegk[ed}ojV^¡k[UHW5¡¢cHWl]#\bX[W5}e£{}Wlo1⁄4\^jV¡¢}]g]djl

*ç à}È}È?¥HjKe~\<é  ç â}È}È Ë aé ,+ ç Èèßá} ̧É]dÁHZ_bj ±á^ ́

UHWYX[W * \boHf-+ , \^XKW5kzUHW5¥HXKWljKj[cHXKWo\^ofÄZ%\^jKj ̄H° Xz\bk[W^§TVUHW¥HXK}¥WlXKk[edWYjV^¡k[UHW¡¢cHWY]μ±¶}·- ̧} ́ ̈\bkVkzUW

edo]dWYkV\^X[WM\^]gj[?}e£{}Wlo1⁄4\^j

ã-äç Èè  ̧} ̧@ ̧}Émk[cÆ_b]dÁZÃμvé . ç ^è }0/× È2123	]gÁHZ_¡`kKj|é

Figure 1.—Sketch of the manifold located upstream of the ramjet

 fuel injector.

0.500-in. o.d.×

0.065-in. wall

1.0-in. o.d.×0.083-in. wall

10 in.

8.24 in.

Fuel

in

Fuel

out

Fuel

out

Fuel

out

Fuel

out

NASA/TM—2006-214455 2
ê ç Èè Èy}á^â}ÃmÝkzcÆ_¡`k6μUHX--vé ë ç }è^Èyá}É]dÁHZ_¡`k ì é ç ^èßÈy ̧^ ̧ ±¬} ́

UHWYX[W ã6ä é .3é)êézë1é\^oHf:\bX[WkzUWÂj[¥Wlple£­1pUHW \k &{egj[pY}j[e£kμi}§kzUHWYX[Z%\^] ̈pY}oHfHcHp|kze£{e£kμi}ÝfHWloj[egkμi^\boHf

j[¥WlpYeg­1pMUHWl\bk.Xz\bk[edHX[WljK¥WYpYk[eg{}WY]gi^TVUHW1v.W|i<oH}]dfj.o@cHZoÁWYXl}Æ\^oHf	Ö\^pqU1⁄4o<cZÉÁWYXl
1p \^oÄÁW

pl^Z%¥HckzWlfÄÁyi

 ç ë
#%	.3é 
 ç 
 ±Fy ́

UHWYX[W
 \^oHf1⁄2\^XKWÉkzUHW?{}WY]d<ple£kμix\^oHf¿jK}cHoHfØj[¥WlWYf=XKWljK¥WYpYkze£{}WY]gi}Ãa1cHX6kzUHWYXl
 ç ,+ H±¢ë# b@ ́

\^oHf ç*bëegkzU !ÁWlegoHM\pl}oy{^WlX[jKed}o%pl}ojKkq\bo@klÝhedoplW#% ç Èè â}^edoÉ¡¢^X3kzUHWUH}XKedÞY}oykq\^]

kzcÁWbWU1\ {^W"
 ç y ̧<è H§¡`kq_bj
\^oHf# ç °á}¡`kq_bjl°UHegpqUo}e£{}Wlj ç èyy /È 3 \^oHf$
 ç Èè È}

W.pl\^oÃpl}opl]dcfHWVkzU1\bk§k[UHW ̈ ̄1Óegj§edoHpY}Z¥HX[WYj[j[egÁH]dW ̈\^oHf?kzcHXKÁHcH]gWloyk 3TVUW.UW \bk&kzX[\^oHj6¡¢WlX§pl<W&%pYedWloykl

')( HÁWYkμWlWlo1⁄4kzUHW5¡¢cHWY]#\^oHfÄedoHoHWYXVj[cHX6¡F\^plW^¡
kzUWk[cHÁWMpl\^oÄÁWpl^Z%¥HckzWlf1⁄4\^j

