!'_i I 'J

NASA Contractor Report 172212

I

MINIVER UPGRADE FOR THE

AVID SYSTEM

VOLUME I: LANMIN USER'S

=:- MANUAL

_x

-...%.

Carl Do Engel

t Sarat C. PraharaJ

-_::, REMTECH, Inc.

- Huntsville, AL 35805

j:

-- Contract NAS1-16983

August 1983 'L
_-

FOREWORD

This final report presents york vhioh yes ©ondu©t©d for Lenlloy Resesreh

Center (LaRC) in response to requirements of Conttsot NAS1-16989, The york

presented yam performed by RFJ4TECHIuo., Huntsville, Alabama and is entitled

" "M]_XV]m Upjtade for the AVID System.'' The final report consists of three

vo|umes.

Volume 1: LANMXNUser's Manna1

Volume 2: LANMXNInput Guide

Volume S: EXITS UserPs and Input Guide

I The NASA teehnioal coordination for this study yam provided by Me, J[athryn

E. Wurster of the Vehicle Analysis Branch of the Spaoe S,vstems Division.
' TABLE OF CONTENTS

VOLUMEI

LA._MINUSER'S MANUAL

SECTION PAGE

f

100 INTRODUCTIONo. . . . . . • . . . . . 1

2.0 GEh'I_,ALUTILITY ROUTINES. . . . . . . $ .

2.1 MAIN • • • • • • • • • • • • . 3

2.2 SUBROUTINEWRINP....... . 3

2.3 SUBROUTINEVANOUT. . . , , . . . 3

2.4 SUBROUTINETBLIN , . . . . . . . 4

2.5 SUBROUTINETINT6 . . , . . . . . $

2.6 FUNCTIONSD_I'P1 M_D INTP2... . 7

S.0 FLUID I_OP_TYROUTINES . . . , . . . 9

3.1 SUBROUTINE AIR62 _. . . . , . . . 9

3.2 S_BROUT/NS ATMS4 . . . . . . . . 9

_4

;. 3.3 SUBROUTINEVRA71 . . . . . . . , 9

3.4 ROUTINESNOLXER, BLOCE, BLOCi_, .10

$.S SUBROUTINEBINTRP............. .12

9.6 SUBROUTINEHANSEN. , . , , , . , . . , , , .15

4.0 ln.,OWFISLDROUTIh'ES............... .14

4,1 SUBROUTII_ FLOW • • • • • • • • • • • • • ,14

4.2 SUBROUTINEDWNSTN............. .19 _

4.3 SUBROUTINEPCSW • • • .... . . . . . . .22 '

i_.. 4.4 SUBROUTINEDOWNID............. .24

: 4.S SUBROUTINEPMEXPN. . , . . . . . . . . . . .2S

_/ 4.6 SUBROUTDq'BPMID • • • • • • • • • • • • • .26

_' $.0 HEATINGROUTINES......... , . . . . . . 28 i

_" 5.1 SUBPOUTINKFAYRZD....... .2q

5.2 SUBROUTINE R.I_Ii_.. , . . , . . . , . . . , ,, ._J0

•:' $.3 SUBROUTINESTB_T. . . . . . . . . . . . . .30

' $.4 SUBROUTINESFJfHF,.ATAND ERP . . . . . . . . .91

s., smo_ swc_...... . . . . . . . . . . . , . . . . ..

• s._ svno_ ._........................ ',__.

i " _ .8 SUBROUTINESWCYI,$. • • • • • • . • • • • • • • • • .$4 i_

:,. _ 5.9 SUBROUTII_ DBTRJU.,. • • • • • • • • • • • • • , , , ,.q4 '_

: __: i] =5.10.11 SUBROUTINE SUBROUTZ]_SBCSPCHI KERT...... AND FSUBC. : .• .• ....... . . . .. .. .. .. .. .. .. .. .,$.$6 _:

5.12 SUBROUTINESPFP • • • • • • • • • • • • • • . . . . . . . . .$8

. . . . . . . . . . . . . . . . . . . . . .

0_9

_!.,_ :J.14 SUBROUTINERHOMUR.......................40

"" S.I5 SUBROUTINBLBSII2....... • • . . . . . . . .41 •

s.. su.orr_s_. Din.p. si. cP_ _'B_icl.......4s

.... " S.17 SUBROUTINESFINB, I_INPEB, ANDFINPEP . . . . . . . . . . . . .42

5.18 SUBROUTINEBADEQT. . . . . . . . . . . . . . . . . . . . . . ,43
6,0 LENGTHAND TRANSITION ROUTINES,-- , , , , , , , , . , . , , , . . .S3

6.1 SUBROUTINESTRANS ANDEDPi_.M , , , , . , . . , , , , , , • • ,83

6,2 SUBROUTINEVP.UI_ , , . , , , . , , . , , . , . , , , • , • , ,85

6.3 SUBROUTINE(ISFLW. . . . . . . . . . . . . . . . . . • • • • ,87

. 8,0 REFERENCES, , , , , , . , , , , , , , , , , , , , , , , , , , , , 121

• i

i

ttt
..... Section 1o0

INTRODUCTION

The successful desl|n of therncl protection systems for vehicles operatin8 e

in atmosphere and neaz-spa©e envi:onnonts requires accurate analyses of heatln|

rate and temperature histories encountered alone a trajectory. For pzellnina:y

dest|n calculations, however, the requirement for a©curacy must be tempered by

the need to_ speed and ve:sattltty in computational tools used to determine such

'thermal envi:onneuts. _ w

i

l

The MINIVER p,_o|rm (Ref. X) over the last decade has been found to pro- i

vide the proper balance between versatility, speed and accuracy for an ae:othe_-

sutl poediction tool. The advancement in computer aided desisn concepts at Lasslay Research Center (LaRC) in the past few years has made it desirable to incorporate the MINIVER ptosran into the LsRC AVID system (Rat. 2). The purpose of

i the AVID system is to provide the prelLuinery desisn ensinee: vtth a useful tool

i tot multi-discipline interactions to perform partial or complete vehicle syria i

thesis. •

In order to effectively incorporate MINIVER into the AVID system, several

ohanje8 to J/INIVER ve:e made. The thermal conduction options in MINIVER gere

removed and s new Explicit Interactive Themal Structures (EXITS) code vas de-

_J

i veloped. J/any up|fades to the MINIVER code vere made and a nay Lan|ley version _

_ of MINIVER called LANMINwas crested.

-ii

f •

.4

• I This report is divided into three volumes° Volume I describes the theotet-

*I lcal methods and subroutine functions used in LANMIN. Volume II provides a user

r _

" !

:! I

.i

• i

_-\_T ........ --_ ..... V_-_--_ ........ _-_-_. _-_=_7 _ _=__-__ U-_T _ .... _--_ ..... _ ......... _-_- _-_,----- -
input Buide for LANMIN. Volune II! describes the BXITS code and provide5 an

input 8uide,

4

The documentation presented in ¥olume X uttlixed prior documentation vhore

applicable and added new asteriel for upjrade areas. The prinarF sourceJ of

prior documentation are Ref. ! for the oriaiaal MINIVER code, Ref. $ for eubroatine descriptions and Ref. 4 for rarefied flow updates.

2
I"

_I Ssatlon 2.0

O_Ei_L UTILITY ROUTINES

_ . The projrsn uses several subroutines of Ionersl utility such 8e spoottloa-

_ • tion of prtntinl of input and output data, interpolation techniques and the men-

, Q

.' alias of all other _ubrouttnes. This so©tion lives a description st those utility routines vtth a discussion of thot_ oapobtlttiee.

_.' 2.1 MA-IN

",i, IIAZN performs the task of n_tnelin8 the rest st LANMIN. This routine is

•_ best described by the tlov dlelrtm in Ftlu_o 2-1. The MAIN routine sets up the

_i!iI input, o811s the calculation subroutines in proper sequence, saves and controls

)

":._ the output, sad controls the case to ease input. Most of the input is accomi plishod throulh an array V(7O0) Many of the input array elements are

/I

'!_ equivalent to other variable names. A complete description of the input is

!

'_i" liven in Volume IX of this report.

",_.-I 2.2 SI_ROXn'I_ P.I_

_.1 Subroutine WRINP is called by MAIN to print out all of the input data for

_ii each separate sale. This routine prints out the pertinent input information.

!

o_!" 2.9 SUBROUTI_ VANOUT

Subrouti_ _/d_0UT is sailed by MAIN sad t8 used to print the output in 8

_i specified format. The parameters in the CALL statement of VANOUT are as

"I tel lovs:

,/

"_I • Da -fuactio (input) n ofThistime.matrixThe di1men 5 variables sioned (100ere:, 13)timconta e, ialtitude, ns 19 varviabl elocity, es 88 i

,, Mash number, susie of attack, Reynolds number/ft, host transfer coot- '

fioient, recovery enthelpy, equilibrium vail temperature, convective

bestial rats, hoetinl load, local presume, and flow type.

J IF - (input) Number of time points.
TITLE- (input) This array dimensioned (18) oontetus 8n input title

"-_: for the _sse.

"i_., _ ANST- (input) This variable cotrespondtn| _,o W1646) deternlnos the

._'- output _tt8. AJ_T - 0.0 corresponds to English units and AMET ) 0.0

©orrespoude to metric units for output.

,,,' BIM- (input) Body point number corteepondin| to W(611).

_' This subroutine writes to paper and to e file. Each case on the file i8

.l

: ended vlth a flaB having • numerical value of -100. for the variable TIR.

1,

! 2.4 SUBROUTINE_BLIN

° !, Subroutine TBLIN ts • utility linear interpolation routine which is used

J,

_ }; eztenslvely throughout NIN by other routlne8. The followlng discussion con81dare the use of this routine in conjunction with an atmospheric table vhloh

...... does not exist as t routine in the program, but rather cones into the program

vle input data.

_- T_e argument of the routine is TBLIN 11, XX, Y, YY, Z, 7_, N). The parses- :

• ,:-_i tar • acts 88 en independent variable end the parameters Y and Z act as func-

..:._ Stuns of I. When a value. I t8 input to T2L]_, the values Y and Z are returned

/sx _ st the corresponding X. The array g contJlns 811 of the table ve_ue8 of the

,. ,_ independent variables • in s one-dimensional array. The one-dtmonslouel arrays

°°,;i[ YY end ZZ contain all of the table values of the dependent variables. Sines

',. r

?_,,, each of these arrays (XX, 7Y, ZZ) contains the same number of elements, the

Q _ ,I}

.|

'1 parameter N t8 used to tndioete how many value8 a_e contained in etch array and

_ thus how large each stray t8 to be dimensioned in TBLI]q.

,,"): It should be noted that this routine can only be used vhen the value8 In

array ZX e_e input in nondec_eaain$ order. The rat-_It8 of this ltuesr Interpolation routine ere not valid if the velae8 in t_e independent vatteble array ILl[

4

!

00000001 TSAO
are not listed in lncre•sin| order. An ,xanpl, of the use of tht_ routine uscuts vhon u value of altitude (X) is input. The routine vii1 return v•luo• of

anbient tenpat•tn_e (Y) end pressure (Z) vie linear interpolation frou the ten-

, per•tufa end pressure •trays, 3_•nd ZZ.

Upon carotin8 the routine, • shack is nsde to detemine At the independent

vlriable • Is less then the first (smallest) value in the array X•. If it is,

then the first elenont of array YY ind the first element of array ZZ •re returned as Y end Z, raspaettvely, to the eelltn8 routine. Zf the independent

variable • 18 8reater than the leer (1st|eat) elenent in •tray l-r, then the last

elumont of array YY and the last elanent of •tray ZZ are returned as Y end Z,

respectively, to the esllin| routine. If the valne of the independent variable

• is not out of the ranse of the array XX, then linear interpolation is enployod

to dotex_ntne the oorreepondin| values of Y and Z.

2.S SUBROUTII_ TIMTd

Subroutine TXNT6 is • linear interpolation routine. This routine lnterpol•tes six or less dependent variables sinultaneously corrospondin| to an input

independent variable. The arjument of TXNT6 oontains 16 elanent8. The first

two olenents in the arsunent are values of the independent variable end the

array of stored values of the independent variable. The next 12 locations of

the subroutine sr|umont scour in six pairs ootrespondin| to the sin dependent

vart•bles. The first elenent of the pair Is the value of the dependent variable

_eturned by the pro•ram, end the seoond elanent of the pair is the array of

input values correspondin| to the values in the independent variable array. The

• independent end dependent variable strays nay each contain • neainum of 20

values. The last elenent of the subroutine ar|umont us•responds to the number

of values Qontsgned in the independent variable input •tray (10 st less).
The eoxt-to-leat olaneut of the subroutine sr|ument oontltns an inte|ez

_e_ue. Zf the value of this tnte|er is |rester than O, than TIFF6 perforns interpelation aseunin$ the independent vartable is nontnoresstn|. If the value of _

this lntejer is less thzn zero, then TINT6 performs linear interpolztton sssum _

in| the independent variable to be nondeorozsin|.

Now aonsidor the ease where the i_dopendent variable 18 nonde©resstnS.

Before interpolation is attempted, the input value of the independent variable

t8 ahe©ked to deteraine if it ie less than the first element in the independent

variable arraF. Zf the input value Is less than this first element, then the

values of the 'dependent variables returned to the oslltn| routine are set equal

to the first alenent of sash array. If the independent variable t8 larser than

I

the first element, then another _heok so©urn to determine if the independent

variable ts Stouter than the lest element in the independent vartable array. If

it is. then the values of the dependent variables returned to the ©allin8

routine are the last values in sash dependent variable array. If the independent variable peases both testa, then TI_F6 tnapeot8 to resolve whet_er -r not. _j

the independent variable is equal to one of the values in the l_dependent variable input array. Xf equality assure, then the value returned fo_ each depen- '5

dent variable t8 that value in each dependent array correspoudtn8 to the independent variable. .,

If the value of the independent variable ts not found to be less than the

first element. |rester than the last element, or equal to any of the elements in

the input nrra7, then linear interpolation occurs uJin| the rye elements of each

dependent array which oorraeponds to the rye input t_dependsnt variables brackotin| the input independent variable.
An anelosous prooedura t8 p,rfo_nod b$ T]_T6 if the tndependsz_t variable is

noninoreastn| instd_sd of _ondeo_¢ssl_|.

• I

This routine is vritten tar either e nonde_reasin| Independent variable or

4

• noninoressin8 independent variable, such as tin, lnoressim8 dntin| s traJsotory.

2,6 FUNCTIONS D/TP1 AND 2qTP2

These funotions are used to pattern linear tnterpo_ations in seal

lois. spoo,. The sz|uments of D/TPI ere:

I - (tnput_ Pressure lndez

32- (input) Hljhsst tenpotat_te indez

J1 - (input) Lovest tenperatuze lndez

I - (input) Theme1 property index

1_ - (input) Delta value of independent variable le (X-I1)/(Xl-Xl)

Values are interpolated fron the G(I, 3, r) nttrtz.

The atSuments of _?FP2 are:

• - (input) Lovest value of dependent variable

• - (input) Rtshest vslu_ of dependent variable

F - (input) Delta value of independent variable

Both funottons linearly interpolate in lo|20 epees of the dependent variable.

!!" I J

f
!," OF POOR QUALrI'_f

¢

_ I ZERARRA o IYS

READINPUT DATA ARRAY

WRITEOUT INPUT DATA

CHECKINPUT DATAFORERRORS

INITIALIZE PARAMETERS

i BE.IN CALCULATIONLOOP

L

I COMPUTEFREESTREAMPROPERTIES

.[

COMPUTEBOUNDARYLAYEREDGECONDITIONS

!

COMPUTECROSSFLOHCORRECTERUNNIN D GLENGTH

VIRTUAl.ORIGIN CORRECTIONFORTURBULENTFLOW

COMPUTELAMINARANDTURBULENTHEATTRANSFERCOEFFI.CT_NT..j .

, ._ .1

! ,RADIATIONEQUILIBRIUMTEMPERATUR]E

[ WRITEOUTPUT,[

[ Ftg. 2.1 Routtne MAIN :_i

...."'

,. ,:J i i:_ 5
So©ties $.0

FLUID PROI_RTY ROUTINES

• i

Ir this seotion, the options of oonputin| the free-sttes._ air properties

sis eat forth. These lnolude ideal and real See offsets.

9.1 SUBROUT_ Arn62 _

This is one of the atmosphere routines in MZNlYSR. The tontine desoribes

the U. 8. Standard Atmosphere, 1962 (tat. 2). Given altitude (ft_, the routine '

ytslds ambient tenporaturs (desrees R). density (81uS/fts), pressure (lbf/fts),

and speed of sound (ft/eso). The altitude tense of the table Is from 0 to

2,068,776 feet above sea level. The thornodynsnio proper*lee, t_r,_errtute end

density, are exponential serve-fits to the U. S. Standard At.5osph _. 1962. The

snbient pressure end speed of sound ere oonputed from .h_ t#.'..; equations.

This routine does not sail any other tont.l_ _ _ns only to the es .line

rOUt ins.

$.2 SUBROUTINEATMS4

.,.

This is the 196_ Petriok atmosphere routine. The input into the tontine i8

altitude (ft) ted the routine returns ambient tonperetuse (destee8 R), densiLy

(81n|/fts), pressure (lbt/tts), end speed of sound (ft/seo). The tense of altitudes Is from 0 to 2,300,000 feet vith esters of lees than $ poteont baler

400,000 feet. This routine is entire vtthtn itself end Ooe8 not eel1 any other

subroutines. The routine breaks up the altitude span into several tenses. Bsoh

altitude ran|e then has the atmospheric properties oaloulsted via • combination

of polynontels end exponential eel, s-fits. i

3.3 SUBROUT2qBVRA71

This is the Vendsnbers 1971 reference atmosphere. The input into the

routine is altitude (ft) end the routine returns ambient temperature (desres8

9 i
- Tlssqb_ _ ,

; _}, _,. _ty (sins/its), pressure (lbflfts), and speed of sound (ft/seo). The

ran|e of altitude is fron 0 to 2,300,000 ft. This routine does not coil any

other routines. The subroutine calculates anbient viscosity and molecular

#

veisht, but these vslnes are not uPed.

9.4 ROUTINES MOLIER, BLOC'E, BLOCEAAND SLOPS

These ere the routines eonstitutinl the sir Mollier dtasran and act as an

equation of state to account for reel 8as effects. The data are contained in

the G(I, 7, r) matrix. i r

i

_ G(I, 7, !) -Temperature

G(X, 7, 2) -EnthallqV

°- G(I, $. 9) -Entropy BLOC[

O(I. 7, 4) -Viscosity

G(I, 7, $) - Prandtl Number

G(X, $, 6) - Speed of Sound BLOCEA

G(X, 7, 7) -Density

! The block data BLOC][contains the pressure array PT(X4) and the variables G(X, i

$, E), E = 1.4. The block data BLOCEAcontains the varlables G(X, 3, r), • =

r_ S,7.

i_"

!it Four options may be used to look up properties based on two independent

variables. These options are:

i! "

NOPT = 0 P,H (Pressure, Enthalpy)

12 PP,,ST (Press (Pressururee,, ETemntropy) perature) i

, $ H, $ (Enthalpy, Entropy) d

Based on the options selected, the linits of the projrsm e_o cheoked

--to 8

l0 ._ P ._ 10 AtJn.

48.._ H ._ 75580 l_tu/ltm

200. X T ._ 30000 R

.925 ._ S/R _ 12.368

_f the independent variables are outside of the precedin8 ranis of validity, the

routine sets all thernodynanio variables to zero and returns wtth IDEAL = 1. t

Given the independent variables, the dependent variables are obtained by

10
'_, :3

interpolation in the G matrix. For NOPT - O, 1, and 2, the interpolation pro-

. eel,s# is the some. The pressure lndez is found ooztespondin8 to the table

: Ptessuses baler end above the input pressure level. At the loves pzesaurs

level, the dependent variables are deterntnod by two o8118. First, the tunotion

8LOPEis celled to eel©slate

• - •1

:

' vhere • ts the 10810 of the other Independent vsztablo and the ][1 an4 12 values

aze the 10810 values of the nearest points in the G natrlx tot the lover pres-

_" , suze. Given the value of FT1, 811 st the dependent variables are oalenlated by

li

_! linear interpolation in 10810 specs usin8 PT1 in a eel1 to INTP1. Likewise, the

_, dependent variables are determined at the htshez Ftessute level in the tables.

i) Pinslly, the dependent variables aze deterntned tot the input l=essuse level by

!,..

._:;_' ltneaz lnterpolstto_ in 10810 (ptess_te) apses by ealltn8 DITP2.

:_._, l_or NOPT - I the lntezpolstton prooeduze ts stnilaz but uses dtttezent

!_ 1o8to° The G natziz is so, ted to obtain the sutroundin8 points of enthalpy and ..,

_" entzopy. The nondimeneional ant=oF7 ts need in 8 eel1 to SLOPE to obtstn the

.... "r ' patio _0Z

_ S- 81 t

")!-_ PT1 -

" ,i'::', •!

....e at the 1oyez ptessuse level whe=e 8 Is the 10810 of the entzoFT. A sail is made

1i

?':'_ to ]I_I']L"P1to obtain the dependent vsttabls8 at this ptossuzo loyal, This presses

i_ _

"_ 18 repotted foe the hi|hot pressure level. Plnelly, the dependent _arisbles ate _

i dets:nined at the 81yen snthalpy level by s sell to INTP2.

" ' " .='-_-"............'_ 2........_....................... i _=-:-:: -: _"2....... -_- :2 "_ ,'.", .......
After the calculations amd intatpol•tions are made, soma variables •re ©o_-

vetted in units and the compressibility and speoifl_ hast rstio •re calculated Pl

for output,

The st|uments of the call for NOLIER are

H - (input/output) Enthalpy

P - (impnt/output _ Pressure

NOPT- (input) Independent Variable Option

T - (input/output) Tenperatuze

Z1 - (output) Compressibility Factor

S - (output) Rntropy

R - (output) Density

GI - (output) $peoiflo Heat Rstlo

In addition the viscosity is output via the common st•tenant /RANK/.