')( ç+*-,. ê/#% ±^ ́

UHWYX[W *-,. egj ̈kzUHWMr	cj[j[WY]gk.o@cHZÉÁWlXYÆ\^oHf

*-,. ̈ç Èè Èyá^1032 465879032 ì ±¬à} ́

¡¢}X.kzcHXKÁHcH]dWYoyk ̄1j© á°«UHWlXKW:5;7 ç3⁄4ã6ä .<}ê1⁄4edj.kzUHWÉ·&X[\^oHfk[]o@cHZÉÁWlXY5TVUHWÉUHWl\bkk[Xz\^oHj6¡¢WlXpYW=%?

plegWloyk  '



1ÁWYkμWlWYoÖkzUW1\bZÉÁHedWYoyk.\^edXV\boHf1⁄4^ckzWYXVj[cHX6¡F\^plWM^¡
kzUHW5kzcÁWb1p \^oÄÁW5pY}Z¥HckzWYf1⁄4cj[edo

'

 ç }è@áH±[±
> l ́3) ́?032  3 ± ̧^ ́

¡¢}XVUH^X[edÞY}oykq\^]BpYi<]degoHfHWlXKj1© á«®\^oHf

'

 ç }è yáH±K±@> l ́A#('q ́ 032  3 ±¬â} ́

¡¢}X¤{^WlX6kzedpl\^]3p|i]gedoHfWlX[j©á«¬(®WYk8B( ÁWÉkzUWUW \bk5 ̄1c<xÁyi1⁄2¡¢}XKplWlf¿pY}oy{}Wlp|kzeg}oegoHj[egfHWok[UHWÃZ\^oeg¡¢}]gf=

B

 ÁW¤kzUH\bkVÁyio1\kzcHX[\^]BpY}oy{}Wlp|kzeg}oÂkzÉkzUW\^ZÉÁHegWloykV\^egXl\^oHfCBì ÁWkzUH\bkVÁyiX[\^fHe~\kzed^o%}ckzj[egfHWkzUW

Z%\^oHeg¡¢^]df= ×Wp \boÄfWY­1oHW

B( ç ')(ED;( ±K±GF !z ́A}áH> = ́|é B

 ç 'D

±I>   ́)é B

ì çKJ3LD



±NM > NM  ́ ±O} ́

UHWYX[W D;( ç #%
)V D

 ç #(')Û\bX[WÉkzUWUW \bkkzX[\^oHj6¡¢WlX5j[cXK¡F\^pYW%\bX[W \bjl Jç Èè á}áegj¤kzUHWÃjKcHXK¡F\^pYW

WlZedjKj[e£{e£kμi}
\^oHf LPç Èè£° ̧  /PÈ 14 mkzcÆ_U¡`k3K-vM egj5kzUHWh<kzW|¡F\^oμm}]gk[ÞlZ%\^oHo¿pl^oHjKkz\^oyk  ®WYk ,

\^oHf ,CP ÁW1k[UHWÉZ%\^j[j	^¡§kzUW1kzcÁW?\boHfÖkzUW1¡¢cHWY]BXKWljK¥WYpYkze£{}WY]gi}¤TVUHWÉUHWl\bkÁ1\b]~\^oHpYWoWYÅ<cH\bkzeg}oHj	¡¢^X

Á^kzUÂkzUWMjK}]degf\^oHfkzUHW5 ̄1cedfÄ\^X[W

,ã-ä åæQRQTS&ç B( >B >Bì

±6Èy ́

\^oHf

,CP°ã6ä1Q!6QTS&ç >UB( F ,ã6ä + ±
> ![ ́ ±6}° ́

r	bkzWkzU1\bk&k[UHW.k[UHWlXKZ\b]1X[WljKedj6kq\^oHpYW¤ÁyiÃpl^oHfHcHp|kzed^o%kzUX[}cH^Uk[UHW.\^]g]egj&ed}oH^X[WlfedoV§ÅÆ.±6Èy ́3jKedoHpYW

kzUW\^]g]=edjVXKWl]~\kzeg{^Wl]£ikzUedo=ÝhcÁHjKk[egkzckzedo:V&ÅÆ¤±Oy ́egoykzV§Å<jY	±6Èy ́ ̈\boHf±-}° ́)WMU1\ {}W