9.5 SUBROUTINEB]_qTRP

Subroutine BINTRP san be used to calculate the Pr•ndtl number Pr, Levis

number Le, and dissociation enth•lpy Hd for sir. The Prendtl number is computed

• 8 • function of temperature (desree8 R) and 8s 8 function of the ratio of the

pressure •t the stagnation point to standard pressure, The Levis nunber and

dissociation enthslpy are calculated as a function of temperature (depress R) ._

and st a function of the ratio of the density •t the 8tajnation point to the _I

density at standard conditions (2.S7 • 10 slui/fts). Routine _XNTRP is composed of three tables. Table I corresponds to dissociation onthslpy, Table II !

l

corresponds to Levis number, and Table III corresponds to Prandtl number. The

first two elements of the routine arsument are the temperature (desraee it) and

the • assure ratio, or the temperature (dejrees it) and the density ratio. Tha

third eluent of the routine arsument is the table number (I, II, III). The

last (fourth) element of _" routine arsument to either Hd, Le, or Pr. dependinj

upon the input. Upon enterln8 this routine, various checks o_our to insure that

the input values are not less than those values fOr which • calculation can be

performed. If the temperature is no|salvo, the pressure retie is less than 10 i_

lZ ,

2' .,
4 or the density teals is less then 10 , then 8n error nesse8o Is printed end

NSnOU - I is returned to the collins routine. Zt the tests sro passed, then

. BINTEP _roooods to use double intOrl_lstlon to dotomlm the oppzopzleto outputs #

If Hd _ 0, then Hd- 0 t, returned. Zt Bd ) 12450 Btu/lbm, then nd - 124S0

b

Btu/lbn Is tetuzMd. Zf Lo < 0.5, then Lo = 0.5 is zotur_od to the eallin8

zoutlno. It Pr _ 0°678. then Pr u 0.678 is returned. If Pr ) 0.794 and

T ) 24000 doltoos R, then Pr - 0.714 is returned. Presently this routine 18

used on17 to determine Hd and Pr. Thus. the other one-tlLird of this zoutiue 18

not used.

• II,6 _l_ItOlrlrxl_ I_I,NSlDI

ii Subzoutine HA_Smq is ¢alXed by toutiue FLOW to 8alculate vlsooslty as a

..i._ function of tomperatuza and pzossuzo. This sub:outino @aXis MOLI_R and zetuzns

.I, visoooity via oommou BANE. If t_o visoosity is 8roatoz thau the ,witoh value of

,!,

....; 0,29551K-08 sluJl£t 8e8, tho visooslty tzom MOL_ERis rotuznod. Xf the visoosii'

-_' ty tzoo NOLIKR t* 1**8 than the 8witsh value, the visoosity is osXoulatsd based

"_,'i on the relations st Hanson and nexus (NACA234 49S9).

P = P8 BID

where

H. = Is|l, P/2116.

I = ((T/1800)(1-O.12Slq.) - 6.S)/(1.$ 

B = 1. 

C .. (T/1800 - 14.5 - 1.51q.)/(0._ 

D - oC 

.8

" _s = 2.27 z 10 Tz.s/(T (Snthetlond8) 

T " Taupe:stuns (Dojtees R) i!

p m Presses (lbf/ft s) i

If the vein, of BID { 0.04 then BID is set oqul to 0.04.
!l

Section 4.0

FLO_]_D irOniSES

,: S

+ This section of the report deals with those subroutines that are used to

compute the local flowfield and boundary-layez edse ©onditions around the body

udet consideration. The methods used to evaluate shook smiles, flowfields

after shocks, and PrandtI-Neyer ezponsions ere F:esented.

4.1 SUBROUTINE FLOW

Subroutine FLOW is called by MAIN. The subroutine srjument contains two

parameters, FF and ALPHA. _e element FF is s one-dimensional array cents/nine

8 possibility of nine consecutive flovfield and pressure flame (always oocutrin8

If

i in pairs with the exception of the swept cylinder

flovfteld FF 8K 39 and the

Prsndtl-Meyer ezpsnsion fits FF - 29). The elmnent ALPHA is a one-dimensions1

'* array containins 8 possibility of nine consecutive flowfield su81e8 correspondin8 to the tlovfield flajs. The transfer of other information, such as upstream

conditions, downstream conditions, etc., is performed thtoush common blocks.

The free-stream temperature and pressure ere first needed to compute f-,e-strean *

viscosity vie subroutine RAN_. The first check performed by FLOW aete_mine8 ,.

- tf the Much number upstream Nu of the first flowfield flus Is |rester than

unity. If Nu < 1 and this is the firs, ._t second tie| in the array 1_, then the

pzojr_ llnores the flee and proceeds _'_ calculate 8tssnation conditions baaed

on the tsentropi© ideal |as relations. If the flus followinj the Mu ( 1 verification calls for a Prandtl-Meyer expansion (FF = 29), then a deceleration of the " *t

flow occurs. The flow decelerates to s hisher pressures calculated by modified i

Newtontan theory, i

1

l_novin| the local stajnatlon conditions and • local subsonic modified

T'
Novtonian pressure, 811 of the other 10081 pro.potties arc dotornined by the

6

ideal 8as lsentropie relations. If the deceleration ansle Is steerer than or

' equal to 90 desteos, then the local conditions are sat oqul to stajution con- d

dition8. For subsonic tier, the 1oc81 conditions determined above are also set

w

equal to the 1o081 conditions alone the st•suction line of an infinite svept

cylinder, hvin| the local tlovfield conditions, the ga_ett reference properties axe next calsulatod. If the heat transfer fla8 ts equal to $ or 7, then

the pt_f properties •re •1so calculated. The routine then returns to NAZN.

If Ifu ( 1 and this is act the first flovfiold or pressure fie|, then the

1o081 st•s_ttion conditions •re taken to be the same as tho•e cotrespondin8 to

the conditions dovastrssn of the previous pressure or Prandtl-lfeyor flax. If

tha flovtiold fl•8 followta8 Jlu ( 1 calls for a Prandtl-Meyer expansion (F¥ =

2P). then • deceleration of the flow occurs. The flow decelerates to • hlIhet

pressuza aS•in conputed via modified Nevtonian theory. Enovin8 the pressure and

also havin8 the entropy from the (isentropie) upstrean conditions, the other

local thetnodynsnic p_oprrttes ate detezlntned by ustn8 the Iollioz diairom (on- •

hroutine HOLIER). If HOLmR rotusus IDEAL ) 0. then the proszsn Britches to the

ideal 8as calculation previously discussed tot Jfu ( 1.O. If MOLIKR returns

_AI.- O, then FLOW ohechs to determine if the deceleration •axle Is 8reetez

than or equal to P0 dejrees. It the deceleration •nile is Ire•tar than 90 de-

|tees. then the local conditions ate set equal to the local stain•rich conditions. For subsonic flow, the final conpnted local conditions •re also set

equal to local conditions alonj the stasnstion line of an infinite svept cylinder. Enowin| the local flow properties, the Schert reference properties are

nest calculated. If the heat transfer fin8 is equl to either $ or 7, then the

prpr properties ere •los calculated. The FLOWreturns to MAZN. The difference

lS
I

:i

,_ between Nu ( 1 and FF - _. or 2, and Mu ( 1 and FF ) 2 Is that for FF - 1 or 2

the fluid is treated as an tde81 Ins, and for FF ) 2 the fluid is treated as s

real |as. Only the equations of state are different.

o

Now it Nu ) 1, PLOWchecks to determine if FF - 35, FF - S6, FF - 98 (there

is no 1_ - 37) or FF - 99. Each of these flovfteld fleas oorrospond_ to s different t, _ntque for determinin| the shock amble J. For FF - 35 or 36, the

:' value of AI,FA is taken as the flow deflection ansle for a sharp wcdjc _r sharp

cone, respectively. For FF- 38, the shock smile is read into the proSr,m as

ALPRA.. And 1_ - $9 corresponds to the swept cylinder flovffeld end the shock

•'_i •male is equal to LdJ&. Subroutine PLOW (for FF = 35 oz 36) ca118 routine PCS_

,.. to determine the attached shock angle as a function of M and the wedje or cone U

:_ deflection ansle. If NERROR_ 0 is returned from PCSW, then the input deflec-

!

•_ tion shale must have been either nesative or equal to zero. FLOW then immedi-

• ately returns to MAIN and transfers to the next data case. The next check is to _.

'f

?,, detezlnine the value of OFT. Xf OFT = 1, then the flow upstream of the wedse

'_: must have been subsonic. If OFT = 2, then the shock associated vtt_ the wedse

_i:_ ts detached and the shock Shale is. therefore, taken to be 90 dojr_.es. (If the :

_., shock 18 detached, PLOWperforms • normal shock expansion (mo_ifted lqevtonian)

_". to the _rees_te alas smile associated with the flowfteld shale.) If OFT - 0,

, then PCSWhas successfully determin_d the shock shale as s function of u;_teem

'- i_

'_i Math number and deflection aujle. If OFT m 1. then the routine _roceed8 to make

s subsonic calculation as discussed above.

Havin8 obtained a shock •nile p (either input for FF - 38, _ - LLI_FAfor PP

- 39, or fez a sharp _edse or cone f_on PCS_) (90 desrees fo._ s detached wadis

il of cone shock), PLOWnext calls DWNSTMto determine the properties downstream of

•• 16

i1 

It FI_ - 17, the p_...,ur, ,nile is the surf Joe snjle-ot-attaok or flow detleotion shale. This pressure tl,j provides the ptess_t, solution for s suttee,

whose shook shale is sltlhtly Stouter than the surts©8 snjle-ot-sttsok or flow e

deflestion shale. The shook en818 nust be _own and input under F¥ - _8. The

,dis of the boundary-layer velocity is oonputed tron the surf see

anjle-ot-atteoko the shook shale end the upset,am velosity. Then the lees1 enthalpy is oomputed fron the ,horSy equation. Enovln8 the 10081 ,nthalpy end the

entropy behind the shook finn DWHSTH(l_ - 98)w the other local tbetmo_ynantc

properties are obtained via the sir )Jollier diajrem routine. The wall pressure

is sn output of t.he MolItsr diajrsm, rather than beinj obtained fton the pros-

• .CI

_; sues ooetttslsnt (fron PCSW) a8 was done for FF = 15 or 16. It the suffuse

,4

'.-_i_ enIlo-of-attsok is lariat then the shook shale, then the pzosram pressed8 to

oonpute the edIe oondition8 via the parallel shook technique (with p as the

.._ shook anal,). If this onsets, then any tollovinj tlovfield flees ere tInored, _'

+/i and the ptolran pro©cede to oomput8 pr_ end/or Eokert reference properties be-

- I fore zet_tninl to JfAD(.

-I

_l It 1_ = 14, 15, 16, 17, 18 and no abnornality snouts sash as u ) _ (l_P 8

•_ 18), than before prooeedin8 to Ftooess the next flowfield fle_ a shank ooo_t8 to

_etez_nine if • P_andtl-Hsyer expansion is desired. If s Pt-.ndtl-J/eyer 8spanston

is desired, than FLOWnail8 PHE]LPHto osloalete oondition8 downstr#s.m of ".he expansion, lrf no Pztndtl-Heyet expansion is desired, then PLOWbypasses PMEXPN.

Next 8 cheek ooour8 to deternine if nddittonel _owfield finis (with or without

pressure fleas) ere present. It there are, than the present a_aJlabl, 10081

oondition8 ere taken as upstream conditions for the next flowtield. It no note

tlovt181d elsie are present, ¢h,n FLOWpesos,de to oalonlet, Pr_r and/or Eekett

reterono8 properties. :i
i+ t

':%

_: i ̧ ̧

If _ - 39 to used, then FLOWuses the downstream entropy and the stains-

" ties line ,nthalpy to _omputo the other loo81 tbetmodynanio properties. Hevtn8

" the loss1 thormodynsmio properties, the looal stejnstion end steele flow proper-

• ties are computed. Then the ptpr and/or Bokert zetezonoo properties are oomputed. The swept oylindez flovfteld option may be used alone or as • last tierfield fits in • aeries. Any fl_ .'/old option used after FF = 99 viii be t|nored

. by FLOW.

: If in the use of the J/ollier dialrsm touting the error mescals IDEAL - I or

,i 2 ts returned to FLOW, then FLOWskips the real 8as oalonlation and performs an

'-.,, _, ideal Its oalonIsttou. The J/oilier disjrtu routine (j/OI,II_) is sap•big of han-

_"+ dliu8 both ideal and real gas oalculation8. The ideal jaw rolattona used in the

_,ii:;_ pzoltsn are prhnartly used when nothin8 else works. This is to keep the l_oSzsa

_ runntn8 rather than stop the prosran because the J/olliet dialran routine oannot

/-.ii

,:._;/ extrapolate to • value off the table. Ones FLOWswitohe8 to the ideal 8s8 eel-

. . J

_, oulatton, all the flovfield and pressure options are ozeouted usin8 the ideal

++j

IJ

_ San relationships. The Ideal Ins equation of state Is InpIioitly used instead

_+_'+'.,. o£ _IOLIER. The shook anslos and pressure ooeffioiente are determined ezeetly -t

• ._l + ,i

_i+!_ the same v•y as fez • real lee oaloulatton, The downstream conditions are nov

1

|

,_;_ determined by the ideal los routine DO_NID instead of DWNSTNand the oondtttons .

_i,_ downstream of the Pzendtl-J/oyer expansion are oomputod in the ideal ps tontine

_'

_+ii_,! PMJD instead of PJ/SII_. All lojio and error oheoks ere prootsely the same as !

tot the zeal Us osloulstion tnoludinj the ideal |as determination of the prpt

• and/or Eokert rotorenoa properties. I

4,2 SUBROUTINEDMqSTM

Subroutine DWNSTNis sailed by FLOWto unionists the oondltton8 downstream

of a shoekwsve (normal, oblique or parallel). This routine is used to eel©slate

zg !-

1⁄2

. + : + L + .... .
the downstream conditions for both real and Ideal |sees. However, the calculation procedure Is based u_ the assumption _bat a reel ass calculation viii

I

take place. If subroutine NOLXERdetezlnines that an ides1 8as calculation is

sufficient, then the ideal 8as equation of stets is used instead of the Nollier

dia8ran values.

The shock shale p is input into DWNSTMthroush the subroutine arsument.

For an attached wades or cone shook, p Is determined in subroutine PCSW. If the

shock is determined to be detached by PCSW, then p is taken as 90 dearees for

input into NNSTN. If the parallel shook optic-- i8 chosen, then the shook susie

ts set equal to the effective susie-of-attack.

Herin8 an input shook anglo p DWNSTNnext requires the input of conditions

upctzean of the shook. The upstream conditions are input into DWNSTMvie a connon block vith PLOW. Ones the upstream conditions end shoekvave amble are

available, DWNb_I/proceeds to calculate the downstream conditions. First, the

normal components of ths upstream velocity e and Much number ere c,,Aoulated.

Then an initial 8mess ts made for Ps/Px. If Vx _ 4000 at/see, the ideal 888

equations are used to ,sake the initial incus. Xf Yx ) 4000 ft/sec, the initial

8uss8 for Ps is ,,ado main| various empirical equations depon_in8 on vhcthet 4000 !

ft/sco ( Vx _ 8000 ft/soo, 8000 ft/seo _ V: _ 14000 ft/seo, J4000

ft/seo ( Vs _ 26000 ft/see, or 2600U ft/soc ( Vs. Thsn s chock occurs to insure

that ps/ps ) 1.0. Subroutine DWNSTNthen bssin8 the first of a maximum of $0

iterations to detorniae the dovnstrsan properties. \

e

This discussion employs the tellurium subscripts: 1, 2, N, T. The subscripts

I and 2 correspond to conditions upstream end downstream of the shock, respectively. Subscripts N end T correspond to veIocity components normal and tensest

to the shook, respectively.
,4

• t

Havln| an tnitia! suess for the 4ownstrean density Ps , the dovnstrsan

normal oomponent ot velooity, VaN, is oslouleted .*roe _uation 14-1),

d

" VZN• VZN(Plple(1)'/_ (4-I)

end then the do_nstteau enthell_7 end pressure are ¢onputed based on Ps

ha = hz + 14-21

['o_V,Ne (')VaNe]

Pe " Pl + " Pe (4-3)

: NQv ps Is) te determined free subroutine JfOLrRRvii _uatlon (4-4),

,_ p8 (I) ,, P(h2, P2) (4-4)

_: It) 111

_! P, - Pe < 0.01

" It ' (1") , then oonvetlenee is oonstdered to have been

"I ash/eyed. PlZt aonverjenoe _t8 mot aohteved, then Pa(1) i8 =spliced by j)S(S) and

•-:: the oalcnletions, be|tnntn| with Kqustlon 14-1) aze zepee_ed, This presses Is

I oontinne_l until two oonseoutlv,| iterations ate vlthln I percent st one another.

{ or until _t maximum of 2$ iters1_lons is attained. After 2S iterations alternate

denpin| oooftielents ate ohosox_ to obtain a 8uossed density

., ps1.1 . o_,(el • I1 - o)p_*)"

whore • - 0,7 between 26 and IS Iterations and o = 0o4 between ._6 and $0 /tote-

" tlon8. Onos ooaverlenoe 18 obtained, 811 of the 8tatio oonditione behind the

. shook are hnovn via B4iuetton8 (.t-l), (4-2), (4-3) and snbtoutlne IfOLIKR, The

t

voloetty behind the shook is li_Pon by !

Vt " kO,/ V,N + (V,costSlt (4-S) :t

i,
'i .....

• inca VXT- Vs Qua p - VaT.

: H•vlns the t_.t• _. enthalpy and 8s, all of the total conditions behind the

shock are computed. Also this zontin8 calculates the stssnstion line ©nthalpy

for the parallel shock. The stasnation line enthalpy is 8ivon by

V2N2

. hSL - h2 -_------- (4-6) 2

Subloutine DWNSTMdoes not :mlculate the other stssnstion line properties for

the parallel shook (•wept cylinder 8tejution line flowfield). The other pro-

! patties are calculated after return/us to FLOW. Subroutine FLOWuses Sa and haL /'i

_ a• input• to NOLI3_Rin deterninins the other parallel shock properties.

i

I

4.9 SUBROUTINSPCSW "c

I Subroutine PC_W is called by routine FLOW and has the purpose of providins

i the shock ansles and pressure coefficients for sharp wedsee and ©ones. This

I routine contain• four table•: one for the sharp-wades shook shale as a function

_t of upstream Much number and deflection for the ahoc_

anjla_ One •harl_-oo_ anMle

as a function of up•tress Much number and deflection susie, _,8 f,r the

•hurp-wed|_ pea•sure coefficient 88 a function of upstream Much n_ubez end deflection sails, and the last ou for the •harp-cone pressazo coefficient as a

function of upstream Much numbe_ and deflection susie. _na ar|ument of PCSW

contains five parameters. The first parameter corresponds to the _pstrea8 Much

number, and the second psrametez corresponds to the deflection susie. The third

parameter ITABLB, Is an int888t value:

_: ITABLZ - I lndica_es •hook 8n|18 for a •harp wedse 18 desired

XTABLB= 2 indicate8 shock •nile for • sharp cone 18 desired

ITABLK- $ Indic•tea pressure coefficient for a sharp wadis is desired

ITA2LE- 4 indicates pressure coefficient for s sharp cons is desired

...... I "'>'

....................... o0ooo0ol TAB
The fourth per•rioter, OFF]BL. is eel,hisSed in PCSW and may hate on• of three

possible values. If OF°rilL - 1.0 l• returued, then the upetreeu Ns_h number and

, the daflootion •n|le sort•spend to oonditione produo|n| a detaGhed •hook. If

OFFFaL = 0.0, than PCSW has su©oessfully oonpleted its funotion. The last

par•meter in the subroutine era' sent is the value of the shook an|Is or presage

• oaf it.lent for either the ved|e or cone, dependin| upon vhioh is requested iron

the subroutine.

hvia| on©see•fully entered the routine, •evetel .honks .sour. If the

upstresn Naoh number Is Ire•tar than 26, the Jf (up•tre•n Mash nuber) Is set u

equal to 260 If ]fu ( 1, then the routine reLurns OPFTBL *, loZf 5 (deflootion

sn|le) _[ 0, then PCSWprints out an error ne•sa|e and returns NZRROR- 1. This

o•u•ee PQI to return to the HAZlqprelim. The MAIN prosran then will skip to

read input data for the next ease if W(642) = 0.0o or rill print the stored output in routine VAaOUT and then read input data for the next oa•e if g(642)

f 0.0. Tf 5 ) 60 de|toes, then the •hook is taken to be da_tohed for the ,one

°j

and 01_TBL - 2.0 l_ returned to the oalltnl prosran. Tf 5 ) 55 de|rose° then

the •hook is oon•ldered _o be detaehed for the rodin end OFFTBL n 2.0 Is re- I

turned to the .tilth| routine.

:_ext° the value of 1TABLK (1, 2° $, 4) 18 .hooked to determine vhioh table

Is to be need. For o•eh valne of FFABLS several she.k• .sour to deternino tf

the shook is dot•shed. If these tests are passed, then PCSWproceeds to selene

late either s shook shale or • pressure o(_effiolent.

The ved|a and oone tables for shook an|Is and _zassnre .serf isLand, are

represented by suave-fits. The pressure ooaffieient and shook an|Is are

23 4
_:_,,i on, we-fitted 88 a function of Maoh number and deflection emile. Each of the

•

" four tables consists of several patches, osoh ootrospondin8 to various rsjions

for each table. _I

After the vaI_e of shook auslo or pressure oooffleient is ca_,oulatod, a

final cheek ts made to dotorntna if p _ 90 de|ross or Cp ) 1.8. This implies a

detached shook end OFFTBL= 2.0 is returned to the collins program.

4.4 SUBROUT]_ DO_ID

8ubroutiu DO_ID Is celled by subroutine lq.OU to calculate the conditions

, /

downstream of 8 shookweve (normal, oblique, and parallel). This routine only

,/

.£

patterns calculations applicable for an ides1 8as. The shook emile p ts input

0 into DO_ID throush the subroutlne arjunent. The upstream conditions are input

t

•._; into this routlne via s canaan block with FLOW. Slues an ideal See oalculatlon

-_! is bolus undertaken, there is no need for an iteration process es in DWNSTN.

!i The calculation procedure basins with the calculation of the normal component °

"_-_!i of free-strain Maoh number

MxN = J/1 81n a (4-7) '

n

This dl6eusnion employs the followin8 subocrlpt8" 1, 2, N, T. The subscripts

1 and 2 correspond to conditions upstream and downstream of the shook, respectively. Subscripts H end T correspond to velocity components r.ozlnal and tansent ,_

to the shook, respectively.

i

,t

24 :i

A ", , "
an

... The downstrosm pfosouro, temperature and Hs©h numbo_ ezo liven by

Pt 2YM:N. - (¥- 11 14-81

' • Pa (_"+ 1) 1

:; 2

":' _ Ta Pl (Y- 11Ml N +2 '

:_ --- " -.- 14291

+ 11MZaN

_' - 14-10) ".'; M2 • -

i? T, (y + 1) P, TiP: JJ

;. The total ptesstLTe behind the 8hooh, the etstlo density, loesl spool off

i'* sound, dovnstzeea velootty sad ststto enthalpy end liven by

-"_,;" (4-111

}i/ii_ Pet " Pz + H2

5 .. Pz

_ : Pa = --"" 14-12)

•;,"-/, RTI

i= )_

•% ._,

1"2 -,

•* Vt " M2aa (4.141

":!f

:':; ht • .24T_ 14-1S)

,. and then DOWHZDreturns to PLOW.

'=._i,._' 4. $ SOBROUTD_ PJ_ZI_

"*_.. Snbroutlu PJ_ZPH Is the reel 8is P_andtl-leyet ezpanslon routine tot st_.

Cl The input oonditton8 to the touttne are npstresn ststio ptope_tio8 and steins- _

!i tton enthelpy. It the Pzendtl-leye_ expansion an|le epSll18 8reete_ then 109.2 i

=., delteee, then the ptojra oonveys in error neseaIe to the user. ,

il .f

i ................
The differential equation describinj the real ass expansion is

with F = h - h = u /2

0

end a = a(h.s), 8 = sa = oonst,

where a = a(h,8) is a f_notlonal representation of the J/olllor chart (Subroutine

NOLXER).

Enovin8 th_ value of e_, one desires to detetnlne enthalpy, }, at the end

of _he expansion fan. Ones h is detsrnined, all other properties are hmedtstely available. To deternino h, the above equation nuat be solved for F. This is

aehteved by enployin$ the _onrth-ordsr Run$e-£utta hashed.

If 86 dejroee ( epm < 109.2 destees, then e_ is divided into twelve egnal

sepents for nunotioal tntestatton. Zf 68.8 desree8 ( 0pro _ 86 de_ees then

epm is separated into 10 egual divisions. Xf $1.6 ( epm _ 68._ desroes, then

epmts spits into etsht equa! intervals. If 94.4 desrees < e_l.6 dearees,

then epm is separated into six equal seanents. If 17.2 de|T_ss ( ep_ 94.4 de-

|tees, then e_ is divided into tour equal intervals. And, it e_ ( 17,2 de-

|tees, then epmis divided into two equal divisions. HavtnS sueeessfully deteraintd F st the end of the expansion tan, all of the properties downstresn of the

tan ate returned to the nain prosran.

4.6 SUBROUT]lqKIMID

This Is the Ideal |as Prsndtl-Neysr expansion tontine. The input is the

Ptandtt-Meye_ expansion ansle, the upstreaa temperature, pressn_e and Mash

26

i
r

"1. •

1

nunboro The output oonsists of loss1 Mesh nunbet, tenpetstuze, preseuzo, densLtyw enthalFT, speed o! soud and velooity 8ftaz the ezpansLon. The J_oh nuaboz

sfter the ezpanelon ten is detorntned by usLn8 the Nevton-Raphson itezstion

method. A xazlnun o! 25 ltotetLon8 is allowed.

27
_ Seotion S.G

RATING ROUTXI_$

The subroutines used to calculate hess transfer cosffictents to various

• |eonettlee are presented in this section.

t.1 SUBROUTINEFAYIXD

i! Subroutine SA_RXD is called by MAIN and is used to compute the hearths at

!, the stsj_stion point of a sphere., The az|unent8 of the CALL statement are RN

!: and _J_CL. The nose radius, RN, Is input and the laminas value of the heat

;: transfer ooefflolent, ENCL, is output if a boundary layer calculation is made.

fir _0 FLORID subroutine has been modified to compute free molecular flow heattn8

_" end rarefied flow hesttnj in addition to boundary layer flow hearth| by the

" method of Fay and Riddell. The boundax7 layer flow method has been modified to

•!: calculate subsoulo flow hestin8 by a modification of the velocity srsdlent.

I;;:':_i'i The first subtoutlne called by FAYRXD Is REGXI_. Based on the value of

,.,", IRE, the output from RBOXB, • boundsx7 layer, _arefied or free molecular flow

;;_I calculation 18 made.

_ :_ If IRK = • Boundarw LsygF l_low

A boundaz7 layer flow stajnetlon point heat/mS calculation, is made based on

the method of Fay and liddell as described in Table 1.1. Tb© specific d*,ssoolation enth, lF7 Hd Is obtained from BXI_IRP as _ function of the stsJ].lt4o_ t©mpstatura behind the =ozmsl shook and the ratio of the stsjnation den|slay behind

the nounal _hook to the density at standard atuospherto conditions. If NERROR

0 is roan=ned by BINTRP, then FAYRXDreturns to MAIN and MAI3qtoads ,_hs next

dsta ease. Bevin8 obtained the host transfer coefficient ENCL, FAYIIID :returns

to the cellini routine. POT is set equal to 0.0 tot output description putpOSeS,

!

28 I

.!

t

" ..................... " ' ' " ""'r"" 0 00000001
Zf _= 2 2atefied F19W

A tar•fled fin etssnstion point hestiu8 o•leulstion l• ned• by ••Ilia|

STHEAT. PCT l• •at •quml to 2.0 tot output desortption purposes. The h••t

transfer us•if tot•at l_ output throush the labeled oouon /FREMO/ by the variable rFL,

Zf tRit= $ Free Boleoulaz Plo w

A tree nol•oule: flow hoatiu8 osloulstiou Is mode tot s plate perpondieulsr

to the flow dtreotion by eslltnsl+JfllEAT. PCT is •st equal to 10.0 for output

deseripttou purposes.

One labeled COMMONhas bee_ added to F&YRXDend it i8 sailed /FREMO/. The

variables t_su•ferzed throulh t_t• statement ere:

13W - (output) I Boundary Leyer

2 hrefled Plow

3 Pree Moleoular Pier

PCT - (output) A variable spoeifyin8 the osleulstion method used

HT_. - (output) Beet transfer film ossifieS•at based on enthalpy

H - (output) Beet transfer film so•trio/ant based on temperature

&TPB& - (output) Anjle of attach plus 1o081 body smile

NONCON- (output) Znt•ser value of g(646)

Zf NONCOH) 0 a re:stied tlov osleulsttou eta

be aide if IlK ) 1

If NONCON._ 0 only boundsz7 Isy•: esleulstlon•

eta be made (i.e. the prosran

operate• tdeutieslly to the

unmodified NZNZYBRProstam)

- (output) Rarefaction parameter ZeE s from STREAT

CUT - (output) Stautou nuRba_ fros STKSAT

CRI

ZSTA

C_MI Not derived from this subroutine or sssoolsted os110.

AI2C_L

• 3rY

Sine• 8WCTLo•118 FAISIXD, this subroutine should be dlsoussed her•. No _i

modlfio•tions have been n•de to SWLmIL. However, it I(646) = NONCONis input ss

!

It•eta: thin zero end SW_/L l• mailed, then • rarefied esleulstion oould be pot- i

turned it ZRB ) 1. This as+hod is not reoonmeoded. ++_+

Z9 '++
I

-1

I

I 5.2 SUBROUTINE_ZJB

1

[ This routine determines which flow regime Is sppoopriate for hosting calcui'. lotions. The Mach number (AN), veloeity (UZ), density (RZ), temperature (T),

i pressure (P), end characteristic length (X) ere input through the argument. The

subroutine sells DWNSTMto determine the post-shock eompressibility factor. The

' flov regime Is determined by the relations given in Tsble $.2 and returns the

integer 1_.

IRZ = X Boundary layer (continuum)

= 2 Rarefied (transitional)

= $ Free Molecular

Subroutine R_DIE is called by FAYRXI), SPGII and SWCYL2,

$.9 SUBROUTI_E STHEAT

This subroutine calculates the heat transfer ooefflolent, HTZL, to the

stagnation point of a sphere in the rarefied flow reglne. The equational basis

!

for this calculation is given in Table 5.3. This subroutine calls DWNS_ to get

the post normal shock temperature, TD, and compress|bility factor, Z.

Subroutine HANSENis called to obtain the viscosity, XMU, st post-shook presses

and reference temperature levels.

Subroutine STHEAT is called by PAYRID. The arguments of :he CALL statement

• ere:

UI - (input) Free strum velocity

" RX - (input) Free stream density

T - (input) Free stream temperature

P - (input) Free stream pressure

AN - (input) Free stream Rach number

GAMMA- (input) Free stream specific heat ratio

HI - (input) Free stream static enthslpy

". _ - (input) Wall temperature

HW - (input) Wall onthslpy

B - (input) Body radius

: QD - (output) Convective heating rate

:. B - (output) Beat transfer film coefficient based on temperature

RTrl, - (output) Beat transfer fits ©oefficisnt based on enthslpy

ILq,W - (input) Laminar adiabatic well enthelpy

TAW - _output) Lumtnar adiabatic wall temperature

'_" _"__b_ . . ,._:. ........... -__- :-_,_:_-_:_-_-_e-_-_-_ ........ -__ e_=_ _ -_:_/_:-:_....._=_'_:'_'=_-7__-.__ _'_
""J'i r

AlL2 - (output) Rarefsotion parameter

(:lit - (output) Stsnton number

Labeled eouons IFRSTIgl sod /DNSTRN/ ire used to transfer lufornation tot _i

the shook eeleulsttou.

5

$.4 SUBROUTINESFJlEAT ANDRRF

Subroutine FMKIAT ts used to oonpute tree moleoulst flov hesttn8 to any

vindvsrd resins aortaes. The tunotion prosram ERF ts the error ruination o811 in

subroutine I_T. The equations prosranned in subroutine FHHSAT sod funetiou

SILFare liven in Table $.4.

Subroutine FJaLSAT is oalled by FAYRID, S_I. sod SVC1_.2. The srjunents of

the oa12 etstenent ate:

_ UX - (input) Free sttean velooity :i

RI - (input) Free stresn density

T - (input) Free stream tenporstuxe i

P - (input) Free etrean pressure

AN - (input) Free 8troan J/ash number i

GAJ_- (input) Free strean epooitio heat ratio

HI - (input) Free otrean starts enthalpy

Tg - (input) Vall tenperatuze

• HV - (input) Wsll onthslpy '_

QC - (output) Conveotivo hearths rate " _.

H - (output) Heat transfer tiZm ooeffiolont based on tenpotatu_e

RTIL - (output) Host transfer tiln ooetfiolent bssed on enthslpy 'I

HAW - (input) Laniner ediabstlo yell enthslpy

TAW - (output) Laalner adiabatie vall tenporstute

TH - (input) Thets,0, suzfaoo soils

No sermon blook ststenents are used to transfer lnSormstlono

$.5 SUBROUTINSSWC_L t

Subroutine SWC_L is earned by NAnq to oonputo the heat transfer ooetfielont

• alone the etalnatton line of a svept oylindet tot lsninat or turbulent tier.

This to done usin8 onpiriosl relations based on the work of Cats for leo/nat !

tlov end $ohnson for turbulent flow ss siren in Table 5.5. Both toohniques sre i

based on enpirioel edJustnente to the steSnation point heat transfer ooeffielont
• °

_i_ on a sphere obtained fron FKYRID. The sphere is ta_on to have a radius oqul to

the radius of the oyltnder. It the up,trees Mesh uunbez is less than 1.12 the

_oAoeity srsdient is adjusted per the relations liven in Table $.1 to yield the

appropriite stssnatiou point heat transfer ooeffielent, l_l_, fron F._YRID.

After oonputinj hL and h, the Reynolds enslojy faster S 8 pr 2/3 is ealouluted and SWCTLreturns to MAIN. Presently SWCIL oonteiue four parameters: RN

the oylinder radius, PHX the sweep an$le, SNCL the laminar heat transfer ooeffiolent, and ENCT the turbulent 8wept oylinder heat transfer ooeffioiont. The

parameters RN and PRX are i_puts with ENCL and ENCT as outputs.

.. _ S,6 S_B_OUT]1_ SWCYL2

1

Subroutine SWCff,2 Is used to compute the heat transfer ooefflelent alone

- the atasnatton line of an infinite swept eylinder. This subroutine has been

,, nodified to oompute rarefied flow heat transfer ooeffi©lents.

An initial shook ts nude on NONCON= W(646) to determine tf rarefied flow

i_!'i i8 to be oonstdered. Subsequently, it NONCON > O, the subroutine d_G:ME is

;-_;.,:_ oalled by 8WC3_2. Based on the value of IRB, the output from RF_]3_S, s boundary

_. layer, rarefied or free noleoular flow oeleulation is nude. There are three

"_ parameters in the arjunent of the CALL stateneut for subroutine SWC_2:

' _ RN - (input) Cylinder radius (ft)

...._ KN_ - (output) Swept-eyliudez stsjnstion liu lamiur host

, transfer ooeffiolent

i:_i KNCT - (output) Swept-eylinder stasnation llne tusbulent heat

!_ transfer ooeffielent "

If & =bounda 1 noryundlt vayerLaver flow Flowoelouletion Is nude as desortbed in Table 5.6a and

$.6b both for supersonle and subsoulo flow eondltions. PCT Is set equal to 0.0

for output purposes. Subroutine HOLIER is Galled to obtain wall properties.

32
]

IIANSENis sailed to obtsin wall visoosity, FAYRID is oslled to obtsl_ the

sphere stslnstton point hast t:snstof ooettioiont.

i If B = 2 htofiad Flow

.

A rarefied flow esloulatton is made by aniline CTT. PCT is sat equal to

" 3.0 tot output purposes.

Zf ZRE= _ Free Holeoulur Plow

! A free molooulaf flow oaloulation is made for a plato at the loosl swoop

i smile. PCT is sot equal to 10.0 tot output p_tposoa.

The labeled COMMONhas been added to SVCfL2 end it is oalled /FREHO/. The

variables from this subroutine transferred through the CONMON/FREHO/ate:

AX2CIL - Rsrefaotion parameter, _s ^

XZ - Stanton Number parameter,

, plus the variables defined in seotton $.1.

m

$.7 SUBROUTINECYT

; Subroutine CYT is used to oompute rarefied flow stsjnation line heatinj

sates for s right oiroulsf oyllndaf at srbitraz,y yaw shales. The equations 1_o-

. 8tanned in this subroutine are siren in Table 5.7.

Subroutine cTr Is oallo_ by SWC_L2. The sfsuaente of the CALL statement

_' SrO:

:' UZ - (input) Free stream volootty

i!_* . RI - (input) From stream density *

.: T - (input) Free stream temperature

i.: P -- (inpUt) Free stream prosaLts

• • AM - (input) Froo stress hob number /

_ GAMMA- (input) Free stress speotfio heat ratio

HI - (input) Free stream ststlo enthslpy

TW - (input) Wall temperature

ii_ HV - (input) Well onthalpy _

_Y

_ • - (input) Dtstsuoe slo=8 the sutfaos

QC - (output) Conveotive heatiu8 fate

_:_ H - (output) Heat trs=ster film ooefticieut based on temperature

HT]], - (output) Heat transfer film ooefftoient based on euthalpy

33

. . •.';.., .- .,fT, ...... . ........ ..

.... r]
HAW - (input) Lsninat adiabatic wall enthslpy

TAW - (output) Laninsr adiabatic wall tenperatu:e

DLANB- (tnrut) Sweep an|le . J'

AK2CYL- (output) Rarefaction Psrauoter, KSA

XI - (output) Stanton Number Parameter, _

Subroutine CYT cells DI_iSTN to calculate post hemal shock temperatures and

pressures. Subsequently subroutine HANS_ is celled to compute viscosity.

Labeled commons /FRSTN/ and /DNSTRN/ ate used to transfer infornstion for

the shock calculations.

$. 8 SUBROUTINESWCYL3

Subroutine SWC3_.3 i8 also called by NAZN and enploys the prlAr technique for

conputin8 the heat transfer coefficient alonj the stasution line of an infinite

!

swept cylinder as described in Table $.8. This routine ©alia subroutines NOLZER

and BINTRP. The argument of the CALL statement for SWCYL3 contains the three i

follow/n8 paranotors:

RN - (input) Cylinder radius

ENCL- (output) Lumlnar heat transfer coefficient elon8 the staanatlon . _

line •

_CT- (output) Turbulent heat transfer coef'_'tcient alerts the

stasnation line of an infinite swept cyllnde;. 'I

All other input Infornation necessary for coaputetion is b:ousht into SWCYLS

throu$h eonmon blocks.

$.Q SUBROUTINEDETRAL

Subroutine DETRALis called by HAI]q and 4s used in oalculatin8 the lantna=

and turbulent heat transfer coefficients about hemispherical nose shapes. This _: "

routine enebles the evaluation of circumferential as well as stejnatton point

host transfer coefficients. The laminar equations of Lees, siren in Tabl_ $.9a,

are used to conpute the lminar heat transfer coefficient. The turbulent equations of Detta end liidal8o, |/yen in Table S.gb, are used to conpute the turbu- _

'I

lent heat transfer coefficient. _

Q

¢" r
The 8rSumeuts of the CALL statement foe DETRAL©ontain the followins parasstore:

JUq - (tnput,_ Sphere rsd:Lus

" _ - (input} Runnin8 lo_sth from stsSnetion point

PHI - (input) Body smile (90 dojtoss st the stsjution point)

_.- (output) Lminer host transfer sooffiolont

I_qCT- (output) Tubulant heat transfer oosftiolont

DSTRALsells FA_tID to obtain tbo lminar stsinetlon point host transfer souffle/ant sad sails BINTI_P to obtaiz the dissooistion onthsllqV. BD.

S,10 SUBROUTINKBCKI',RT

Subroutine BC_SRT Is sailed by MAIN and t8 used to unionists the laminar

sad t_rbulont host transfer ooofficient8 tot flow over s flat plats with no811-

81ble pressure 8radta:_t, The CALL statement tot subroutine BCI[KRT oontstns 6

• : par-motors:

• ; _ - (input) Lamtur _unnin8 lonsth (already oorrooted for

-_, orosoflow tt orossflow option yam ohosen)

KIT - (input) Turbulent runninj lonsth (already oorrooted for

orossflov and virtual orijin adjustment if those

_-_ options veto ohoaen) i

i _qL - (input) 12mlnat Nsnjlor trsnsfornatlon fester to aooount 1

for axis$1metrio flow oorrootton to fls_-plata

hoatin8

- (input) Turbulent Nsnllor transfozlnatton faster to museums

for azlsymaotrlo flow oorrootlon to flat-plato _

hosttn8 .

KNO_- (output) Laminar host transfer _ooffi_iont based on onthslpy

KNCE- (output) Turbulent host transfer oooffioient based on onthaZpy "

_1 Subroutine BINTRP is called to doternine the Prsndtl number PrL as s funoi tion of the Bokort reforouoa temperature tot laminar flow (tooovory faster Is

I ,

j 0.85) and the ratio of the boundszT-layer odsa pressure to standard stnoophsrio

,: pressure. The Eckert host transfer oooffioisnt for laminar flow is oslcnlstad

l uein8 the relations in Table S.lOs. Next subroutine BINTRP Is sailed to doter- _! i i

: nine the Pzsndtl number PrT as 8 funotton of the Eokert roforanoa temperature ,

for t_rbnlent flow (tooovory faster ts 0.881 sad the ratio of the boundszT--lsyor

r_ 36 i

!: j,

., e t,. ,_ _ " " " ,. L 'n
t

edje pressure to standers atmospheric pressure, The turbulent flow hmst /

/

!

transfer _oeffiJient is calculated usinS the relations elves in Tsbld 5.10b.

Jl

If t',o parameter NHILROR_ 0 is returned from BINTRP, then ECI_RT ro_ ,rn_ to

MAIN and proceeds to road in the uezt data case. The E©kert rofersn©o properties (l--lnar and turbulent) are calculated in subroutine FLOWbased on a constant Prandtl number (l..-iur recovery factor is 0.85 sad the turbulent recovery

factor is 0.88). Usinj this constant Prandtl number the Ecksrt referenoe tenperatuzs Is deterainad. This reference temperature is then used in oouJuuetion

with BIIqTRP to deternine the Prsndtl number (now considered as a function of

temperature and _:essu:o) vht©h was otijtnally taken to be s constant. Strictly

speakin8, the Prandtl number should be determined by an its:stirs procedure.

However, this probably does not _aues any appreciable error.

5.11 SUBROUTINKSSPCRI AND I_UBC

Subroutine SPCHI is sailed by MAIN and is used to oalculato the turbulent

heat transfer coefficient for turbulent flow. and also the Ecksrt referenoe

technique is used to oompute the laminar heat transfer coefficient. Bot_ oor _1

respond to flow over a flat plate with a nasltstble pressure s:_dieat. The CALL i

!

statement tot subroutine SPCII eontains seven parameters:

,4

ELL - (input) Laminar ru_nin8 lensth (already corrected for ,_

crossflow if crossflow option yes ohosen)

BIT - (input) Turbulent ru_nin8 lenjth (ai_resdy oorrecte4 for

orossflow and virtual oziliu adjustment if these

options were ehosen)

EIqL - (input) Laminar Jfansle: transformation factor to account

for sxisynmetrio flow correction to flat-plate

hestin|

KI_ - (input) Turbulent Nenjler transformation factor to account

for Jztsytmot_io flow correction to flat-plate _i_

heatinj _

EMCL - (output) Lminar heat transfer coefficient based on enthsllry

_CT - (output) Turbulent hast transfer coefficient band on euthslpy

- (lupu_) If a value |tester than sets is input into location _!