,ã6ä åæQW Q/SÝç 'X(ED8( ±[±
YF ![ ́3}áZ> = ́[> '

D

±I> l ́[> J3LD



±
NM > NM  ́ ±6°á} ́

NASA/TM—2006-214455 3
\^oHf

,CP°ã6ä Q! QTS&ç > ')(ED8( ±[±
GF ![ ́3}áH> ® ́<F ,ã6ä + ±
> ![ ́ ±6y ́

kzUH\bk5\^XKWocHjKWlf1⁄2k[j[}]£{}W ×\^oHf!|¤s¤jKj[cHZedo ± SVç Èy ́ ç  ̧bÈ}ËaÆWop \^o1⁄2pY}Z¥HckzW ! ± S ̈ç È} ́

ÁyiÂcHjKedoH

')(ED;( ±K±/F ![ ́3^áH> = ́ ç ,ã-ä + ±> ![ ́ ±6 @ ́

UHegpqU1⁄2iegWl]gfHj !l± Sç Èy ́ ç  ̧^y ̧èyËaÚ¡¢}X	k[UHWoUH^X[edÞY}oykq\^]#kzcÁWo\^oHf¿àyá^È^Ë¤aP¡¢}X.kzUHWM{}WYXKkzegp \^]
kzcHÁW^

V§Å@c1\bkzeg}oHjo±6°á^ ́\boHfÌ±-y ́V\^X[WjK}]g{^Wlf1⁄2cHjKedoHÃkzUW1¥HXK}}X[\^Z Ö\bk[UHWlZ%\bk[edp \% ÈÃ¡¢^X.Á^k[UÖUH}XKedÞY}oykq\^]

\^oHf1⁄4{}WlX6kzegp \^]
kzcHÁWljYTVUHWÉpl\^]dpYcH]~\bk[WlfÄkzedZWMUHedj6kz}X6i1⁄4b¡3kzcHÁWo\^]d]#kzWYZ%¥WlX[\bkzcX[Woegj	¥]d^kKkzWlfÖedo1⁄2aedH

áUed]dW	kzUHW¡¢cHWY]=kzWYZ%¥WlX[\bkzcHXKW5fHX[^¥1⁄4\bplX[^j[j ̈kzUWMZ%\^oHe£¡¢}]df\bkVkzUW5jKkzWl\^fiyμj6kq\bk[WedjV¥H]g^k[k[WlfÂedoaedH

TVUHW?XKWlj[c]gkzj5jKUHWYfØk[U1\bkk[UHW?UH}XKedÞY}oykq\^]#kzcHÁWÉ\^]d]
kzWlZ¥WlXz\kzcHXKWÉX[Wl\^pqUHWlj1 ̧}  Ë a:\^oHfxkzUW

{}WYXKk[edp \b]
k[cHÁW1 ̈\^]g]XKW \^pqUWlj ̧byËaPe£kzUHego1⁄2\^Á}ck¤}ÈjY¤TVUHWÉU}X[egÞl}oykq\b]
k[cHÁWM ̈\b]d]#kzWlZ¥WlXz\kzcHXKW

edj	áß Ë aÔ]gWYXk[U1\^okzUHW{}WYXKk[edp \b]#k[cHÁW\^]g]®fHcHWkzÃkzUHWM]~\^XK}WlXVUW \bkkzX[\^oHj6¡¢WlX.j[cHX6¡F\^plW1\^X[Wl\ÝTVUHW

¡¢cHWY]=kzWlZ¥WlXz\kzcHXKW5fHX[}¥j¤\^¥¥HX[ edZ%\bkzWY]gi}ËaÚ¡¢XK}ZÍk[UHWedoH]gWYk ̈k[?kzUHWW|e£k	b¡k[UHWZ\^oeg¡¢}]gf=

 Q L	E
 N
E

 D  GN  L"E1N
DG
FÐ

sP­1oegkzW)μWY]dWlZWloykw ̈a32»jK^¡`kμ\^X[Wb<w ̈afHWljKed}oB^edj
cHjKWlfÉUHWYX[W¡¢^X#k[UHW ̈^2Ó\^o1\^]£i<j[edjYTVUWo@cHZWlX[egp \^]

¡¢}XKZÉcH]~\kzed^oÖedoxw ̈afHWljKed}o¿egjfHWlXKeg{^Wlfx¡¢X[}ZnkzUWhÙEÖ·RVÝvujKpqUHWlZWÃedoykzXKfcHplWYfxÁ@ix·\bkz\^oHÇ^WYX©al«¬

Ùμo1⁄2kzUWÉplcHXKX[WYo@kM\bo1\^]gi<jKedjlB\­1oHe£kzW|Wl]gWlZWloyk¤Z<fHWl]#kzU1\k5U1\^j5\b¥H¥HX[ edZ%\bk[Wl]giyáßÈ^È}ÈoH<fHWlj5egoÖkzUW

 ̄1cHegfÓ\^ofÛ H È}È}È¿oH<fHWlj%edoÚkzUHW1⁄4j[}]gedfÔedjcHj[WYf=ÒTVUWÖ ̄1 ­1Wl]gf»egj%jKedZÉcH]d\bkzWYfÔ­HX[jKk\^j[jKcHZedoH\

Figure 2.—Time history of the tube wall temperature.

Time, s

Tw horizontal

Tw vertical

Wall temperature, °F

0

0

100

200

300

400

500

600

700

800

900

5 10 15 20 25 30 35 40

NASA/TM—2006-214455 4
pl^oHjKkz\^oyk¤kzWYZ%¥WlX[\bkzcX[W^s	¡`k[WlXkzUHWMjKk[W \^fiyjKkq\kzWoegjX[W \bpqUHWlf=ÆkzUW1kzWYZ%¥WlX[\bkzcX[W5­1Wl]gfÖegj.pY}Z¥HckzWYf

cHoHfWlXMÁ^k[U¿jKkzWl\^fiyμj6kq\bk[W\boHfØk[Xz\^oj[edWYoyk1XKcHoHjYs ̈kMkzUWegoH]dW|k =¥X[WljKj[cHXKW^
kzWlZ¥WlXz\kzcHXKW%\boHfZ%\^jKj

 ̄1ÒXz\bk[W\^XKWj[¥WlpYeg­1WYf1⁄4\bjkzUHW¤Á}coHf1\^X6ipl^oHfHegk[ed}ojl&okzUW}ck[WlX ̈jKcHXK¡F\^pYW^HoH\bkzcHX[\^]BpY}oy{}WYpYkzeg}o

\^oHfXz\bfHe~\bk[ed}o?Á}cHof1\^XKiÃpY}oHfHe£kzeg}oHj&\^XKW.jK¥WYple£­1Wlf%edo?kzUHW.jz\bZ%WV\i\bj&k[UH}jKW	egok[UHW2 \^oH\^]gi<j[egjl

TVUHWVj6kzW \bfiyμjKkz\bkzW ̈{^Wl]gpYegkμio\^oHf?¥HXKWlj[jKcHX[WpY}oykz}cHXKj§}oÃ\^oH1pYck§¥H]d\^oHWV\^XKW ̈j[U°oedoÉaed}jY\boHf

%XKWlj[¥Wlp|kze£{}Wl]£i}TVUHWo{^Wl]gpYegkμi1⁄4pl}oykz^cHXj[U°j5Ued}UÖ{^Wl]gpYegkμiÄoHW \bX¤kzUHW1kzcHXKoHedoH%¥^edoyk^¡§k[UHWo ̄1