J19, then the Von J[srmsn fern of the Reynolds !

a_alojy factor is used.
An initial aback t8 ned, on NONCON- W(646) to dets_nine it boundary layer

flow is to be considered (yes if h_RCON ) 0). flubaoqoently, if NOR_N ) O, the

aubtout|l_e RBGINK is aslled by SPCHI. Baaed on the value of IRE, the output #t

from _IIE, a boundary layer, rarefied or free noleoulsx _eloula_lon is made.

It IRE 1 Bounder 7 Ls_.t Flow

A boundary layer flow ealculstion Is made so des©tibed in Table 5.11 for

tuzbulent flow sRd Table 5.108 for lsuinar flow, PCT 18 sot equal to 0.0 tot

output purpose a.

SPCHI sails subroutine FSUBC to oonpute Me for • real 888 usin8 IIOLIER.

The 8rlunent of FSUBC oontalns five parmotere:

HB - (input) Enthalpy st the edjo of the boundax7 layer

• I - (input) Wall anthall_v !

- (input) Turbulent E_kert rafetanoo onthelF7 !

J

PK - (input) Boundary-layer odin pressure '4

¥CI_V- (output) I/F ° 1

It no problem Is onooutored with the Bollier dts8ram, then ¥ Is returned to

O

SPCHI. If the Lhornodynanio properties _8nn_t be determined by MOLIER, then

IDKAL - I Is returned to SPCRI end an tdea_ 88s oslculation of Fo 18 undertaken, ji

Havin8 obtained ¥o" the turbulent heat transfer cgeffto_ent 18 then deterntned _!

fzon the Spsldtns-Cht equ4ttons vhioh have been oheoked sad fo,_ud to be oorreet. 'I

If s value 8rester then zeta Is stored in Ioostion 919, .*.hen the Van Etrnan Roy- "

molds tnelojy fsotoz t8 used in detarnininj the tusbulent heat transfer eo_ffialeut. Hearer, it sere le stored in location 919, then the lleynolds sneloiy

teeter ta nod sa 1_219.

After the turbulent heat transfer ooeffielent hem been determined, SPCHI

neat proooeds to oonputo the 18miner host tts_ofot oooftiolont by the Eckott

reference toohnique. Both the Imin_r end turbulent host transfer #oeffioionto

37

)
_' ate oorr•ot•d for ores•flow and for •zisymm•trie flow effects (via the lamin•r

and turbulent Nan$1et transformation factors) before b•ln| used in the he•t |

' transfer coefficient equ•tions. _1

Tf TIIK = 2 Rarefied Flow

NI_CS ) 0.0, NFCS = W(914)

If I_CS ) 0.0, then SPCHI sails SPFP.

The r•refied flow host transfer coefficient for a sh•rp flat plate at

zero smile of attack is oomput•d. PCT i• set equ•l to 4.0 for output

purpo •e •,

0.o

_ If I_CS _ 0.0 then SPCHT emil8 CONK. The rarefied flow heat transfer

coefficient for a sharp nose cone is computed. PCT is set equal to $.0

•: for output purposes.

_ Tf IRE = $ Free Molecular Flow

...'_'. A free molecular flov heatin$ calculation is made for a plate at the local

_:i body ausle by ¢allin8 F_RKAT. PCT Is set equal to 10.0 for output p_zposes.

_.:_ S.12 SUBROUTII_ SPFP

ii Subroutine SPFP is used to compute fltt plate he•tin• fates l_ the _arefied

_-_ tlov resins. The equations pro|rammed in this subroutine ere •lyon in Table

s.2.

_r

....""i:, Subroutine SPFP is celled by SPUiT. The atiuments of the CALL statement i

i_ are: *

_.! UI - (input) Free st_.eam velocity "

i_. RZ - (input) Free stream density T - (input) Free stream temperature

//t P - (input) P_e• stream pressure _'

"_ AN - (input) Free stream Mash number

GAMMA- (input) Free stream specific heat ratio

Ill - (input) Free stream static enthalpy

TW - (input) Wall temperature
I

! • - (input) Distance slams the suttees

QC - (output) Convective hostinj rate

B - (output) Heat transfer film seattle/ant based on temperature

HTIL - (output) Heat tranAfer film eoefftolent based on enthalpy

: BAW - (input) Lumtner sdlabatto veil enthalpy _

• TAW - (output) Laminar 8dtabetto vail temperature

. CHill (outp.u_).Rsr.e_8_t3Lon,psrmeter, Bo_

Subroutine SPFP ea_ls LM_SEN to compute visaosity for use in ealeulatin8

the Cha_man-_ubestn constant.

No cannon statements are used.

,_ S.I$ SUBROUTINECONE

:; Subroutine CONE ts used to oompute rarefied flow heating rates for a sharp

oi sane. The equations ptosrsnned in this subroutine are stven in Table $,19.

Subroutine CONE is sailed by SPCBI. The arsunents of the CALL statement

are:

UX - (input) Free stream velooity

HI - (input) Free stream density

T - (input) Free stream temperature

P - (input) Free stream pressure

- (input) Free stzetn Mash number

GAMMA- (input) Free stres_n spuoifto heat ratio

HI - (input) Free stream statio enthelpy

TW - (input) Wall temperature

HW - (input) Vail onthalpy , _,

l! • - (input) Distance alan8 the suttees

QC - (output) Convective heatin8 rate 'I

H - (output) Heat transfer film eoeftiolent based on tempurat_te

HTIL - (output) Heat transfer film ooeffieient based on enthalpy

RAW - (input) Laminar adiabatle yell enthalpy

TAT - (output) Laalnar adiabatlo wall temperature

TCD - (input) Semivertex an|Is of the sane

_k - (output) Rarefaction putsmeter,

(output) Stanton Number perimeter, _

NB - (input) NSB = W(650)

° NSB = 0 Sharp sane curve fit t

if" NSB- 1 Blunt sane ouz_e fit

" 39
],

Subroutine CONEcalls DWHSTMto calculate post nornsl shook tenperatura and

pressure. Subsequently subroutine HANSENis called to compute viscosity based

on s reference temperature, i

Labeled sermons /FRSTM/ and /DNSTRM/ ate used to transfer information for

the shock calculation.

5,14 SUBROUTINERHOMOR

Subroutine RHOMURis called by MAIN and is used to compute laminar and turbulent heat transfer ooefflolents over a flat plate uslnj the relations in Table

5.14. Subroutine BZNTBJPis called by RROMURto oonpute the Pzandtl nuaber as a

f_notion of reference temperature and as • function of the ratio of the

boundary-layer edse pressu=e to standard atmospheric pressure. Also BINTRP is

called to compute the specific dissociation enthall_y as a function of reference

; temperature and 88 a function of the ratio of the reference density to standard

atmosphario density. The expressions for the laminar and turbulent heat

. transfer coefficient have been sonewhat sinplified from the orisinal pz_r expressions. The equivalent runninj lenith is determined from CRSFLWat. the otis

8tnal prpr erosstlow expressions are not used. Also there is nc adjustment to

;i the heat transfer coefficient to account for the increased her.atria due to az-

:..i lsynnetrle flow (Man81er transfornation factor). The ariu_nt of the CALL _\\

,f'

statement for RBOMURcontains the four follovin8 pataneters:

_ ELL - (input) Laminar runnin| lsnjth which nay have been oorrecte_ !

_ for crossflow effects _i

!_, ELT - (input) Turbulent runnins lensth which nay have been "

corrected for crossflme effects and virtual orijin

adJ ustnent _

KNCL - (output) Laminar hast transfer coeffioient

' BNCT - (output) Turbulent heat transfer coefficient

All other tntornation necessary for conputation is bron|ht into RHOMURthroajh 1

i

_[ common blocks, i

t

i an
S. lS SUBROUTI_ LES

Subroutine LRSIDE is oalled from MAIN after s osll to PA._ID. to osloulate

the svetaSe host transfer ooeffiolent to the leesids of an otbf.tst. The 8vorsSo /I

heat transfer ooefficient is osloulated usin| the relations An Table $.IS. This

• subroutine is oslled if MNff.A6 = P. The atSuments of the oall ate:

RN - (input) Radius of seals, full seals RN = 1.0 at.

' - (input) W(21). Windward Wall enthslpy (Btu/Ibm)

KNCL- (output) Kveta|e turbulent or lminar leeward side heat

.i transfer oosfflolent

'_' ]_ICT- (OUtput) = ENCL

The oonnon FLgFLD is used to transfer post no..-nal shook values obtained by the

•/ sell to FAIRID.

$.16 SUBROUTD_-.SFLAPH. DF,]PL,DSTML,. CPZ,4_ANDBTIlICE

Subroutine PLAPH ts oalle iron MAINvhen _ - 10 to oaloulate the peak

rsettachnent hearths to a flap. The equations used for this oaloulatton are

|ivan in Table $.16. The u|umonts of the oall are as follows:

RL - (input) RunninZ lensth

FLI_IG - (input) Flap lensth

PANG - (input) Plep shale

ff - (input) Wall tenpersturs

HT - (input) Total enthalpy

ENCLO - (output) Laminar heat transfer ooaffioiont

_CTO - (output) Turbulent host transfer ooefftotent

IQUXT - (output) FIe| IQUXT = 0 Separation oocurs .

IGUIT = 1 No separation ooouzs

PCT - (output) Transition peroentsse

A oonmon statenent, MLPHTG.ts used to transfer the followin8 sdso properties

from MAIN into the subroutine:

I_GEP(1,I) - Pressure

:" EI_£P(2,I) - Temperature

EDGSP(3,I) - Density

. BDGBP(4,I) - Speed of sound

SDGRP(5.I) - Velooity

EDGBP(6. I) - Mtoh number

EDOEP(7,I) - Visoosity

EDOBP(8,I) - 8peoifio heat ratio

vhete X - 1 - Before the flap shook ed|e oondition8

X _ 2 - After the flap shook ed|e oondttions

41

v ,

.- __ . : -.:._- ,. .... . . .._ ,, _'_
Subroutine Iq,APH calls BTRICK to obtain s laminar and turbulent boundsry

layer thlcknos8. This oalculatlon is made nsln| Eckert reference conditions in

the followiu8 equations: p

8 = 1.21/ : Lamlnsr boundary layer thickness

0.1$4X/(Rex°) 1/7 : Turbulent boundary layer thickness

6 88

Next subroutine CPZAF is called to calculate the incipient separation pressure

coefficient. This is followed by 8 call to DEPL _o deterntne if the input flap

anjle is sufficiently lares euoujh to produce separation. If the input shale te

insufftcie_t to cause separation. IQUIT Is set equal to 1 and the subroutine returns to the MAIN. If the subroutine returns to the MAINwith IqUIT = 1, then

the hoatin8 ts calculated by • eel1 to SPCHZ.

If separation is found to occur, the plateau pressure ts calculated and

DKFL Is called to calculate the dividing streamline angle. Next the separation

lenjth ts calculated by • call to DSTM,. If the separation Seonetry indicates

I

that tnptnsenent will not occur for the input flap lensth, IQUIT = 1 and the 8u-

%

broutino retuxns to the MAIN. _

.!

i

If hnpinjenent scours, the shear layer thickness is c_Icplated. Subroutine

HAHSENi8 called to calculate the wall viscosity. Finally, the heat transfer

coefficient t8 calculated for either laminar or turbulent flow wit_ PCT set

equal to 0.0 or 1.0. The Iminar end turbulent heat transfer eoefftciente are

.J

equated since this routine can calculate only one type for a siren flowflsld. i

Note that in MAIN if NBFLAG = 10 and IQUIT = 0 then the call to TRANS is !

skipped, i

5.17 SUBROUT_ES FINH, FINPEH AND FI_IPgP .-_

Subroutine FINI! Is called by MAIN when NHFLAO= 11 to calculate th_ peak _

42
lntetferenoe hestin8 produoed by 8 fin on the edJsoent surf Seas The equations

used for this oaloulatton are |lyon in Table $.17 The ar|usonte of the eel]

are as follows:

ALP - (input) Kffeottve tin enjle of attaok

]UP - (input) Lensth alone fin suzfaoe

• YP - (output) No_81 dtetanoe from fin to peak heetin|

RL - (input) RunninS lensth to tin leadtn8 edle

TV - (input) Vall tenperaturo

HO - (input) Total enthalpy

AJ/PPT- (output) Tuxbulent pressure om_llfloatlon

AIIPI_- (output) IAminer FtSSSUZe am, fioation

ANPHL- (output) IAninar hoatinj 8npl,floation

AMPHT- (output) Turbulent hestin8 anpltfioation

KNQ.O- (output/input) IAmtnsr heat transfer ooeffiotent

BNCTO- (output/input) Turbulent heat transfer ooefftotent

The seamen stetenent, FLPHT0, is used to transfer edae properties upstrean of

the fin shook from NA_q into the subroutine. The variables transferred a-e defined in eubseotion 5.16.

Subroutine FD_ oall8 BTHICK to obtain the lanlner and t_rbnlent boundary

_ayor thickness usin8 the relations 81yen in subsoetton $o16. Next the shook

ansls prodnoed by the fin is oonpnted ustn8 a sell to PCSW. If the shook is attaohed, the peak pressure mpliftoation ts seAt,Z-ted for laminar and turbulent

flow usin8 two 08118 to F]_P. The peak hestins mplifteatton for laninar and '

turbulent is then oonputed ustn8 two sails to F_PEH. The input heat transfer

ooeffioients ate nodiftod nsin8 the heatin8 anplifioatton factors.

Subroutine SPCHI Is always sailed before the osll to F]3qH to obtain the us

distusbed heat transfer coefficient. Note that in MAIN, if NHFLAG = 11, the

" hestin8 anpliftoetion faster and sdjs p_eseurs ate oaloulatsd based on PCT after

the oall to TRANS.

$.18 8UBROUTINRRADI_T

Subroutine RADEQTis sailed by MAIN and Is used to oonputs the radiation _

43 _ -,
._ equilibrium temperature, The radiation equilibrium temperature is determined

via the Eewton-naphson iteration technique. The wall temperature is used as an

tuitial |uess and oonverjenco to the radiation equilibrium temperatu=o is cons/- Jl

dared to be achieved after SO iterations, or after two successive iterations a_e

within 0,$ percent of one smother, The first of these two conditions to occur

de f ino s oonvorsence,

E _q

_ The argument of the CALL statement for subroutine RADF.QTcontains the re1-

. lowing five partners=s: I

:i ]_qC - (input) Host transfer coefficient i

•i HR - (input) Recovery enthalpy i

KMIS - (input) Effective emissivity- product of shape factor and !

emissivity !

TW - (input) Couduotlon or thln-skin wall temperature which is

used as an initial 8uess to the radiation _

equillbrlua temperat_e in the iteration scheme 1

THE - (output) Hadiatlon equilibrium temperatu=e

_r j

t:
OF POORQUALITY

STAGNATIONPOINTHEATING

!

t i L L in t

6 • t | •

Stagnation potnt heattng ls basedon the theory of Fay andRtddell.

. ,

• Nu

%

where

{k,, _DI_/" _0._ I .S2 I

- o.76prw(o__ 1, (Le _)._.

Pt

• .g (1.5 - 0.378Mz - 0.02525 14_ ) for a sphereand H=<_1.22

R

• 'g_ (2.0 - 0,872Me- 0.328H_=) for a cyl|nder and M=S 1.12

and the dissociation enthalpy

"d" Cob; +

h_ - 6636.26 Btu/Lbm

h_l - 14456.53 _tu/Lb,

i N°menclature

I " q - Heattng Rate (Btu/ft=sec.)

• _ Pc " 1 (slug ft.llbfsec. =)

• g • 32.174 (Lbm/slug)

P • Denslty (slug/ft.s)

• tJ • Viscosity (Lb.sec/ft =) :!

U • Veloc|ty (ft._sec.)

:_ P = Pressure (:Lb_/trt.=) H - Enthalp3,(Btb/lbm) ._

e

i

45 _':
Table S.1 (Cont. 1)

ORIGJNALPAGE_

OF POORQUALrrd

Le = Lewis Number

Hd = Dissociation enthalpy of atr (Btu/Lbm)

Ct = Mass fraction of species t (t - O, oxygenand t - N, nitrogen) i

R = Noseradius (ft.)

Pr = Prandtl Number

0 - Sphere BodyAngle

SubscrlJ_ ;s

e = Edge

t = Stagnation (post shock)

w = Wall

® " Free stream

• , J, --,-',..........

• ;:": Potentlal_ .;... ® _ 1.6 '*: " _-'- -" " ....... ;............

,__ 1.2 i.]!::"l::;i .. _ NewtonlanL. : t_"_R:_ " :_ " ' ' ......... '

0.8 -!_!::i!.:i:l:: :: i--J:_:-.:_ ..' .

0 ,:.-i:::I :::i:':" .':'i":" ":';.::. t" ::{"" l ":' '-t' I :1: "i' ":I :::I" • :.i..::t'lL:.::.l:..I:::. ::;:-:,_ .: .": -!

:---:.r:::l..:':..." L_-:-'.. ....' .... ....... ---L_:'_L_: _-:',-:'-,_;.! _'-:F"" _:%' "i-l--"-;:]]_.:_"-, ;___-:

> ;::l.::il!:.:_:_.i::,= qy!Iper!j. d,#- i,:,:..!!.;_:i::l::.?::i:i.;-.:_.j:!=_=.!._:!_ili=-l:-i4=_ii;l:

"': ' " :: "_" ; : '-. -1 . ; . • " " ' ' ' .-_J.'_ :!" --':':::'::, ":7 1.

0,4 ' ::::l::{i:Y::_!.,: .::..::I:;._:.i/i_{.::ii_:i=:_":"_i:' :" :::!:J._::::l?x;-:-: :.h=_l..-..:-._

:::!;::_:_i::l_-:._::-F-::t_:_: ....... ..,:.:-_ ,:.:',.:,=::_ .;:_. T:_

:": "* ..: :-,-:, :.,

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

M.

References

Fay, _. A. and Riddell, F, R,, "Theory of Stagnation Point Heat Transfer

in Dissociated Air", J. Aeronaut, Sct,, Vol, 25, No, 2, Feb, 1958, pp,

78-85, 121.

, 46 -
'; Table 5.Z

BOUNDARYLAYER,RAREFIEDAND

FREEHOLECULARFLIGHTREGIMECRITERION

m m m m | m. m m

, . | m| m • | m, ml .

A = . F11ghtRegtmeSelection Parameter

Ze(Re.x)u

If A _ 0.05 BoundaryLayer

'_ If 0.05 < A < 3.0 Rarefted

If A > 3.0 Free Molecular

I

where

14. = Free StreamHachNumber _

,(

Re.x - Free StreamReynoldsNumberBasedon Runntng

Lengthor Radtus I

Ze = Post NormalShockCompressibility

:I

" ii

i

_w

I

i'>

| , |,. ,m .m• |

m m m, , ,. ,= . ,| m m

i,

1

/
; OI_IC_NALPACi_ ;F._ '

OF POOR QUALITY

i;_ Table 5.3

RAREFIEDFLOWSTAGNATIOHPOINT HEATTRANSFEREQUATIONS

Therarefted flow heattngto the spherestagnationpotnt basedon the work /

of EngelandPraharaJts as follows.

(1) Tr - (T6 + TW)/_ (Referencetemperature}

(2) To'T'°_+_'IM_ (Freestreamstagnatt°ntemperature)2

(3) Km" ¢(P'U'R_(Tr_ (Rarefaction parameter)

\", / \to/
, ..,

,_ Table 5.3 (Cont. I)I ORIGINALP;'_0:_i:_

;oL:_/..I

i2

_'_ & ltddell

I-

• 1-61! ,-I] [xpertnmnlal Data

10" _ Htttllf, .nd l

|

10"s , 10' 10' 10s 10s

pr_le

r,!

Stionatton Point Heat Transfer tn Low ReynoldsNumberFlow

• _ Homenclature

-:;_:_ CH Stanton Number

: H [nthalpv

Z'q

:7 Hm Free StreamHachNumber

", T Temperature I

": U Veloclty "'_

;_: Z Post NormalShockCompressibility

._., p Oenstty

?; _ Spectftc Heat.Ratto

:.... _ Viscosity

_!. ,_ Subscript,s,

:i _ Free Stream

, W Wall

t 6 - e Post Nomal Shock ':

. o Total _ "

-_'! Referenc, i

,f !

fl { Engel, C.0. and Prahare_l, S.C., "External Tank Rarefted Aerothermodynamtcs, ,

REHTECH%nc,RTR022-I, Oanuary1978.

i ........... 'i

.} 49 :

,I

'r i- , ;
OI_IGINkLP;_C[",:_:.

OF POCi_QUALIIY

Table 5.4

FREEHOLECULARFLOWHEATINGEQUAT!ONS-

(I) N - P (partlcleslunlt volume)

NU.

(3) , - _

2_'S

(4) n - S sin B

(5) n _[e "n2 ]

• + erf n) 

• numberof moleculesstrtkfng a untt area per untt t_me

where n

erfn • _2_. /_ _o e'xadx (error function)

Rattonal approximation(o < n < -) from Abramowttzand Stegun_, .i

,t')e'n' _4

err n • I. -(alt + alta + a + c(n) i

I

l+aan

aLo • 0.47047

a • O.3480242

1

a • -0.0958798

2

a • 0.7478556

|

<-2.5lo"s

5n

i

3.:. ,-, . -
,+

"-+_ Table 5,4 (Cont. 1)

OF POtjt_ QUAL,l"f

(6) + - _-e"n'

I

+ l + l.t _+1 nkTw. a + n - _ kT (7) q" _ 2(_-_)

; These equations are basedon the work of Oppenhetm.

Nomenclature i _ Jl

k - Boltzman'sConstant

4+ _- Freestream_ch Number

P - Freestream Pressure

Heattng Rate q_TW Wall Temperature

T® Free StreamTemperature

: U_- Free Stream Veloctt¥ Heat Ratto

Y - Free_Stream Spectftc Heat Rat4o

= - Accommodat|onCoefficient

_ References

Abramowttz,M., andStegun,.I. A., eds, Handbookof _them_ttcal Functions,

Dover Publlcatlons, NewYork, 1965. :

Oppenhelm,A. K., "Genera1_zedTheoryof ConvectlveHeat Transfer In A

Free-Molecule Flow", O. Aeron. Sc]._ Jan. 1953, p. 49.

, 51

.-..- _+ . .._ • ._ ............. .......
[

Table 5.5 OF POOR QUALITY

CATO/aOHNSONSHEPTCYLINDERHEATING

_-,_, __. . • L_ i ...... L [ I I] ..... , m = .... . j, j j

• , = i . . J. ........... J ......... i | m I e

" The empirical ¢orrelat4ons of Ceto for lamlnar flow end of Johnson for i

turbulent flow are given belowalongwtth o comparison w4th experimental data.

hL • 0.?S ho 1 - 1.857 + 1.097

For turbulent flow, I

[ ]o'[ [

20uVuRN 0.01714 * 0.01235 stn 3.53 (^-I0)

),

,t . 0.75_,oL ", J

i The laminar multtpllcatlon factor, KL, ts 4ncluded 4n the deflnlt|on of hO.

"-_,-_5 =_- , .. _-_ _" ,,_ _,- •.................... - _ " . "_,' ,_ . . 00000001 TSE(
Table§.S (_nt. l)

Nomnql.ature _i

ho StagnationPointHeatTransferCoefficien(St phere)

hL LaminarHeat Transfer Coefficient

' ht Turbulent Heat Transfer Coefficient

K Multtpl ter Factor

RH Cyltnder Radius

Vu Veloctty (Upstream)

Pu Density (Upstream)

A SweepAngle

_U Viscosity (Upstream)

References

Cato, G.C., "Heat Transfer to the LeadingEdgeof a ¥.wed tilng",

MemorandumA-260-TH-57-115.

Oohnson,W.A., "Turbulent Heat Transfer to a YawedCircular Cylinder",

MeamrandumA2-260-TIt-59-218, September1959.
!"

ORIGINAL PAG2 _:',_

Table 5.6a OF POOR QUALITY 

BEC_ITH ANDGALLAGHERTURBULENTREALGAS (

YAWEDCYLINDERSTAGNATIONLINE HEATING

i i i / i

hSL= _(_ \ _o / o_ (go*_*)u (due\= (1) _ k/x.o

(due_ 1.414 tPe- P__ us (Z) '

=o" T- pe

Nomenclature

g 32.174 Lbm/slug

h Heal Transfer Coefficient Lbm/ft'sec

P Pressure Lbf/ft2

Pr PRadiu randtls ofNuCyl mbetnde r@rEdge Conditions Dimen Feel sionless

u Veloctty Ft/sec

x Distance from Stagnation Ltne Feet

A SweepAngle Degrees

VIscosIty Lbm/ft- sec

p Density Slugs/ft3

Subscr|pts: Superscrtpt:

SL Stagnation Ltne * Evaluate at Eckert's ,

Reference Enthalpy & Edge

e Edge Conditions Pressure i

o Total

- - "----_:_--_:-_. _'-_-__="--'::_-_eTUUU_

":'---:. -::-- ----_ "2:'- - .-: L-'| CYLIND[R DATA | J 't " - I".': --:- - .:2 -_----- :. 4 M 3.7 FROH ! I

.... Limtnar :----±___---__..-::-- _._2:: --." _: -_

•! 0 :. :--5 ---.-::--..:- ...... '-.2. -- :.: - - - "_

..i 0 tO 40 60 eO

•{ ^, S_p _gle (0,g)

- i Reference:

Beckwlth,I. E., and Gallagher,d. O., "LocalHeat Transferand Recovery

•.- Temperatures on a Yawed Cylinder at a Mach Number of 4.15 and High Rey-.

..: nolds Number, NASATR R-104, 1961.

i

_A

|

:::=-,,,........................ : . ::::::::-:.............:........ i ::);::,-:: ': ;|"i ':' ;"=.-- ;;;,,;.--:--:: v-- --:-=-:-..,,,, ....... ::-.7,'.--.-,:.-.W,; ,.>--, -:- .::. -:.: .:: T- :;-- :..::.:.: .......... ' :::-: T," ';"=: ........ :....
,'.'i"

Table §.6b OF POORQUALITY " _ LAMINARCYLINDERSTAGNATIONLINEHEATING

, i i ll iii i i i • | i J i i i . i |

| i i i i • i m • J

:.

,. h - 0,707h s Cos"*A

" hs - SphereStagnation Potnt Heat Transfer Coefficient

h -Cyltnder Stagnation Line Heat Transfer Coefficient

A - SweepAngle

,! .301 _. : _;: '. ;, _....... ....... :'_ ....

, _ " _-_ " " _...........; ....... Q- Lamtnar Flow

_:_ _'-'- "-: : t--._;;'-';;:_----" Cyltnder Data ....

__/; -" - 3.7 From ...

;;_' Brewer, HSFC ......

i"r .20 __: --

' I

.................. !..........-4................ 1...................

.--_t O .,

Of 20 40 60 80 1O0

"4

A, SweepAngle (Deg.)

, i i i i ......... , • ,.i • i i |1

............. . i ii i i i

::; 55

I

"o----...........

.......................... -:-'- " "" " ..... " _' .................................. ' °" "' '""" '-........ 00000001- TSEO
J;" m

O_JGINAL__ -

Table 5.7 OF POORQUALrrY

RAREFIEDFLOHYAWEDCYLINDER

STAGNATIONLINE HEATTRANSFEREQUATIONS

, ,, • , m • : i : : • JR : I I ,

II : I | | : I | : I : I' I I J _

The rarefied flow heating to a cylinder basedon the work of Engel and

Prahara,] is as follows:

1

(1) Tr - _ CTw* Tecos'A)

12) Re.-

(3) c, - ,_rT. 1_ Tr

|

P.. R,.z, ....

(4) a y.M.'C,(cose^ + P.stn=h/o®U,'), .s'

(51 g . CH/(COS, ^ + p®stn_A/p=uj).s

(6) Heat Transfer Correlation ,.

_1) _

log,.¢ - t.Zoat (log,_)t .., _ _

i ,I

a, - - 0.377655 ' J A,, _

a: - - 0.368580 I /

a, - - 0.046i064 I ---

(7) HeatTr q - %ansu.ferca (Ho. ..) I[ 90.__-R . ! .
:i Table S.7 (Cont. 1) OF POOr_QUALIFY

.._ .... I CALSPANCYLIrtD£RDATA •

:i:i +1 • ¥tdal and WtUr,ltff q196;)';

:

•

':'i _! |i

'T

;;I! A TO P

" ...... :lllJ

•"_: i .... _ O° 1800" ¢ .1_8

.......... 0 O" 2700* K .08S

---'" *_::: _ 46" 2?00" K .085

[ . i i _ 8om_daryLayer Theory ....

0.1 _ ", _-II1,

_:Tn'" ;'1

', ""

I-', :] "r,l_J• I""",' 1"! 1".• _.[1J '

", "_mil _ I 1 T]=_" I "_ .I I ,d '] • I_ '1 • LJ

r " _ --I I'111 '_'i. JI I':_l'''l':'i :1 ! J L4

T-fl! I_:.: '_ _jlld.| r ._fl'U.iI :4::'_T:_t .._r:_.t:_4._1 ; :;.

o.oi "_

0.1 1.0 10 100 1000

C¥11ndlrStagnation Line Hilt Transfer DI_ with SweepDII_ Included

Nomencla,ture

CH Stanton Humber

H Enthalpy

H. Free StreamHachNumber

T Temperature

U Velocity

Z Post Nomal ShockCompresslbtltty

p Denstty

SpecIftc Heat Ratio

p Viscosity

Subscripts

- Free Stream e - edge '

• W Na11

Post Nomal Shock

o Total

Reference

Engel, C.D. and Prahara:}, S.C., "External Tank Rarefted Aerothemodynamtcs,"

REHTECH;nc. RTR022-1, January 1978.

..... • i • i l

i i iii i m B i i i i m ii i i ,_ *

S7
"p_" SWEPTCYLINDERHEATING OF PO0_ _}_!-_LiC/

,

The "orl_r" method for swept cylinders ts deftned as follows:

Hmc,o " O.5(HTL + Hw) , Omc,o " f(Hmc,o, P_)

t

_o • --"--- , r o - 0.96 -0.5 Pmci o

i

0.5

% = 0.90(

\ PwlJw

ii Prr " f(P_., Tr)

:I E'L " []% I + r o Pr ' ET,o " []% I + 0.77 r o Pr i! ,o

K,,- V--_q,,t i

= XeqT

XeqL • _T

I ' ,0

i . ,0 2Kr_-L, 0 5Kr ,0

,1

I Fx . XeqT,o 0 333

" _ XeqL,o

!

J:

1

i

, stagUstag

p

i-"

,! 58

;'

---. .,
Table 5.8 (Cont. I) OF.POO,_qU,;Lii_y

p

n r

Hmc " Hmc,o + 0"206(HT " H_)pr #I

m

Pmc " f(Hmc' P_.)

_c " "-" , r c - 0.96 -0.5

Pmc

a r

TL - 11 r 

\l.s (Tr ' 

(HT HT ,

Rer'cyl • FZx U2 (XeqL)

0.370

0.664

Cfr,L

"vRer,cy 1 . ' [1og1oRer (,cyl .,ooo,1,-,t

Le - 1.4 , Ho,r" f(Pr' Tr)

!

. HD

_r.. 1 + (Le 0"52 - 11 ,r

• . "_

'1

:t

,i

:_ 59 .,.

• _,r,
; _q_ Tab i* ,_i'._. l_.,

le 5.8 (Cont. 2) C,;_1¢_i_:."r-_'-L_ _!:_

:_::i OF POORQUALITf

For lamfnar flow,

hL " O.5g 0.6KL45 e_\(Xeq "T" Fx) Rer,cylCfr,L Pr r L,o "

For turbulent t"low,

KT _._T"Fx _

ht = O.5g ._'0.645 Rer,cylCfr,t

-: r r \XeqLoo/

-_ _

Nomen¢. I ature

• Cf Sktn Frtctton Coefficient

h Heat Transfer Coefficient

:-" . H Enthalp¥

• Le Levls Number

. P Pressure

.... Pr Prandtl Number

_ Re ReynoldsNumber

__" I_ Cyllnder Radlus

:,- 1"" Temperature

:-_ V Veloctty

:: p Denslty

•.,_.. _ Vtscostty

_: Subscripts

_.._ L Lamtnar

" r Eckerts Reference j

:i':'. stag Post NormalShockStagnation

_. Stagnation Ltne

:.. T Total

"_..'i t Turbu1ent

"'i References

_'_ Nagel et el., "Analysts of H_,persontcPressure andHeat Transfer Tests '

" NASA .._ on Oelta M1ngswlth Lamlnarand Turbulent BoundaryLayers, I

- CR-535, August 1966.

•_ Thomaset el., "AdvancedRe-entry SystemsHeat Transfer Hanualfor

:._ h_per_ontc F11ght," Technical ReportAFFDL-TR-65-195,October 1966.

;._

• ! : | i i : • i i, : i i: *- i

: 60
Table 5.9a OF POOROUALI'I_f

3

LEES'HEMISPHERICALDISTRIBUTIONETHODFORLAMINARFLOW

- :" ' ' ' : .... dl

Lees' heattng distribution over a sphere for an 1deal gas ts e_pressed I

as:

#) oo,,,#].

h - P ' /D(e)

+ YI_ e'_ - ,_stn2®+

Nomenclature

h - Heat Transfer Coefficient

h_p= Stagnation Potnt Heat Transfer Coefficient

I_- Free Streaml_ch Number

e_ _, Loc FreealSBod treamyAngle Spectflc Heat I_tto

Referenc___...ee

Lees, Lester, "Laminar Heat Transfer Over Blunt-NoseBodtes at

Hypersonic Fltght Speeds", Jet Propulsion, Apt11 1956.

, |m

• i m m|

¢

o . . _ t '" ' . _ r.
.-k4(- Table 5.9b

DETRA-H!DALGOTURBULENTHEATZNG

DISTRZBUTION

J i i ,i ii _ __

i, i | . I ,L,

_tra and Hidalgo developeda methodof calcu'iattng the turbulent

distribution over a hemisphere.

ht - 0.029 g prO.667

"

L l°, 1_e v1.037 L]°f(L) 0"2'Ili + 0.58

where

N t

f(e)0"2 " #o

AtL

• •

t AI (6 < 2s) AI (e_>2s)

; i 1.03754 0.96451

2 0.0043776 0.01107

3 -0.6187 x 10"4 0.842558 x 10"4

Nomenclature

g Gravitational Constant

+ ht Turbulent Heat Transfer Coefficient

H Enthalpy

.... KT Turbulent Multiplier Factor

_ L RunningLength

Pr Prendtl Number

V Velocity

• p Density

__i p Vtscostry

6 SphereTangencyAngle (90 Degreesat the Stagnation Point) "

;: Subscr_pts

_ D Dissociation

_, e Edge

: T Total

'_ Reference

; Detra, H.W. and Htdalgo, H., "Generalized Heat Transfer Formulaeand

i Graphs", AVCOResearchReport 72, Hatch 1960.

": ,i im
f ,

: Table 5.10a

ECKERT'sLAMINARFLATPLATEHEATINGMETHOD

Eckert's lamtnar flat plate heating relatton can be expressedas:

h - 0.332 gc _ (lbm/ft2sec)

where

R_- p*uex Reynoldsno. evaluated at

.* reference conditlons

Thereference conditions ape obtafned from the reference enthalpy

H* = He+ 0.5 (Hw- He) + 0.22(Haw- He)

:" and edgepressure. Other reference properties are evaluated as:

p* = f (H*, Pe)

_* = f (H*, Pe)

: For geometries other than a flat plate, the Manglertransformation

maybe evaluated as:

'

!

" tm • 1 Flat Plate

• 3 Cone

Nomenclature

; gc " 32.174 1bin/slug

I h - Heat Transfer Coefficient (lbm/ft2sec)

I He - EdgeEnthalpy (Btu/lbm)

I HaHww== Wa Adiabatic Wall Enthalpy (Btu/lbm)

ll Enthalpy (Btu/lbm)

tl Pe = EdgePressure (arm.)

ue = EdgeVeloctty (ft/sec. _

• x = Surface Distance FromOrtgtn to Potnt of Interest

p* - Reference Denstty

la* - ReferenceViscosity

Tm- Hangler Transformation

63

.L
Table 5.10b

_t SCHULTZ-GRUNOW TURBULENTFLATPLATEMETHOD

Turbulenl;heattn9 relations for a plate ustng the Schultz-Grunowsktn /I

functton law can be expressedas:

O.1859 p*ue

where i

p*UeX Reynoldsnumberevaluated at Eckert

Re, - ,_. reference conditions

For geometriesother than a fiat plate, the Hangler transformation maybe

evaluated as

_m= 1 Flat Plate

2 Cone

Nomenclature

gc • 32.174 lbm/slug

h = Heat Transfer Coefficient (lbm/ft2sec)

Pr, = Prandtl Numberat ReferenceConditions

ue - _dgeVelocity (ft/sec)

x • Surface Dtstance FromOrlgtn to Potn_ of Interes_

p* • Reference Denstty

_* - Reference Viscosity

_m - Mangler Transformation

Referenc.___.___e

Schultz-Grunow,F., "A NewResfstanceLawfor SmoothPlates," I,ftfahrt , -

Forsc.._..Vol. _h, 17 (1940), pp. 239-246: (translatlon) NACATM986, 1941.
Table 5.11

SPALDING-CHMEI THOMOD DIFIEDFORREALL_ASHEATTRANSFER

FORTIJRBULENI BOUNDAR'"" .Y,_i '_ ,,;F,LOW

l ........ • q

(I)Sp_Idln9-Chdei fineFc, FRB,FRs (Spaldln9and(:hi)whichare

functionsof _ch NumberandTemperaturealonesuchthat

1/2 CfFc • Ce(FReRBe) " Os(FRsRes)

(2) Fc _ d u • ZeTe

,,,-z, -,(,._,),,- (,,__'w-)(_)- (,."e) w- (_,)'

0.?72

o.o,

(4) FRs• FRB/Fc

(5) (:ft " 1/2 exp t=1_ 9(t) n Rs_ • 1/2 CfFc

Where 9(1) • 9.2808635 ,t

g(2) =-4.7340248 1

9(3) " 6.6858663 10''z 't

.-9(4) •-4.1876614 • ,b 10"a

9(5) =-5.5054577 i0 -4

9(6) • 2.6367291 10""

9(7)- -_.12496oeIO-s

9(8) • 8.0162000 10-_

9(9) • -1.5900985 I0"*

9(10) • 1.3236350 10"1'°

p

Res •

lJe

Zm " ManglerTransformation(Komar)

q

65
4r-

..-.'i_ Table 5.11 (Cont.I)

NomencJature

Cf Sktn Friction Coefficient

hTURB !-teat Transfer Coefficient For Turbulent Flow

H Enthalpy .

P Pressure _

Pr Prandtl Number

R%, Res Local ReynoldsNumberBasedon Momentum ,

Thicknesse and Characteristic Lengths

Respecttvely

S Inverse of Von Kazan ReynoldsAnalogyFactor

St Stanton Number

; T Temperature I

•. u Veloclty 4

:: Z Compressbti 1tty I

: p Denst ty J

Subscripts J

aw Recovew i

" e Local

I I nco_ ressi bl e ';'1

_,;, w We11 j

_ References

:_:" Spalding, D.B., and Chi, S.W., "The Drag of A CompressibleTurbulent Boundary

::" Layer on a SmoothFlat Plate With andWithout Heat Transfer", Journal of ,_

.ii_ FluidMechanics,Vol.18, Part I, pp. 117-143, Jan.1964. .,

.,:: Wallace,J.E.,"HypersoniTuc rbulentBoundaryLayerStudiesat ColdI;a11 '

....' Conditions", 1967 Heat Transfer and FluidMechanicsInstitute, L_,Jol!a, CA

June 1967.

_... Komar,J.J.,"ImprovedTurbulentSkln-FrlctlonCoefficlenPred t ictlonUtll s - ,

_: tzing the Spalding-Cht Method", DouglasAircraft Company_uglas Report

.',. ,: DAC-59801,Nov. 1966. i

i L - -- i _l i i _ _ i[ _I

,gP

, " J

.i :-.:'

;,j
, Table 5.12 + , .....

RAREFZEDFLOWSHARPFLATPLATE OF FOL,_<QUALI_Y

HEATTRANSFEREQUAT]ONS

|

i i i

: Rarefted flat plate heattng correlations baseden the work of Shorenstetn

and Probstetn are gtven below.

O) TO -T. (1 

---.lU"

g--

(21 Re.- N.u___ I _ x

z[m ", __;.;.;.;.;o;.;.;,;,-+

C3)c. -

.'I,_Tw

". (4,) II " (Tw/o) T zla ._ C.IP.e.

I

(61_I °,. [, (0.,,o,.., , +,.,o)]

i

for IZ< 0.1 FromShorensteln and Probste_n' !

" _ .... I-'"T-........ _"1

(7)H.tT.n,,,. /!ill/ll i I-ITIl ll-l-

: m--f_ _ -]+.--.E.... -4-- -.... t,,v, +olorwurmc_ .

._I 1 I i-'_*,+o r. l -t -.-,.,,..om,_1_i

q" PmlJ.CH (Ho - Hw) "'--r-t-r-t-T, -_-.+'. + l---"*"" , " .

o,,--H-l-_-t+:+__ *,+,:-+ __ +-_ 4 : !.I +_

,o,.nc,.,+,. : .,! l I I I--I I-T-F-T _:

H Enthalpy ,, -: + ,.,,.,u,. ,,, ,-,- 1

U Veloctty "_""'+--'-"--- +.,.,., + ,, • +

X RunntngLength ,/_',_ !

p Den s _ ty ,. Keat-txans(er irate eomlatlon. 1

Speclf+c Heat Rat+o

" _ Viscosity

Subscripts I

• - Free Stream

w Wall

o Total

,Reference

Shorenstetn, H.L. and Probstetn, R.F., "The HypersonicLeading-Edge

Problemo"AIAAJ., Vol. 6, No. 10, October1968.

i i

67
Table 5.13

RAREFIEDFLOWSHARPANDBLUNTCONE

HEATTRANSFEREQUATIONS ORIGINALPAGEI$ OF POORQUALITY

, . i

The rarefted flow heating to sharp end blunt conesbasedon the work of

Engel and PraharaJ ts as follows:

(1) T r • T w + (T6 + Tw)/2 - T6 cosiec/3

(2) Re=- p.u.x i

(3) c*

• tj6 Tr

! X

.9 CH

(4) _ "(stneec+ P-c°seec/°-U-2)'Js

Re. Ze

• ' i

(6) CoPulation E_uatton

log_(_) , - i 't (l°g,,_ct ) "

ao --0.344074 ao " -0.647813

aI - -0.349130 az - -0.365587

Sharp Blunt :

a2 --0.104455 a2 " -0.0143793

as - +0.022766463 as - +0.003281793

(7) Heat Transfer _

q , p,,UmCH (H0 . Hw) i

t

Table 5.14 ORIGINAL PAGE IS

'_/1_" FLAT PLATEHEATING OF POOR QUALITY

i i, The ,"prUr" method was developed , | by Hanks.., from Boetng andi tsi dL ',mented

by Nagel and Thomas. I

For lamlnar flow,

hL- o.332_po.646

rp

•For turbulent flow,

KT g_. Pr_rVe

ht" o.l,g p1"o., I, 5 "T"[IOgi(o,e_• 3000)] 2.584

where

;;r.- 1 °'s2- 1) 

"e

HD'r : f(Pr' Tr) and Le = 1.4 .q

j_

" T v HT_

PT" PriEr/ I r_ Hr_ _ !J

Nomenc!ature

g Gravitational Constant

h Heat Transfer Coefflclent

H Enthalpy

L Runntng Length

Le Lewts Number

KI. Lamlr_er Multiplier Factor

KT Turbulent Hulttplter Factor

Pr Prendtl Number

70

t

t"

0
Table 5.14 (Cont. I)

Re ReynoldsNumber #

T Temperature

V Veloctty

p Oenstty

p Viscosity

Subscripts

• Edge

D D1ssoclatlon

L Lamtnar

r Eckert ReferenceCondlt|on

t Turbulent

T Total

References

Nagel et al., "Analysts of Hypersonic Pressure andHeat Transfer Tests

on Oelta WtngsWtth Laminarand Turbulent BoundaryLayers," NASA,CR-535,

August 1966.