¡¢X[^ZÍkzUWMU}X[egÞl}oykq\b]kzcÁW5kz?k[UHW{}WYXKkzegp \^]=k[cHÁWljl&TVUHW¥HXKWljKj[cHXKW1pY}oykz}cHXjKUHj.k[UHWWYÕWlpYk.^¡
kzUW

pl]g}j[WYfWYoHf^¡kzUHW.UH}XKedÞY}oykq\^]Hk[cHÁWegk[U\bo%egoHplXKW \^jKW	ego%j6kq\bk[edp¥HX[WYj[jKcHX[W5\bj&k[UHW{}Wl]gpYegkμiÃfHWYplXKW \^jKWlj

oHWl\^XkzUWVpl]d^j[Wlf?WYoHf=3TVUWVjKkzWl\^fiyμj6kq\bk[W ̈kzWYZ%¥WlX[\bkzcHXKWpY}oykz}cHX§¥X[WlfedpYk[Wlf?Áyiok[UHWVjKk[W \^fi@jKkz\bkzWVXKcHo

edj¥H]d^kKkzWYfÂedoÂaegH§à§Ùk ̈edj ̈}Áj[WlX6{}WYf1⁄4kzUH\bk ̈kzUW¡¢cHWl]W|egkVk[WlZ¥WYXz\bk[cHX[W5\k ̈kzUHW¡¢^cHXKk[U{}WlX6kzegp \^]Bk[cHÁW

edjV{^WlXKipY]d}jKW5kzÃkzUHW5¡¢cHWY]
egoH]dW|k ̈kzWYZ%¥WlX[\bkzcX[W^	WY{^WlXlkzUHWj6kzW \bfiyμjKkz\bkzWMkzWYZ%¥WlX[\bkzcHXKW5}Ákz\^edoHWYf

Áyiok[UHW ̈kzX[\^oHj[egWloyk§XKcHoÃ¥H]d^kKkzWYf?edo?aegH ̧¤j[UHjÝ\^X[^cHoHf%á^È}Ë§a1⁄2fHXK}¥É¡¢X[^Z3⁄4k[UHWVedoH]gWYk^¡ÆkzUHWVZ%\^oHe£¡¢}]df

kzÃkzUWMW)egk.^¡
kzUHW¡¢}cHX6kzUÂkzcHÁW^a1cHXKk[UHWlXY1kzUHWjKk[W \^fi@jKkz\bkzWkzWYZ%¥WlX[\bkzcHXKWfHedj6kzX[egÁHck[ed}o\^]g}oH?kzUW

plWYoykzWlXK]degoHW^¡#kzUHWUH}XKedÞY}oykq\^]Bk[cHÁW1\boHfÂkzUHW5­1XKjKk	\^oHfÂ¡¢}cHX6kzU{}WYXKkzegp \^]kzcHÁWljedjV¥]d^kKkzWlfego1⁄4aed}jY§â

\^oHf #X[WYj[¥Wlp|kzeg{^Wl]£i}ÃÙkMp \^oØÁWÃjKWlWloØkzU1\k5kzUHWÃkzWYZ%¥WlX[\bkzcHXKW?fHX[^¥Hj5egkzUedo¿ÁbkzUxkzUHWUH}XKedÞY}oykq\^]

\^oHf{}WlX6kzegp \^]&kzcHÁWljo\^X[WUHeg}UHWlXMkzU1\bokzUWX[WYj[cH]£kzj1}Ákq\bedoHWYf×Áyik[UHWj6kzWl\^fiyμj6kq\bk[WX[co=1⁄4TVUW¡¢cHWl]

kzWYZ%¥WlX[\bkzcX[WoHW \bX&k[UHWpl]g}j[WYf%WYoHf^¡kzUHWUH^X[edÞY}oykq\^]kzcHÁW	egj&\^Á}ck Ë a¿]dWYX§kzU1\^oÃkzUH\bkÝj[UHo

edok[UHWj6kzW \bfiyμX[coÄXKWljKcH]gk[jlÝm ̈\^jKWlf}okzUW5jKkzWl\^fiyμj6kq\bk[W5X[cHoXKWlj[c]gkzjYkzUWkzWlZ¥WlXz\kzcHXKWfHX[^¥¡¢X[}Z