Thomaset al., "AdvancedRe-entry SystemsHeat Transfer Manualfor

HypersonicF11ght," Technical Report AFFDL-TR-65-195,October 1966.

t

• i i

i J i

71

.4

!
T

OHIGINALPAGEIg

_" OF POORQUALITY

" ,. : Table 5.15

AVERAGESEPARATEDLEESIDEORBITERHEATING

"m,

The average separated leeslde heating relations are basedon correlations of

- wind tunnel data for the SpaceShuttle Orbiter configuration by BerLin and Gondrtch.

The average leeward healing (turbulent or windwardflow) Is given by:

....: EL -(1.067(H._/+ 0.7905)(O.O0282(Rens)'0"37) t /

; Rens- p.U.Rref/1Jns

_, Rref = 1.0 foot for full scale

I

_. q = p.U. (Ht - Hw) _t

" ' wherethe windwardto total enthalpy ratio neplacesthe temperatureratio

i, in the original paper.

!,,

_ NomencIature

Hwwd WindwardHall Enthalpy

::b i

Ht Total EnthalW /

:.:. Hw Local _al I Enthalpy

:_ Re ReynoldsNumber

•- R Radius

!::_ p® Freestream Density _ .! ;._

i"_'' U_ Freestream Velocity !_,_ tour|raceitem o_er which lhe h_l-lranmfer _,

i._ melsurtment_wee i_eragedtoobUlln,S't'_. ,'.

q AverageLeestdeHeating Rate

_nsl Post Nodal ShockViscosity

ii_'"

L

'" - --- "::'_'-:.":'._ -2;--_---- " _-"_'_ ..... "" _- --'" _;' ';-:"_" :.-.:2_". ,_" "" " ) ' " ." :' _'"............ " .......... _)_*'
Table 5.15 (Cont. I) ORZ_I_,_.LF._

OF POORQUALITY

A comparlsonof the correlatlon and data from the oHglnal paper are

gtven below. /I

14 ' ' _' Mmsl2 Mlf'flllN'Tml11=0.11 T;

'_' ¢, l_mm flllN Twml_009T!

_: I0 1110.319 0

_l_OII o M Re RI ". 5.1D4_ 0_" (has)'03'

Io o 22 OSgllO m. 140 J _ ¢ •

A I0.1 0.t4ma0s Y40

• I . • I * I , l • •

000'_ 0.1 O_ 0 $ 0.4

VGind_mrd-surlrllCe.temperslure effcton them_er_ehealing #, ._¢a|e5_nlon numberforthelee_xrd"%eparsled"region.

ksIheleeward"sepsmled"rt,sion,

Refer'ence 'i

Berttn, O.0• andGoodrich, W•D•, Effects of Surface Temperatureand Reynolds

Numberon LeewardShuttle Heating," Journal of Spacecraft, Vol• 13, No• 8,

August1976, pp. 473-480.

i

73
r,,_,;._.1:5

:_" Table 5.16 OF pOOR QUALITY

PEAKFLAPINTERFERENCEHATING

i ii i

i i i i • •

The procedurefor calculating peak flap interference heattng follows that of

Ftvel except for the separation length calculations.

q

¢/ @ I@.

" _ Flap Flowfteld t

+

.i

..! TRANSITION,

' Re61M_ < 400 Laminar

> 400 Turbulent

+".

,_); where Re6 = Undisturbed B.L. edge Reynoldsnumberbasedon boundary

=_ layer thickness

'- 6 = BoundaryLayer (B.L.) thickness

• Me - EdgeMachNumber

_ I,NClPI,ENT,SEPARATION(Kessler, Retlly andMockapetrts)

._:. Cpt = Incipient separation pressure coefficient

._ Laminar

_' IM:) ' 'i,., log1oCpl- -0.361397 1Oglo (Re6 - 0.662427 ,

::_ Turbulent

.' If 2.6 _ logI eB/M _ 3.8 ,..

•i Cpl - 0.2615 (lloglORe6/M: - 3.81)3"5+ 0.405

' , 74

._i_

t
.,

• Table 5.16 (Cont. 1) _,'-' ......

• OF POOHQU/_LIYY

:i If loglORe6/H_ > 3.8 71 "

CpI = 0.0354 (loglORe6 - 3.8) 1"6 + 0.405

t

!;

'._ DEF, LE,CTIONANGLE

=*"i_' P3 !i ,1⁄2 _ .2

;i F1 "1 "p e

:!" - P3 + 1 -

?, rl (y+1)P@ y- 1

i <.

_: Cp - Separation RegtonPressure Coefficient

I"

_: eD = Deflection Angle of SeparatedStreamline

!'r

Note tf Cp- Cp = Inclplent Separation Coefficient

.: then CO- ei - WedgeAngle for Incipient 5eparatlon " :_

-_'. PL.ATEAUPRESSURE(guerer and Clayton)

/ .,,o -,>]-','

- (CppLA,) "1 70(Rex)'l/lO (H:-1) "1/4 ::' T

CppLAT • Plateau Pressure Coefficient

" Re • ReynoldsNumberBasedon Otstance along a Streamline

,.. x to the HtngeLtne >

75

":- ...... . .. _,: _._._ ,.._...:-....,.. _..,_r_.- " :_ • ...,_---'."__ -'...'-'-'_,:-_...... .- -.,,....-.... "_.,.: • -

U ' _, , c : 0 fJ "
Table 5.16 (Cont. 2)' _*,_:_.'_;,. ,_ "

OF POORQUALtI_f

S,EPARAT, IONGEOMETRY

#

Laminar(Gtles andThomas)

Turbulent (Poptnskl and Ehrllch)

.2 (PF _1.025

M - I)1.17(1og10Reex)g.58

where

- Pe - UpstreamEdgePressure

" PPL = Plateau Pressure

PF = Post ShockFlap Pressure

x - B.L.RunningLengChto HingeLine

. 6 - B.L. ThicknessUpstreamof Separation

Geometry

.:_] LH • Ls sln (eF - eD)/Sln(180 - eF)

., LF • Ls slneD/stn(180 - eF)

,"i

b--__ -_--:............_ .................. _ ..................... _ _ .............. i>":......... _ . _ &
Table 5.16 (Cont. 3) OF P('(_: ::;, :i_"

PEAKREA.TTACHMENT HEATING(Bushnell & ICetnstetn) *

PwUF6s

' Reshear - .

_,stn(e F - e0)

where

UF • Veloctty at ReattachmentReglon

Pw • Oenstty at ReattachmentRegtonat Wall

I_v = Viscosity at Reattacr_ent Regtonat Wall

/Ls"s _

(6,)L- _+s\p--_;-/

(as)T- e + 1.6Ls/13

where

Us = ShearLayer EdgeVel0ctty

Ps - ShearLayer EdgeDenstLy

Ps • Shear Layer EdgeVlscos|ty

PEAKSTANTONNUt4BERAT REATTACHMENT

(St)pK • Cst(Reshear)nSt

where

Lam Turb i

Cst 0.199 0.0204

nst -0.5 -0.2

t

!

77

........ o C3

.w

:_ Table 5.16 (Cont. 5)

REFERENCES

Five1, H.J., "Numerical Flow Field Programfor AerodynamicHeating i

Analysts," AFFDL-TR..79-3128,Vol. 1, December.1979. *

Kessler, H.C., Retlly, J.F., and Mockapetrls, L.J., "Supersonic

Turbulent BoundaryLayer Interaction With An ExpansionRampand

CompressionCorner," RcDonnellDouglasAstronautics CompanyS, t.

Louis Report HDCE0264, 17 December1970.

Wuerer, J.E. and Clayton, F.I., "Flow Separation tn High Speed

Flight. A Reviewof the StabLe-of-the-Art," DouglasReport SN-46429,

Aprtl 1965.

Gtles, H.L. and Thoms, J.g. "Analysts of HypersonicPressure and

Heat Transfer Tests on a Flat Plate With Flap and a Delta WtngWtth

Body, Elevons, Ftns, and Rudders," Nattonal Aeronauticsand Space

Administration, Washington,D.C., (NASACR-536), August1966.

" Popinskt, Z. and Ehrlich, C.F., "DevelopmentPestgnRethodsfor

Predicting HypersonicAerodynamic.ControlCharacterlstlcs," AFFDLTR-66-85, September1966.

Bushnell, D.R. and getnstetn, L.M., "Correlation of PeakHeatlng for

Reattachmentof SeparatedFlows," Journal of Spacecraft and Rockets,

Vol. 5, No. 9, September1963, pp. 11_IL_112.

79
t

}

_. Table 5.17 O_N._L P_'_[_ |3 i

, FIN-PLATEPEAKINTERFERENCEHEATING OF POOR QUALITY

.... .]

• The peak fin-plate Interference heattng can be calculated using the Inethod i

presented by Ftvel, whtch basically came from Hayes. The peak Interference

heating occurs along a l the near the

fin on the plate, The peak heattng

angle ts correlated ustng:

epk = 0.24 (es - _F) + _F

_" The locatton of the peak heating

_? 11ne ts gtven by:

!" i

T°I.i_' YFP = XF Tan(epk " _F) i

.I The boundary layer thickness

:,,_ at the leadtng edge of the

•:;?_; length to the ftn leadtng

:_::"J::"r_'_........edge, _ Xo, Is requlred. ;f'F _ / "_'

_-'_? TOPVIEW :

:. ,t

i The peak pressure ratto Is based on correlated test data

:i,_I'

!._. Ppk

;..,. ------ - (Me Slnes)npk

_" Pu

,_ .

80 -
,

! Table 5.17 (Cont. I)

_!i Likewise, the peak heating ratio ts basedon a correlatlon of test data

i_ hpk

!i "" -- - (Me Stnes -1.0)nst + 0.75

io hu

i li The exponentn_k and coefficient nst are obta|ned from Interpolation !!1! o,,e, Xa/6 npk

• i i |

0.0 1.25

1.25 1.5O

Z.50 1.71

3.75 1.87

5.00 1.98

6.25 750 2.03 2.09 If Xa/6 > 30, npk - 2.4

8.75 2.14

10.00 2.18

11.25 2.20 npk ts obtatned by llnear

12.50 2.23 Interpolation gtven Xa/6. 13.75 2.25

15.00 2.26

17.50 2.29

20.00 2.32

22.50 2.34

25.00 2.36 _

27.50 2.38

'" 30.O0 2.40

Xa/.... 6 . ,nst If Xa/6_< 0.183, nst- 1.0

1.0 1.62 If 0.183 < Xa/6 < 1.0,

_[::. 2.03.0 2,2"2098 nst - 0.35612 ln(Xa/6) + 1.62

i 4.0 5.0 3.57 3.87 If 1.0 .<Xa/6 < 7.0

: " 6.0 4.00 nst determinedby 11near

": 7.0 4.05 tnterpolatlon gtven Xa/6

_ If Xa/6 > 7.0

nst - 0.35612 ln(Xa/6) + 3.357

81

[

i , r'"
Table 5.17 (Cont. 2)

Nomenclature #

h Heat Transfer Coefflcent

P Pressure

Me EdgeMachHumberUpstreamof Ftn

Xa Otstance Aft of Fin LeadtngEdgein Strea_tse Direction

Xo RunntngLengthto Start of Ftn tn StreannvtseDirection

XF RunntngLengthAlong Ftn

YFP PeakHeatlngLocatlonNormalto Fin

oF EffectlveAngleof Attackof Fin

epk Angular locatton of PeakHeating

es ShockAngle

6 UpstreamBoundaryLayer Thickness

Subscripts

pk Peak

u Undisturbed

References

F1vel,H.J.,"NumerlcalFlowFleldProgramforAerod_amlcHeatlng

• Analysls," AFFDL-TR-79-3128,Vol. I, December1979.

:_ Hayes, R., "Prediction Techniquesfor the Characterlsttcs of Ftn

Generated Three Dimensional ShockWaveTurbulent BoundaryLayer

_ Interactlons,"AF_L-TR-77-10,May1977

• ' t

".'E

•c-_ 82 ,
i+

I

Scctton 6,0

LI_GTH AND TRANSITION ROUTINES

_ This section describes the subroutines which deternine bounds:7 layer trau- i

sition, runnin8 lensth oo:roctlons and ©ross flow adjustments.

- 6.1 SUBROUTINE TRANS AND EDPRAN

The purpose of routine TRANS is to deterniu if the flow is laminar• tram-

, 8itionel or turbulent• The equations for each of the transition criteria are

- presented in Table 6.1• If 8 transition option 8reater than 8.0 t8 used, then

_ an error measese is printed from TRANS and the routine returns NERROR = 1 to

+ i MAIN. This causes MAIN to void the remainder of this problem and read in data

'l

for the next case. If the flow is determined to be laminar, then the heat

* transfer coefficient returned from TRANS is equal to the laminar heat transfer

' coefficient. If the flo_" is fully turbulent, then the heat transfer coefficient

. i returned from TRANS is the turbulent heat transfer coefficient• If the flow t8

determined to be transitional, then the heat transfer coefficient returned from !

: p

TRANS is determined by linear i_t_tpolation between the laminar and turbulent

_ values.

: The interpolation parameter for TRANS = I and 2 18 time (TIME) The Intez-

_,,_

!it'' polation parameter for TRANS = $ is the Reynolds number based on runninl lensth

! *I (corrected for of.sallow) or body diameter and free-stream properties. However,

l no correction is made to account for astsynnetrtc flow. For TRANS = 4, the in-

; terpolatton parameter is compressible monentua thickness Reynolds number.

Transition option 5 uses

p, ,+I+ PAItA- 0

"i as the Intetpolatlon parameter. For transition option g, the interpolation

83

+ +"..' + ' '++ +. , .... %+
parameter is the laminar runnins lensth corrected for crossflow and corrected

for azisymmotric flow (Manjler transformation factor). Transition option 7 usel

the input runnlnj lenjth as the interpolation parameter. Transition option 8 i

e

uses Re e/Me as the interpolation parameter. Whenever the flow is laminar, then t

PCT- 0.0, turbulent PCT = 1.0, and transitional 0.0 ( PCT ( 1.0. The psrametQ¢

PCT represents how close the flow is to bein8 fully turbulent based on the above

interpolation parameters. The parameter PCT is also used in the output routine

(VANOUT) to identify the flow type. It should also be noted that the recovery

enthalpy for transitional flow is also determined by linear interpolation

between the laminar and turbulent recove_ enthalpi_s.

The followins is a list of the parameters used in the CALLTRANS statement:

ENCL - (input) Laminar heat transfer coefficient

ENCT - (input) Turbulent heat transfer ooeffi©ient

PARAI - (input) O_set of transltional flow parameter

PARA2 - (input) Onset of fully turbulent flow parameter

PARA - (output) For transition fla8 4, this is equal to the

compressible momentum thickness Reynolds number.

For transition flas $, thl8 is equal to the MDACHAST transition parameter. For transition flaj 6,

this is equal to the corrected (crossflow and

axisymmetrlc flow) runnlns lensth to the onset o_

transition. This It not used for the other

transition options.

TIME - (input) Trajectory time

ENC - _output) Heat transfer coefficient

HR_._¢ - (output) Recovery enthalpy

NTR - (output) h_R = I corresponds to laminar flow

= 2 corresponds to transitional _low

NTR = $ corresponds to turbulent flow

PCT - (output) Fraction of turbulent flew

PCT= 0.0 corresponds to laminar flow

PCT= 1.0 corre3ponds to fully turbulent flow

0.0 ( PCT ( 1.0 corresponds to transitional flow

TRFLAG- (input) Transition option

EL - (input) Geometric runnlnj lensth _

ELFAC - (input) Multiplication factor which, when multiplied time, _hs

tunnlns lensth to the onset of transition, |ires the

runnins lensth to the onset of fully turbulent flow

ENL - (input) Laminar Mtnsler transformation factor to account for

azisymmetrio flow corrections

ELL - (input) Laminar runnlns lenath corrected for crossflcw effects

%

84

r
Another routine which is closely related to TRANS is EDPARM. Routine EDPARN is used to deterniue the )4DAC-E onset of transition psrsneter solely ss s

function of Shale-of-attach. The snjle-of-attsck tense is from 0 to 70 dojroes. #-

There are six date points in the dets table (a = 0, 30, 40, 50, 60, end 70 de- /

areas) alonj with the correspondin8 values of the transition psrszeter.

Interpolation at shales-of-attack not in the table is perfumed with the aid of

routine IBLIN.

6.2 SUBROUTDmVRU_

Subroutine VRU_, is calIed by MAIN and is not called unless host transfer

technique 3, 4, or $ (flat-plate laninar and turbulent nethods) is baths used.

t

Subroutine VRU_, insures that the lensth parameter used in the turbulent heat

transfer equations (when uain8 transition options $, 4, 5, 6, or 7) is corrected

for the assunption that the runnznj lenath should be ness_ed fron the onset of

transition. The srsunent of subroutine V_, contains the followin8 paraneters:

il/*i TRFLAG - (input) May have values 3.0, 4.0, 5.0, 6.0, or 7.0 !

_' correspondins to transition options $.0, 4.0, 5.0,

i_ 6.0, or 7.0. (It should be noted that VRUNLwill

• not be called unless s positive valne is stored in

i_. location 29.)

ELTRAN - (output) Runnin8 lenath st onset of transition with or

:_' without crossflow correction

;_ ELL - (input) Eou_vslent runninj lenjth vlth or without crossflow *I

i., correction for lanlner flow

i/.:i ELT - (input) Equivalent runnlpj lensth vlth or without

and crossflow fo_ turbulent flow and is corrected in

'_ (output) VRUI_, to account for virtual or/sin from the onset of

_--i transition

".'* ELTP - (output) Equal to input value of ELT

PARA1 - (input) This poraneter denotes the onset of frilly

.., transitional flow

PARA2 - (input) This pstaneter denotes the onset of fully turbulent

flow

mqL - (input) Lanlnar nultipllcation factor

b

t

• ! If PARA2 ( PARAI, then PARA= PARA2. If PARA2 ) PARAI, then PARA = PARAI.

L

_'_i If TRFLAG < 3.0, then MA]_ does not call VI_NL. Th,refore, VRUNLis really only

"i

t
meaningful for TI_LAG = 3.O, 4.0, 5.0, 6.0. or 7.0. The values _3_AG _ 1.0 or

2,0 correspond to time dependent transition and ere handled through the main

routine. If TRFLAG = 6.0, then VRUNL calls EDPARM ss s fnnctlon of

angle-of-attack to determine PARA. The value of ELTRAN is given by I

T f

ELTRAN = LTR

If TRFLAG = 7.0, then the logarithm (base I0) of the transition Reynolds number

R_G, based on edge conditions, le determined as a function of edge Mach number

M from a ouilt-in table (North American Rockwell technique). The value of EL- o

TRAN is given by

£LTRAN = (i0ReTR _e )/PeUe

The interpolation to determine lOJxoReTR is performed with the aid of routine

TBLIH. If TRFLAG = $, then ELTRAN is the same as for option 5. However, the

value of PARA = PARAI is input through the routine argument to define transition

onset instead of being determined by EDPARM. If TRFLAG - 4, then the running

length at the onset of transition Is determined based on the compressible momenii, turn thlekness Reynolds number"

-_'I Ile 1 _

ELTRAN " _!

.664 0 _ ue

"; where PAPA = Ro_ Is input to define the onset of ttensltlon. If TRFLAG - 3,

then the runnln_ length at the onset of tTansitlon is determined bJsed on the

{i Reynolds number ©omputed using boundary-layer edge condltlon8"

ReL_ e

ELTRAN q.

0eU e

[i i where ReL = PARA.

Ii°! 86

j, ,_ IJ
After the running length •t the onset of transition is calculated, the turbulent runnin| lensth is stored (ELTP - ELT) and • check ts made to determine if

ELL ( ELTRAN. If ELL ( ELTRAN, then ELT = ELTP. If ELL ) ELTRAN, then ELT -

ELT- ELTRAN. Thus when VRU_. returns to the calling routine, mTP cent•in• the

input value of E],T and HLT may of may not cent•in the input value of ELT dependinj on whether ELL ( ELTKANor ELL ) ELTRAN. If ELL ) ELTRAN, then ELT contains

the turbulent rnnni_8 length me•snzed from the onset of tr•nsitlon.

6.3 SUBROUTD_SCRSFLW

Subroutine CRSFLWis called by MAIN and the purpo•e of this routine i• to

account for the effects of •are•aline divergence on basic geometrise •t

• nile-of-attack. Two type• of geometry are considered in the• routine: • constant width shape (rectangle) and a sharp-edge triangle (delta wing). For each

of the two geometries it is possible to jet an Ideal or tell gee calculation for

t,oth l_Jn:r and t_bulent flow. In each circumstance, • correction factor is

applied to the input geomtrlc lensth, and this corrected running length is used

i: in the flat-plate heat transfer e_atlons in place of the input geometric

length. The parameters in the argument of the CALL CRSFLWstatement are listed

j.

: and defined below:

CFFI_ - (input) Type of croesflow correction selected

• Constant width rectangle assuming ideal gas

¢hordwise velocity gradient

• Constant width rectunsle using • reel gas

,_ chordwise velocity gradient

• Sharp-edged delta conflgur•tion assuming ideal

gas ehordwise veloelty gradient

.: • Sharp-edge delta configuration using • real gas

chordwlse velocity sredlent

ELL - (output) Laminar running length corTected for crossflow

ELT - (output) Turbulent runnins length corrected for crossflov

• EL - (input) Pb ,ic•l seen•trio running length input into MINIVER

ELMBDA- (input) Delt• sweep angle

DSUD0 - (input) Rectangle width

COR_iR - (input) Rectangle corner radius

US - (input) Velocity at the edge of the boundary layer

PE - (input) Pressure •t the edse of the boundary layer

87
RHOE - (input) Density at the edae of the boundary layer

PU - (input) Pressure upstream of the previous shock (if no shock,

then frcestrcam pressure)

I_PHA - (input) Surface effective sngleoof-sttack

UDOT - (output_ Designates the nondimensionsl crossfJow,

stagnation-point, velocity gradient at a point on

the centerline (of the wing) ss s _stio to the

velocity gradient •t the stagnation point of •

sphere with a diameter equal to the plsnform width

VU - (input) Velocity upstream of the previous shock (if no shock

then free-stream Much number)

]LMACHU- (input) Much number upstream of the previous shock (if no shock

then freestream Much number)

Having entered CRSFLW, the first check that occurs is to determine if ALPHA

__ O, if so then ELL = EL. If ALPHA ) O, then the decision is made as to which

;_-: crossflow option should be used. If CFFLG = 1, the necessary program input is

CORNR and DSUBO. The routine then proceeds to compute the parameter ..- .

_ If w-- < 10 "s , then no crossflow is used. This indicates the velocity Ira-

. '.'o

._._ dient is so small that crossflow is insignificant. If W" • 6 , then the

uO

.:_: routine shifts to a si_plifle¢' calculation of ELL and ELT (this situation corj_ responding to the case of 8 very large velocity gradient).

If ]0 -5 < < 6then the standard crossflow correction expressions ,_e u;ed

to compute ELL and ELT and then CRSFLW returns to MAIN. If C_ = $, then the

i

! ideal gas crossflow correction for a sharp-edged delta is used to compute ELL

_'_ and ELT. When CFI_ = 3, the only necessary input is the de 1.ta sweep •nile,

;

If CFFL6 - 2, then the crossflow correction for • constant width rectangle

using • real gas chordwise velocity gradient is used to compute ELL and ELT. ;

The required input are DSUBO and UDOT. If CFFLG = 4, then the crossflow correction for s sharp delta configuration using a real gas chordwise velocity gradient is employed to compute ELL end ELT the required inputs are tLe d_lta s_eep •

88
normal ©omponont of upstream Math number J.qACHUis less than one, If ZMACHU(

1. then s subsonic technique is used to eompute the ctossflov ©otreeSion. If

,i

]LqACJIU_ 1. then e supersonic technique is used for ©rossflow correction.

However for CFFLG- 1 or 3, no dietinotton ts made for XMACHU_ 1 end

XMACH2U 1.

89
,., Table6.1

_W

TRANSITIONOPTIONS

Therearecurrentlyeighttran,_ItlopntionsIn the LANMINcodeconslstlnq

of the t'ollowt,lg:

1. Tln_ Dependence: Laminarto Turbulent

t .< tI Laminar'

t .> tll Turbulent

tI < t < tll Transitional

t-tI Percentageof FullyTurbulentFlow i i, m i

n -tll.tl

I 2. TlmeDependence:Turbulentto Laminar

t <. tI Turbulent

t .> tlI Laminar

tI < t < tll Transitional

tlI"t Percentageof FullyTurbulentFlow

i n " tIi.ti

3. RejfnoldNumber s Dependence

. Re=)d• 2p®U®R/p. for SweptCylinders

'.. Rex - PeUeX/lJe for PlateOptions

Re .<ReI Laminar

° Re .>Rell Turbulent

ReI < Re < Rell Transitional

Re-ReI Percentageof FullyTurbulentFlow

4. CompressibleMomentumReynoldsNumberDependency

"

ReB - 0.664 CompresslblMeomentumThickness

PeUe_L ReynoldsNumber

m , j

Qn

_m
_qlL' Table 6.1 (Cont. 1)

e

: Re0 _ ReBI LamJnar

; •

Ree _ ReelI Turbulent

ReeI< Re <ReeI I TransttJonal

Ree -Reei Percentage of Fully Turbulent Flow

S. MDAC-ETransition Parameter

Thts transition optton was developedby Masekand Klpp

e

- Ree / [Mo(%Ue/_e) ]

• _ .<_! Lamtnar

->_II Turbulent

• _1 • _ • _]Z Transitional

,. _'_I Percentage of Fully Turbulent Flow

-._.: 6. MDAC-ETransition Table Look-upDepen.dency

_ The butlt In tabular functton of angle of attack from l%sekand Ktpp

was developedfor conical flcws. Transition ts basedon the parameter

,,_; _ from optton 5.

- a l°glO _TR

0 1.0 }

30 1.0

40 I. 0412

50 1.1383 Ltnear Interpol at_on

60 1.30103 ts used

70 I. 69897

Oncethe transition onset parameter. _TR' ts calculated, the transition length ts determined:

pe.4

i LTR' " 2.Z6 (_TRMe)2 _e1'6

o...i 6

p,IJ,Ue"

:' i 91
.!

Table 6.1 (Cont. 2)

If a crossflow option has been flaf]_ed, the following procedure 1_ used:

Since the transition parameter _. was derived for complex shapes using

the lamlnar cros_flow length 4n the calculattnn of Re_, it ts nec_F;sary

tO remove this cor;ectton factor so that the resultln_ tran;;ltton l_nqttl

can be comparedwlth the geometriclength.

i. For crossflowoptions for rectangularshapesthe transiLIonlength is

_ - TR'

;. LTR " -0.5 V In

' For delta wings options the transition length ts

u

: LTR = BLTR,

- Whenthe Mangler tran.,formatton, TL, ts used, the transition length ts

°:;i LTR = _L LTR'

'" Two methods for treating the extent of transitionhave been provided.

/. The first is rather si_,plein that the fully turbulentlength,LFT, is

a factor times the onset length

., LFT = KTE • LTR

The second method defines the factor K_r in terms of the boundary layer

_ edge Reynoldsnumber at the onset length,which is definedas

_, PeUeLTR

ReT[ =

.... ue

=" The table,which Is bullt in, consistsof

._' log 10 ReTE KTE

,,: §. 5.64

,, 6.518 2.

_' 6. 778 1 702

'.' " L_near Interpolatlon

: 7. 1.605 ts used

.: 7. 301 1. n35 ._

,'J.:; 10. I .535

i;I

_:, 92 "

i
Table 6.1 (Cont. 3)

The state of tlow Is detemJned by

LLCF _ LTR Lamtnar

LLCF > LFT Turbulent

LTR < LLCF < LFT Transitional

LFT- LLCF

n • Percentageof Fully Turbulent Flow

LFT - LTR

Stnce the transition crtterta wasdevelopedfor e contcal shockflowfteld,

someJudgement.rust be used In applytng It to other situations.

7. NARTransition Parameter

A cr|terla developedby North AmertcanRockwellts basedon edge Reynolds

numberas a functton of edge Machnumber. The butlt tn table ts

He log10 ReTR

0.5 5.30103 !

1.0 5.54407

I. 5 5.81291

2.0 6.00 Ltnear !i,_erpolatton ts used ,

3.5 6.00

4.5 6.0791_ _

5.5 0.Z5527 I

H

LTR - ReTRpe/(PeUe) Transition length i

The transition extent ts the sameas for optton 6. The state of flow

det_mtnatlch ts basedon LGoo rather than LLCF.

8. CompressibleRe_/HeDependency

.F P'P2 Rex

ee_ - O.Ce4_Pe"e ZL

93

_;:_-i_. .........._....... -_F_'T'_: ......... :': _ _..............." _--_'--":-:_."_-......... -_--_": :- _.....:....................... :............................................. :_"- - "
!-):

Table 6.1 (Cont. 4)

Rf " Re_ /Me Nomina!Values

Rfi " 150

L_J, Rf _ RfI Laminar

' Turbulent Rfli =_F2- RfI

Rf ) RfII

I.__,; Rfi < Rf < RfI I Transitional S;

• _: Rf - RfI

ii n • . Percentageof Fully Turbulent Flow

. RflI- Rfl

'k

i

3

.._! Npmenclatur_

.! B CrossFlowParameter V ChordwlseVelocityGradient

':i 1. Length X Cross Flow Corrected

" ¢'i 14 MachNumber RunningLength

II t Ttme p Density

! U Velocity _ Viscosity

_ ManglerFactor

. D Diameter L Laminar

- eGeo Edg Gece._etrtc LCTEF Laminar TransitioCrn osExtent sFlow

°_} I Inltlal TR Transition

._ II Final e MomentumThickness

".ii R__eferences _asek,R.V.,BoundaryLayerTransitionat HighAnglesof Attack,Sp_ce

__ Shuttle TechnologyS_mpostumProceedings, NASA/LeRC,July 15, 1970.

::!I KIpp,H.W.andMasek,R.V.,AerodynamiHec atingConstraintson Space

_! Shuttle Vehtcle Design, A_E paper 70-HT/SPT-45,June 1970.

_._

I

94 (2-

;)-

:I !
Section 7.0

APPLICATION TEMIQUBS

The puspose of this 8eotton is to provide sons |uidsnoe to the enjineor in

applyiu8 the LANMD4ends in the prediction of heatin8 ©ondtttons, In order to

help sohieve this objective, several eenple oases are shown, Those oases ooltatn eapeztnenta! wind tunnel data oonpazed with different option8 available in

LANM_. Based on these results and past expertenoe with the node, s set of recommended options are siren.

7.1 GENERALAPPLICATION

In order to aohieve the best prediction nethod wains the LANMINends several key paraneters need to be examined.

1. Determine the shook option whioh establishes the boundary layer

edae entropy level.

2. Determine the 8eometrio Manaler transformation whioh 81yes the

appropriate runninS lenjth adjustment for the Siren jeonetry,

9. Dote-thine the pressure option whtoh best matches the s_tfaoe

pressure.

4. Determine the heattnj nethod and associated Reynolds aneloay

faster vhloh best fits the experhnental heatln$ data.

The shook option ts usually seleoted by determtntn8 vhioh option produoes

the approztnate shook anjle whtoh prooesses the boundary layer flow. This te

usually estabtished by wains wind tunnel sohlieren,

The Jftnsler transfornatlon used in LANMIN is the 8eonetrlo ttansfornatton

of the runnlnj lenjth for a body into the equivalent lensth for a flat plate,

• The nathonatioal relations whtoh nan be used for a oonpound 8eonetry body whioh

@

ts aaisynnotrlo ere as follows: _

_S r I S

e i

rds rds

0 :I

Lam:l_ar 96 Turbulent
}

, wh•re r l• th• radiu• of the body norn•l to th• •zl• of symm•try •nd• t5 the

• e

surface diet•nee from the nose to th• point of interest on the body. The

'r preoedln8 equations can be numerically lntesr•tod for compound body shapes to

i! obt•ln the lmlMr •nd turbulent Man•let factor •s • function of ru_nin| lenjth.

!.:,

IL. Selection of the pressure option •nd Reynolds _nelosy f•ct¢,t for • problem

: li ts based primarily on experience. In order to document some of this experience,

,_ several sample cases will be ezantned. Ftsure 7.1 shows • comparison of wind

tunnel pressure data with the _ tan•ant cone option and • method of che-ac-

,_

_ tertsttc (MOC) calculation. The data and theories are for the cylinder section

.i

,!:_ of the Space Shuttle ozternal t•nk at zero anljle of attack. For this situation,

_'._

_._ the tansent cone option does not predict the data veil. This option would also

_:_ co,respond to the modified Newt•mien pressure option. The NOC results do cone ,:

°i pare yell with data. Thus, results from a more exact theoretical method should

_/'J !

,_ be used as input to LA]qMN, where available, to establish the else l_essure.

_: Hearths result8 from LANM_ uslnS both pressure options are sho_ in _i|nre -,

_': 7.2 usin8 the best hestin8 p_edtction method. The overpredt•tJon Irep_ of the

,w

: i'./ tan•out echo option, shown in Flsure 7.1s, is translated l'_to _n over predlotlon

o.:S., in hearth| •8 shown in FiSure 7.2. Likewise, when the pressures from the note

"_' accurate NOC solution are used, the heatlns i8 more accurately p_e._fctc, _.

;i" The Reynolds anal•By factor offset is ezsmined in Fijuro 7.9. The Colbutn !

: ! a_slo|y factor is shown to overptedtot the data and • unity Reynolds analo|y

factor u_derptedluts the data. The yon Ear, nan analo|y factor when used with the

, ilil Spaldtn|-Chi hetttn| _ethod with accurate pressure• provides the best comparison

I 96

f !_
7.4. The pressure at snail to moderate smiles of attaok slonj the windward

stzeeultne is predicted well by both the tanjsnt oone option and NOC solutions.

Thus the heatin| data in Ft|ure 7.4a aonperea well with ©eleuletiona usin| both

• pressure options. The theory and data oonparisons in Flsure 7.4b and o demonstrata that the van Karnan Reynolds tnaloj7 factor |ires the heat predi©tion.

Results from the Spaldinj-Chi option usin$ the yon Warnan Reynolds enalosy

are shown in F/sure 7.$ alan8 with an independent hoatin8 theory fat • different

8eonetry. Hettlnj data for • sphere-sane-cylinder (SRB) body are shown. The

D_J.nq results are from an tntesral momentum solution based on the york of Dirline (Ref. 7). The two theories are in 8sod asreement and oompere well with

the wind tunnel date.

Another application of the LAh_ oode is shown in Fisute 7.6. This ease

is s sharp wedae at three shales of atteok. Three-dimensional effeot8 on the

wed|e l_oduoed pressures htjher than the two-dimensional valse pressure option.

By usln8 the wedje shook entro._y and tnputttn8 the measured pressures, the LAN- J

MD_ results compare veil with data and results from an independent theory of i

Dtrlln8 (lef. 7). 't

1

-_ All preoedtnj results and oompartson8 have been fez turbulent flow. The

laminar method of Eokert in LAh_/_ Is oonpated with wind tunnel data ts Fisure _

! _ 7.7. The tansent oo_ pressure o_.tton yam used for this calculation. Usin8 i

: _ more precise pressures would have slishtly lowered the predl©ted values in the

tsn|e 0.08 ( X/L ( 0.22 and 81tahtly lnoreased the valueb in the ran|e 0.22 ( i

J

X/L ( 0.60.

97
!

Other ©onperisons of data and theory hove been presented in the tobies of

." Section 5,0, These results along with other ezporience were used to deternino 8

reconnended sot of hosting options, Those options are given in Tt'ble 7..t, #

" !

7,2 G_ERIC ORBITER APPLICATIONS

Hosting to • generic orbiter geometry can be calculated by • numerous combination of options for a specific location on the vehicle, The success in accurately predicting the heating to any given location is determined in large

part by the proper selection of options and the engineering skill of the user.

K general approach i8 given herein for orbiter application, Specific geometries

and flow situations may require modification of the guidelines given,

,-._,_ The approach taken follows the selection of the four key parameters given

in Section 7,1 •s specifically applied to • generic orbiter shape, Figure 7,8

_ii $£ves the selected generic orbiter design methods in sun-try foz_n, The approach

J

_ taken was to select methods which would best represent measured data. If •

_.t design conservatism i8 to be introduced, it should be introduced •s a known coni _ grant multiplier, In order to demonstrate and help explain the options select- '_!

ed, a discussion is given of three of the principal areas on an orb*.tet_ '1

Kale notken

The heating to the bottom oentetline of an orb_ter neap can be calculated

:; using the options in LANMIN by deternining an effective sphere value. 5_ ef-

_'i fective sphere value t8 oal©ulated with norms1 shook entropy. The heating

t i

, methods of Lees and Detts-Htdal8o are used for laminar and turbulent flow "

t respectively. Consider the lminar case as an ezupla. The heat transfer cool- t

t .... ficlent 18 doterninod by

h- t.,.

_l.

98
where

he Is the Fay end Riddell v•lue tot radius Re

z ts the Is#el radius of the body

i_ h/he t8 the Lees distribution retie at the loosl body shale plus en_lo #

_' ot sttsoh 1

: An ennple of this nethod bales applied to • sphere-sane 8eonetfy ts |ivan in

,. Fie. 7.9. The Lees dLstttbutton value on the ©one Ls evaluated at

,r.

• 90 - 20 - 15 - $$ delta•s, and the loo81 radius, r. ts 8 function at ezi•l 1oo•-

** tton. This rather stnple nethod p:ovtd, s quite 8sod asreenent with the data

shove.

! This method was also applied to the nose •asian at an orbiter oon_isurstlon

-' •s shove '_n FLa. 7.10. The •sea of application was 0 _ X/L ( 0.05 on the or-

';.- bites batten oanterllne where theory ted dst• 8$:ee tar 811 three shales at at-

'_ ----tent,

""i Thus by input•ins the body stale and looel radius an efteotLve sphere dis-

, tributton value Is oalculsted whtah represents the _ose restart batten oentero:;.* line. The offset of •nile o_ at•ask ts •assented tot by ths ptojr*m cal_ulstln8 'i1

i_' _; an aries•ire body shale.

;i

?!T '* i ,

;/ Zn order to seleot 8 usable he•hod tar LANMD_tot the batten oeuterlLne of

"d:i:i ::i sn orbiter, sash oonponent of the ealaulstlon nest be sonsidsredo The sonpsri-

::..:l sons |Ivan in FI8. 7.10 for Z/L ) 0.0S are sample trials of dif[arent options°

...._.i " At one antis at st•sob, s siren set of nptions mat sires with date but sot asree

_ with data at other en|les of eats•k. This approach aontounds the eats©as of the

1

!ij different options in • set. Thus. tiul ssrssn_nt99 tot one ease dose no_ assure
sppltesbllity over s wide rsnje of conditions.

#

Let us consider the shock shape which controls tha boundary layer ed|e condition8, Fisuse 7,11 presents s correlation of shock shapes first published for

delta wins data by l)unavant (ROle 14), The 8eneric orbiter data from four

sousces were added in the present study. Virtually ell of the data asrees with

tsnsent cone shock theory for eusles of attack from 10 to 4S dejrees. Most all

orbiters fly in this amble of attack ranis durin8 the hijhest heatin8 per_cd.

Thus the shock option to be used is the tansent cone option.

Deterninin8 the conect runnin8 lensth to use Is the most complicated and

; most critical decision to be made, The I_MIN code has cross-flow correction

options and Msnsler transformations to assist in correctinj the actual runnin$

_ lensth to an equivalent runnin8 lenstb. For some jeometries these runnin8

i

• lensth corrections can be quite accurate and easy to select. This ts not the

case fo_ 8enertc orbiter 8eometries,

5'

J j

c: Another approach is selected hero based on the modification o5 v.tlte_ _ork

by Pond et al (Ref, 15), ,niuar host transfer data a_e used to calculete-the

effective runninS lensth to the body location of interest, This procedure finds

: the actual flat plate equivalent runnin8 lensth which is required for input Into _

:_ : LANMIN, This effective runntnj lonsth is then used for fltjht prediction cslcu- ]

" _ lattons, A sample case is described to provide details of the approach.

! •

I

• Other 8ulyses have developed sampler streamline trsclnj methods which requites an accurate and smooth pressure distribution input, These methods are

_.-_ cut beyond the scope of the LANMINapproach,

,: 100
H ';_ i

Pond st 81 (Rot. 15) tooted the |oonotry •hewn in Fi|. 7.12 to obtain

";l hestia| data. The he•tin| data were used with Bokert• he•tin| method to oal_-

_ late the equival•nt rennin| Inn|the shown in Fl8. 7.19. l_or this leon•try it i

l• evident that the equivalent ruanin8 l•nsth• are 8 stzon8 fuaotton st 8n81e of

.... attaok end axial looation.

_. Work by Du_tvant (ha. 14) which van later amplified by Nevnann and Ran-

./

i.._ free (Rof. 16) dealt with obtaintn8 an outflow oorreotto_ for the runnin|

_,_,,_ len|th. Fez hypersonic flow. this ,err•orion san •haply bo written a•

....._. lo = lltan s/tan a) (7.1)

,,i _hbTo_

_,:_ Xo = equivalent tunln| 1•hath

g, ,:

_., • = aotul runnin| lenath

..... a - an|le of att•o_

-, • = P0 - swoop anal•

.;. By 1,shin8 at the 8•,natty in 1_18. 7.12 8 sins1• value to use fez • 18 not evi-

::_ dent. However, by takln8 the data in _t|. 7.15 and nstn8 it in the preoedtn8

o_.:. equation, • san be oaloulated. The results are shown in Fie. 7.14. _11 of the '1

_,,_ 20, 90 and 40 dears• an81• of attao_ data oollapao to live an of festive swoop

; _nalo complement as • fuaotlon of a_lal loostion. The a = 10 data i8 for an in-

,_' time oondttion end is thus not ezpeotod to oorrolate. The data for a = $$ ezhi-

,t

_",. bit 8 trend whleh is not oonpletely uderstood and may be due to lash of quality

_ t " paint data for the ort81nal heatln| data. 81nee the preoodin8 relation does _

• i):;i " eoll•pso t_ho data in the prin•zy ran|• of interest, it san be used alon| with i_

: liait.d wind tunel data to develo_ equivalent _unln| lonatb8 for input. _

o_ i

To •onplete the explanation of the proselyte, the equivalent ru_nin| lln|th

" {

"I
data in Fij. 7.1S was used in LANMXNfo_ s _ompletely different orbits,-, shape.