kzUWÉedoH]gWYk.^¡§k[UHWoZ%\^oHe£¡¢}]dfkzkzUHWÉW)egkb¡§kzUHWM¡¢}cHXKk[UÖ{}WYXKk[edp \b]
k[cHÁWoedj¤áè }Ë5a1UHedpqU¿\^^X[WlWYj¤Wl]d]

egk[UkzUWÉ2Û¥HXKWlfHegpYkzeg}o¿±F}Ë ̈a§ ́)HhegoHplW¤fHegÕWlXKWloykVj[^]g{}WYX[jV\bX[WcHjKWlf¡¢}XjKk[W \^fiyjKkq\kzW\^oHfk[Xz\^oj[edWYoyk

NASA/TM—2006-214455 5

Figure 3.—Time history of the temperature drop of the fuel. 

Time, s 

Ti-Te, °F 

0 

0 

20 

40 

60 

80 

100 

120 

140 

160 

180 

200 

5 10 15 20 25 30 35 40 
X[coHj?edoÚw ̈afHWljKed}o=§k[UHWfHegj[plXKWl¥1\boHpYiÌÁWYkμWlWYoÔk[UHWÂjKk[W \^fi@jKkz\bkzWk[WlZ¥WYXz\bk[cHX[WXKWljKcH]gk[jÉ}Ákz\^edoHWYf

Áyi1⁄2j6kzW \bfiyμjKkz\bkzWÃ\boHf1⁄2kzX[\^oHj[egWloyk5XKcHoHjegj\bkKkzX[egÁHck[Wlf1⁄2kz%kzUHW?\bplplcXz\^p|i1⁄2^¡&kzUWÉj[}]£{}WYXÁ1\^jKWlf¿}o1⁄2kzUW

pl^oHpl]gcHj[eg}o1⁄4¥X[{<edfHWYf1⁄2ÁyiÄk[UHWkzWlpqUoHedpl\^]jKcH¥H¥}XKk	}XK}cH¥1⁄2\km]gcHWMv.egfH}WMr	cZ%WYX[edpYj	Ùμopl}XK¥}X[\bkzeg}o=

a1}XÝpl}Z¥H]dW|kzWYoHWljKjlk[UHW	k[edZW	UHegjKk[}XKiÃ^¡®k[UHW	¡¢cWl]k[WlZ¥WYXz\bk[cHX[W¤\bkÝkzUHWW)egk ̈b¡=kzUHW	­1X[j6kV\^oHf%¡¢}cHXKk[U

kzcÁWYjoedjM¥H]g^k[k[Wlf×egoaegH1⁄2}^j[U°egoHÖk[U1\bk1egkkq\^ÇbWlj?\bÁ}ckoyÈÄj1k[ÖX[Wl\^pqU×k[UHWWYÅ<ced]degÁHX[egcHZ/¡¢^X

kzUW­HX[jKkk[cHÁWbUHeg]dW5egkkq\^ÇbWlj	\^Á^ck. ̧^È?jVkzÃX[Wl\^pqUkzUHWj[egZ%eg]~\^XÝWlÅ@cHeg]degÁHX[egcHZÊjKkq\kzW5¡¢}Xk[UHW5¡¢}cHXKk[U

kzcÁWbh<edoHpYWÃk[UHW2ÊX[WljKcH]gk[jM\^}X[WYW?WY]d]e£kzU¿kzUHW}2ÊjKk[W \^fiyjKkq\kzWÃX[cHoØX[WYj[cH]£kzjY
k[UHW2¦XKWljKcH]gk[j

\^XKWMpY}oHjKedfHWYX[WlfkzÃÁW5{^\b]dedf\boHfÂed]d]BÁWÁ1\^jKWlfÄ}okzÃfHXz\  pl}oHpY]dcHjKed}ojl

 Q1GN

¬Ñ D¢GN

m^k[U:2 \^oHfÚ}2 pY}oKcHy\kzWUHWl\bkÉk[Xz\^oHj6¡¢WlX?\bo1\^]gi<jKWljÉ}ok[UHWÂZ%\^oHeg¡¢^]df¿¡¢}X1k[UHWÂXz\^ZKWYk1¡¢cHWl]

edo°KWlpYk[}X.U1\ {}WÉÁWlWYox¥WYXK¡¢}XKZ%WYf=TVUHWÉo@cHZWlX[egp \^]#XKWlj[c]gkzj¤\^X[W1¥HX[WYj[WYo@k[WlfØ\^oHfÖpl}Z¥1\^XKWlf=j[UHegoH

\¿}<fP\^}X[WYWlZWloyk%ÁW|kμWYWlo»k[UHW×2 \^oHf»}2/XKWljKcH]gk[j%}Ákq\^egoHWlfÔÁyiÔk[UHWÄjKkzWl\^fiyμj6kq\bk[W1⁄2\^oH\^]gi<j[egjl

TVUHWÉWYÅ@cHed]gedÁHXKedcHZ k[WlZ¥WYXz\bk[cHX[W1^¡3k[UHWo¡¢cHWY]\bk.kzUWÉW|egk¤^¡3k[UHWoZ%\^oHe£¡¢}]dfÄfHX[^¥Hj\^Á}ck Ë aÚ¡¢X[}Z

kzUWÖedo]dWYkÃk[kzUW1⁄2W|egk%^¡k[UHWÖZ%\^oHe£¡¢}]dfB\^ofÓegkÃkq\bÇ^Wlj\^¥H¥HXKegZ\bk[Wl]£iÚ}ÈyÈØjKWlpY}oHfHjk[×X[Wl\^pqU

WlÅ@cHeg]degÁHX[egcHZÍpY}oHfHe£kzeg}oHjl




©a}«VÐ
L D¢SNL£! Ñ
DFÐ
L#"$VD¬N
D L&%
¢LL<N 
FÑ
D¬Ð'
¢G(nE1N
Ð)ÄL@E E1N L&* G
,+L 

m]dcHWvedf}Wr	cHZWlXKedpYjlHÙμoHpb® yá6á^È}È^

©á«d	^]dZ%\^o=1¶ ·®#)ÄL@E E1NL Äpt5Xz\  ̈-.ed]d]Bm<}ÇÂw}Z¥1\^oyi^® }â}

NASA/TM—2006-214455 6
Figure 4.—Steady-state velocity contour on an x-y cut plane.

y

y

z

z

x x

0

100

200

300

400

500

600

700

800

900

1000

Velocity 

magnitude,

in./s

9.2

6.9

4.6

2.3

1.25

2.56

5.13

7.69

10.3

Load case 210

last iteration/step

Figure 5.—Steady-state relative pressure contour on an x-y cut plane.

y

y

z

z

x

x

–0.147

0.019

0.186

0.353

0.520

0.687

0.854

1.021

1.188

1.355

1.522

Static

pressure,

psi

9.2

6.9

2.3 4.6

1.25

2.56

5.13

7.69

10.3

Load case 210

last iteration/step

NASA/TM—2006-214455 7
Figure 6.—Steady-state temperature contour on an x-y cut plane

 (steady-state run).

y

y

z

z

x

x

772.839

775.555

778.271

780.987

783.703

786.420

789.136

791.852

794.568

797.284

800.000

Static

temperature,

°F

9.2

6.9 4.6

1.25 2.3

2.56

5.13

7.69

Load case 210

last iteration/step

Figure 7.—Steady-state temperature contour on an x-y cut plane

 (transient run).

y

y

z

z

x

x

738.436

744.593

750.749

756.905

763.062

769.218

775.375

781.531

787.687

793.844

800.000

Static

temperature,

°F

9.2 6.9 4.6 2.3 1.25

2.56

5.13

7.69

10.3

Time: 2073

last iteration/step

NASA/TM—2006-214455 8
Figure 8.—Steady-state flow temperature distribution

 along the flow direction (steady-state analysis). 

 (a) Horizontal tube. (b) First vertical tube. (c) Fourth

 vertical tube.

y, in.

Static temperature, °F

0

797.6

797.8

798.0

798.2

798.4

799.2

799.4

798.6

798.8

799.0

2 4 6 8 10

y, in.

Static temperature, °F

0

799.3

799.4

799.5

799.6

799.7

799.8

799.9

800.0

2 4 6 8 10

y, in.

Static temperature, °F

0

793

794

795

796

797

800

798

799

2 4 6 8 10

(a)

(b)

(c)

Figure 9.—Steady-state flow temperature distribution

 along the flow direction (transient analysis). (a) Hori-

 zontal tube. (b) First vertical tube. (c) Fourth vertical

 tube.

y, in.

Static temperature, °F

02468 13579

02468 13579

02468 13579

y, in.

Static temperature, °F

y, in.

Static temperature, °F 794

796

800

798

793

792

791

790

792

790

784

786

788

782

780

794

795

796

797

798

799

778

780

782

784

786

792

788

790

(a)

(b)

(c)

NASA/TM—2006-214455 9
Figure 10.—Time history of the fuel temperature at the exit of the vertical

 tubes (transient analysis).

Time, s

Fourth tube

First tube

Ti-Te, °F

0

0

20

40

60

80

100

120

140

160

200

180

10 20 30 40 50 60 70 80

NASA/TM—2006-214455 10
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

REPORT DOCUMENTATION PAGE

2. REPORT DATE

19. SECURITY CLASSIFICATION

 OF ABSTRACT

18. SECURITY CLASSIFICATION

 OF THIS PAGE

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this

collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson

Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102

Form Approved

OMB No. 0704-0188

12b. DISTRIBUTION CODE

8. PERFORMING ORGANIZATION

 REPORT NUMBER

5. FUNDING NUMBERS

3. REPORT TYPE AND DATES COVERED

4. TITLE AND SUBTITLE

6. AUTHOR(S)

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT

13. ABSTRACT (Maximum 200 words)

14. SUBJECT TERMS

17. SECURITY CLASSIFICATION

 OF REPORT

16. PRICE CODE

15. NUMBER OF PAGES

20. LIMITATION OF ABSTRACT

Unclassified Unclassified

Technical Memorandum

Unclassified

National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland, Ohio 44135–3191

1. AGENCY USE ONLY (Leave blank)

10. SPONSORING/MONITORING

 AGENCY REPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546–0001

Available electronically at http://gltrs.grc.nasa.gov

November 2006

NASA TM—2006-214455

TFAWS06–1036

E–15719

WBS 22–931164.03.01.02.01

16

Conjugate Heat Transfer Analyses on the Manifold for Ramjet Fuel Injectors

Xiao-Yen J. Wang

Heat transfer analyses

Unclassified -Unlimited

Subject Category: 34

Prepared for the Thermal & Fluids Analysis Workshop (TFAWS) 2006 sponsored by the University of Maryland

College Park and NASA Goddard Space Flight Center, College Park, Maryland, August 7–11, 2006. Responsible

person, Xiao-Yen J. Wang, organization code DEF, 216–433–2333.

Three-dimensional conjugate heat transfer analyses on the manifold located upstream of the ramjet fuel injector are

performed using CFdesign, a finite-element computational fluid dynamics (CFD) software. The flow field of the hot

fuel (JP–7) flowing through the manifold is simulated and the wall temperature of the manifold is computed. The

three-dimensional numerical results of the fuel temperature are compared with those obtained using a one-dimensional

analysis based on empirical equations, and they showed a good agreement. The numerical results revealed that it takes

around 30 to 40 sec to reach the equilibrium where the fuel temperature has dropped about 3 °F from the inlet to the exit

of the manifold.