The results fron _NMIN are compared in FtI. 7.15 with data from a phase B or-

#

biter Seomstry. The comparison is quite seed and silnificantly improved over

•

the comparisons made in Fie. 7.10. Note that t_e tansent wedae pressure option

was used. Unfortunately, pressure data are :_ot available for comparison.

However, Math number data on orbiter shapes are usually overpredicted when wades

;' pressures are used. Thus, wsdse pressures are most likely too low. This uisht

_i explain why the theoretical results are slijhtly lower than measured in _i8.

i....i.- 7.15.

ii_,, Thus far only laminar equivalent lsnaths and results have been discussed.

'_ The laminar heatin8 rates are more sensitive to the equivalent lensth

v ;/ (h ~ XeS/S) than turbulent heatinj rates (h -Xe .* ). The laminar and turbulent

/_ equivalent lenjths are different. For example on a cone the differences are: '_ ,

_/.ib_. XeL = X/3

from Manaler relations

/i.,. Xet = x/2

o/) , Thus an adjustment must be made to the laminar equivalent lenjth to obtpln ,

: o_/ • t_rbulent equivalent leuath. Since no data were •vlilsble f_r torbulent I

,_:"_ equivalent lenath8, the cone ratio was used

_ Xet = $XeL/2

"; ,, to obtain input to LANMXNfez the ease shown i_ Fie. 7.16. Tlta comparison of

_"!_",!'i" data and theory is quite £ood. Note that • $0% Increase in the runnln8 l en|th

..-t when used in turbulent heatin8 equations only reduces the heatin8 by 8 peree_t. -

/ . !

" The procedure to use the equivalent runnins lensth approach ts as follows:

_ii" ,-- , _'' Obt•tn l.ina_ wind t_._el data for the ,euert_ orbiter of interest.

_i,"/"_ ' (2) Use _XN parametrically to 8enerste laminar equivalent runnin8 lensths.

. 102

,.q
i

: (3) Tf data are •vail•hie, repeat •tap (1) and (2) _o verify the lanina_ to

t

t_rbulent ttansfornation

(4) It 1baited data are available use equotion 71 alone with an effective e J

based on the lintted data to ozpand the susie of attack tan|e

(S) It no wind tomnol data uo available use FlSo 719 or closest Soonetry

equivalent lonlth data (Note a sot of plots/tables of equivalent lonsths

for a set of |oonotrios should be developed as • data base).

(6) Use the equivalent zunnins lensth in LKNMD/ for fllIht applications alone

with the sane •hock, pressure and heatinS fate options u_ed to 8enefate the

equivalent tunninS le_sths

This nethod has been discussed in terns of the bottom ©enteflino. However, it

has 8 numb b-oadef application. This method may be applied to any body location

J

which is not influenced by separation of shook interference

F

The stasnation line of • wins is •pprozinated well by 8wept cylinder thoo-

_1 ry. The shock lies parallel to the wins over a considerable portion wins

of the

'" '' ,h'n tn th...hl i.f.n of ,iS. '. l,. Th. ,,. i.f f,ow ,t, ,,re. ,.ll with

the correlation in LANMIN. A oonpaflson tot turbulent flow of

i! Beckeith-Gallaahcf with data Is siren in Table $.6a

!?

i

103
_[ ""

Table 7.1

- RECOI_tENDED HETHODS

HEATTRANSFER

L_EOHETRY HEATINGOPTION OPTIONNUHBER

l l' I nl I . III

SPHERE Fay and Rtddell 1

: m I i ! | I

SPHEREDISTRIBUTION Laminar: Lees 8

:.:, Turbulent: Detra and Hidalgo

.; -- ii i i .i ,i __ I i

.' SHEPTCYLINDER Lamlnar: Correlation 6

.:'] Turbulent: Deckwtth-gelagher

., J i , l.il |1 i j

')!" CONE,HEDGE, Laminar: Eckert 4

,,._ OGIVE& ORBITER Turbulent: Spaldlng-ChI with

BOTTOHCENTERLINE YonI_rn_n ReynoldsAnalogy _]." ,

.,'i • i i |1 | i i i i

_,, ORBITERLEESIDE Bertln eindGoodrich 9

' ._ i i ii i i iJ ii Hi I I

" FLAP Bushnell and Hetnsteln _,0 '_

,_ FIN INTERFERENCE Ftvel 11

,! ONPLATE

S1 ........

104 [
n '0. I_ O. 0

Non-DtmenstonalfzedAxle1 Distance, X/L I

'&O

- 0",_- O',OT- ZeO"

, _ liB3(_ Iffl_l_lC _II(EIJ

MM nlEORY

I]ESOtlPTIQN _ IE

P

o Ik/rmlO,,lira]0

IVJmZO',I_ 29

i 1

=.' i2.o

1,0 -_ & v

& . 0,8 .......

0,6 • = ----, ,,, ............ ii i

0 0.2 OJr .(, 0.! l.O

Non-DtmenslonallzedAxfal Dfstance, X/L i

Fig. 7.1 Pressure Ratto on the SpaceShuttle External TankBarrel

(FromRef. G) _

10S
+.+. ORIGINAL P/_.GiZ1_

+._ OF POOR QUALITY

I

_n- II,_m_ IMIILI_lqI_ AIIIL.III _ _" r_ _

Jill _A _m _ (_ 0,0 III_LI_INI_'f_I¢_I_ FAITTIm _/]IUI.AFIrIq

_,0

_m O_0 _ J.O ......................

6" n _.,, From

q _,o Ref. 5

• _P.S

0,_ ..... o M • --

-. 0 _',0

, P,_ ...........................

o ..... ,

0,1_ _ ._ _

0 0,_ O:q _._ n,_ 1.0

NON-DLHENSIO_/d.IZED AXIAL DISTANC[, X/L

PIG. _ HEAT TRANSFER DISTRIBUTION ON THE SPACE SHUTTLE EXTF_,_ . ',

• o, (_, #- (? _ I_IPHI_ _l_e T .qg._"_ II_

_ I_ _ _N_, o 0,0 _ _zs_

;." O 29,I -- Ox,_ Ik'no.m,_r,, r._c._m

0._ _" I,O - - - _, _ _ F_ ;"rOl_

!!" -. . _.0 Rc_. 5 o _._

,- ,== OJO _o I_,035I'0 r" . n _'S

i i

_.0

o _,12

9.lo .... u . _,0 ...........

--' O,OI .-

0,05 ..._ - ""_ ",,: ":d.-'-." _._-_ .....

,I _ 0,9_ -- _ ..........

O,II

_-_ o,o•_ ,,,

0 &2 0._ 0.6 O.O 1,0

; [ NON-D_J'_NSIONALIZED AXIAL DISTAl,ICE. AlL :i

"; riG. Z$ H_,AT TRANSFIR DISTRIBUTION OH THE SPACE SHUI")'LIEXT _ ER/_AL TANK

..:, i

106 "

.... . • . ,.,, ' :-",...... ,...r....... : .:..-.""-."" .- -. ..."..'z. " ..'..:,:,.,.: ..
.... -,,-.o6_ .- . _ql

ORtGtN_IP-P'_ _J "

OF poor QUALII"V _.t, .Tb.se._.

:-.r Re/ft. - 4.1 x i0 _ yon tenutn

,- 10" IJ-O'. eT- 180" _ NOC

Twst•v_'r,lJl _ltDC Tunnel A) .... Tanpnt.-Cune

Aune 3_, 34$

1.0

• (a) l _

,ip ,2 ,% . • _

• tl • L_

,05

,2 ,4 ,6 ,8 1,0

X/L

...5.3

_/tt. - 6.8 x 10G t40c

i Teat. XH68 (Allen Hk't) _ van I_zsman

": 1.0 Itun8 164e 165) .... Collr)urn

:_ ...... l ..... I l I

., o : .o ,

, ,,'%!I I I I '

(hi,

...2 - i

"° • 1 '

I __ ___ ........

I

0 I

t *04 .... 1

0 ,2 .4 .5 ,8 1,0 _,

:. x/t. ]_

_I,,o ?.3

"_ 1,0 _---o - S', IJ - 0*, Sr - 18G0 _ voa IJ_uln-- ,.

_) ---Teat 11158(Ames1it_2) .... CoZbu¢_ .- _._Rune311, 125

., I j j j I 1

_. I

; °1 -

.o_ "a,..L ..... i _

" _-'_ _-:-° "" 4 ........ 1

,0_ _ ......... _ _._

o0) _ 1

0 ,1 ,_ ,6 ,8 1,0 -it i

; XIL

! Fto. 7.4 Heat-transfer Distribution on the SpaceShuttle_External

_ T_nk for Vartous Tunnel Conditions (FromRef. 6) '_

_.: 107 '_
i,

108 :_

.......... ..... .:.. ,.:..., ?'. ;. ::. . ., ,, - _,. .-._:, ,._ --.--:',':i'_ ".'--- ".... • _.......... ,. " ..... _.. : "" - . -" ..... :-.-,.
,a

q .

:_ i OF POOR QUAL

28 : • I ', ..I ', I :'': : ': " : :[Z: TEiT DATA

. ,_7:3....P.;ugzpszt-_: i Ii :1:_:'.:_:i_l:.'!:_ '" 1 ' " _

i::'i'!;_]S'i:t?:::i:: !:i ::i:I :!':i)!!: Fii :::i-:_i t:'?:i:i' i'::;i.ii i!:i!: ;::i"::il :I:_A11214.841g'g15211532-.

• == :-_::ili:!:,-:qi!F.!!:-)::_:t:i_F:.i _ ti::ti!:il!-Fit-.::-t-i:ti!:li.i:: | NonuntfomPressure_

20 ::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::: ::::: .

. --_:--::-:.-._:=:! _!-_i: : :-'_::-:-. :-::-.:__s_:i-:;t:_:_:_.._:::. ::. :..-.::_-::::.:::.:i_:.::.!!i!_ =========================

.... ,................................! I

.o.]...

............ : --' ................ ::::_ :-: ': !::.:i!::.:'.-_.::iii_?:_ii:1!:.!:": ::"-!

_ ....... ".................. l"" i ..............................1 .........'"" _ '"I............

, I...i...._ .i-_.......l........l......,..,.,_,._..,...........,....,....;_ .......I

I --4 ................ 4 4 ..4 .................... L._ . i i .'_ , "

' ........ i ....... '.................... +"--_......... _" " .... ":::: ::: ::-:":":, ::- ""

4 _ ' _ " " _ .... 1 ..... : ======================================= .... : _0 _ ====================================

:,-"-: :::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::: ::::1:. :_L :!::,:':_::::_:-'::_::I:.:::

...... 8 :'::!:::: :::.:z:::.: :':_::::_-::-_::: :::::::::::::::::::::::::::::::::::::::: -_:":_:.'|F':_"_ ,,;,_.:" .::12"" :.:.i ! !

_:, ::-itii_!_i-_!::!ii,::itit:::9:::'_._Layer Trlpl:ii: !!i-i):::)iil!i::!:.Tti!i!ti_i_t_ii]_:!::]-!!:t-; :::": ' '"

..: ............................................... ."_"_ TP$ $peclmen-: ::::

:." •................... :"....::.....:. .................. :..m,.....Locatton

•: o . t-::l:::t : 1..: :: ::: ::..! ...1::.:1_ .;: .......... I................. ;......

.', 0 4 8 12 16 20 24

i','.-,; X (tnches) '

:) . Ftg, 7.6: Heattng Rate Versus' Length for Three Test Conditions at the

AmesTPS Ca_'bratton Test

i'' _"

:.4; 109

..... ........:;Lh_ ..........................................................................................................................................................................................2f,=
-:.i-! ORIGINALPAGEIS

• OF POORQUALITY

e

I! ,

i i 1.0 !:: t: i:.ii i'i! : t, i,._ ;

: . @ : " _ I k : : _ " ' .... ; ; ' ] _," _ ' : l" 39.38e Cone Shock I_

.... "-'_ ::_: ':_ ::_' :-_:_': "-_:t =:"--- Tangent ConeP_ss,_$_

,_- _ :-_ __3:: ;:. __-::_ _:.:--:: -:::. -t :-i _-_ Re_ ,, 2.48 x 10 L_-:._--_-

:. 0.I............................. --_

.IL,

,,_ _--_-__" _!_ :.'_--7_;-_-";:t:_:_ _-_.L_;_-_-': :_=-----'°-_--"--'. -':=- _-:_-

_-----4........................... :.............. _ ..................

o I ._' .41 .e I .S 1.0 :

sb

b

"'?; Ftg. 7.7 Lam|narHeat Transfer Dfstrfbutton on the Space

Shuttle External Tank

ii,

_ , 110
OF POORQUALITY

v

t

(_) e Norm1 Shock

:. , e Stagnation Potnt: Fay & Rtdde11 "_ With Effecttve

i.... -,_•:,'_ e Distribution :Lamtn Turbulent ar Lee - Det s ra & Htdalgo.j Radtus

(_) TangentConeShock

' TangentHedgePressures

• _, Lamtner: Eckert Ntth Tunnel Derlved Equivalent RunntngLengths

,. _; Turbulent: Spaldtng-Cht With Turbulent _m 2/3

-_: Von Karman

: _,, _ SweptCyllnder

Paralle1 Shock

-,. Lamtnar: Correlation

..-._ Turbulent: Beckwtth-Gallagher

,.:_- (_) ' Tangent ConeShock TangentHedgePressures

'_i:! TangentHedgeShock

_"' Tangent BushnellHed kletnstetn gePressures

:I (_ NormalShock

..l_i . Berttn-Goodrtch

'!

,') Ft9. 7.8 LAtIMINGenertc Orbtter DestgnMethods 7,

,!

_-_ 111

/
' iii

•ORIGIN_t.la_Clr:II;

OF POORQUALITY

Angle of Attack ,, 15 Deg.

HachNo. ,, 7.77

e- Data, Bushnell et al (Re_. 8)

1.0 , , , • •

• • " ! .... I

- , -)_ U_ :.i:_]"i!:.!i:i-_K:i_i.!i7:-i2.!!-!7;2)7! :: -i-i

o ........ 1.....-t--............... - !..............._.................i ...............

, _, ..::-:.:::::L-:-.:.:_/;iEqulvalent Sphere:: :I::-:,. : ::::::::-:_.-:. -:_.,--: :

:i:i-7!:ii-._........ -::i: ::: "::

i............. _r............. ] ......"..............I ..........................

. i: _::-:.::'_::::::_:___.,:::: " -: i_'.::::::::::::::::::::: . ._:-._- ...........

' . 2 L ' I } i ' _ ' r : I i _ I II l

"- ........... ':::i ............ i .....::: ; :' -_........... i': ....

O

0 2.0 4.0 6.0 8.0 10,0"

S/Ro, NondlmenstonaSur l face Distance

i

,... Ftg. 7.9 HtndwardCenterltne Heat Transfer Over a 20-Degree

Half Angle Slunt Coneat Angle of Attack

112

i

ORIOINALPAGZiS

OF POORQUALITY

eo _GENERZCORBITERDATA

• HDAC=DW(Ref. O 10) , :l #

vo • LaRCDelta Wtng(Ref. 11) ConeShock,. f /

41_Shutt 0 ( ) - / /

,,,all / ,/" ./

, ; ; , g g t-- - . '

.,o I.. I.."t', <'/ .

I I. -///

.,_, 4o I , ; /:Iv " ....

i<) t,!::: il ' ' i_ri, i11" /

• / ' " /(l )'/ o x :s°, C_,Sh,_) -

l

" t / /r_i / 121 IZ -#_o Z3^, Shlrp

/ Z Y I 0 XXX "t5o, 26:, Sh_p -- --

, #r'_/ I_ y 60 , 13 , Blunt l

:'! _ ll#_.Y _ 121VII ?5°, 0°, Siilrp - .--

_ [//

' lO )0 4O 50 6O 90

,.-, Angleof Attack (Deg.)

m

,.! Ftg. 7.11 t Shock-Wave-AngleCorrelation _, "

I

I

i1 t

"i 114

.;q

, f

................ "-" _ m _-'"#._"-_ -#,._. "_"'" -" .- _'.':_'.,:,."-"-'y._ , i-

....... _-._..-...... '-..... "...................... )<z-,';) '7=-'--'"--:'-------_--= "- -_-"'_--'--=- :-_-_='_"_'--_ =_+_-- "_ '_---'_: --_-"-'---' " '" _"" '---

..._f

-, ORIGINAL I'C_;;;:::_,::_ ,"

, OF POOR QUALI'i"V

1.0-- b I...... i _-J

•./,-. _ /"°'51 .

"': M..1o" ' _ -/ /:.

Re.- 1x lo6/ft / /zo

' I '

,./

'..... /'/k" '/

.s .... i i .... i

N :: '"i

,'4 _-- I

O" .1 .Z .3 .4 .S .6 .? .B

Runntng Length To Body Length Retto, X/L

Ftg. 7.13: Equivalent Running Length For The Bottom Centerltne Of The

HSFC437 Orbtter

- 116
m

/

OF i'0o_ J._:J_LI'tY

a

Ftg. 7.14',[ffect|ve, SweepAngle ComplimentFor HSFC437 Orbtter

117
yi, _f t

e - Data FromWarmbrodet. al.f -- Theory

M. - 8.0 TangentConeShock

:" --w--hlf*, 2.6 x 106/ft i Tang [ckertentWedgePressures

£qutva!ent RunntngLengths {

p

Man@ler= 1.0 ,

i,,

",'( .

,;: , Rookwell Orbiter (IIIB)

i,

,:.__ " ; : : : . :.i . ! _ : . : '• t . : , • i f , . i : • ', i _ i . . _ ' i

: .;: _1;..L.. _ , i z :-2 ; -:'. : : | : o ,_ 7 • _._.:_.::" :-: -:_- v _; : : '_

"'" 0.1 7--.7--_ .......... --_.......................... _--_......... - "o-

,,_ :.-i:-::-' : .:; ._--._-_--_.:_ -:_-:::-_4-'. ; i-_: :_ -__.--_::-_::-:_'_h -3=_-_-:-'_---':"

'_ -_._::-:-:I:: "_,_: T': :_E-:-_.--_-.-:-_ : ! !-.."::_:_ : _ _ ,,Z.:._.-_._ '-._-7 __ _IT-ZT-___ ._:-:T-Z:'_" "I

':":t :t_':--'T:: : :; ;-:::::t7"_: :I :: : : I:: :;-: '41 ; -:: : ...... :I ......717-":.4L: ' ":

-"....... _......... I ............ '-'--_ ............"-I"_ ..... _-"-_,-'-4-_- ---*.....

_ __;-_:._ :i. :.?_.:._::_:,-::!-:_I _ ;j-:!_-:.:.:..:_..:-: : !--":._-__.:'--_+:.:.-:_-..:

, _:-_-q: ___.___:_._.::-:-:,. -.. .........

•': _:::..:: !:.:..:-_--:.__- .-ii-:_i_iii|!:-_:::_:_i:" i :-i:-4:-::-. :. 

"I 0,01:---:_:l-:_-_:._::: ..... :::::q_- 2.:-I::--:: !:y.: :.. :I:_::::::_:_:::_- --::-l--f----:

:_'i 0_ .2 i .4-i .6 .8 i 1.0'

k

Ftg. 7.15 tJ_.NMINTheor_ ComparedWtth PhaseB Orbtter

Configuration BottomCenterltne LamlnarData

i:
ORI_NAL, rC:.r_f _:,

OF POOR O[JI_,L;_'V

@ Data FromMarmbrodet al (Ref. 9) ---- Theory

i_, - 8.0 Tangent Cone Shock

. Re=/ft = 3.75 x 106/ft Tangent WedgePressure

Grtt on Nose Spmuldtng-Cht d

YonKarman

_rm- .6667

EquivalentLamtnar

Runn|ng Lengths

Rockwell Orbiter (11111)

I

1.0

o

Ftg. 7.16 LANMINTheory ComparedHtth Phase B Orbiter

_nftguratlon BottomCenterltne Turbulent Data

119

- 1
0,7'

0.6
8ootion VIII

RI_EPJ_CES

10 Header, D.R.p 'WA Miniature Version of the 3A70 kerodynsnie Hesttn8 Conpurer Pzosrm, mOO (KINIY3R)," MoDonne11 DouBles Astronsuttos Co., HuntinRton Boaoh, CaXit., JIDCReport G-0462, 7one 1970 (reVised 7an. 1972).

2. Vtlhtte, A.V. and $.$. Rohdor, '°AVI3): A DoetIn 8yeton Pot Teohnol_;y

Studies of Advanced T_eneportation Conoepts,'' AXAA Paper 79-08?2.

AJ_._/NASA Confuronoo on Advanoed Teohneloay for Future Speoe Syotens, USnlrton, VA., ira) 8-11. 1979,

9. Hoax, $.A. and D. _omosyi. ' 'A Reviev of NS1-NSFC Generalized Aotodynsnto

Has*ins Prosru (Ml_qEQ)," _rtbrop Servtoes, Ino. TR-230-1202. Suns 1973.

4. Easel. C.D., '*MI_IYBR Conputer Preston Modtfiuations tot Rarefied Flov

Aoroheetin8. ' ' RN 008-05, REJflYCH, I_,, Nsroh 1975.

$. PraharaJ, $.Co, *'Undisturbed Heat Transfer Data Analysts on the Speoe

Shuttle External Tank Barrel Seotton.' * AYAA Paper 78-41, AL_A 16th Aerospeoo Solenoee Meetin8. Huntsville, AL, $anuary 16-18. 1978.

6. PraharaJ, 8.C., **Undistusbod Plovfield and Turbulent Heat-_ranster A_-

alyetl on the Spaoe Shuttle Ezternal Tank.'* A_ Paper 7J_0578. A_A 17th

Aerospeoo Scienoes Heotinl. Nov Orleans, IA., _anuaty 15-17, 1979.

7_ Easel. C.D. and R.C. Levis. *'Roush Vsll Aezodynsnto Hearth8 Cos_puter

Preston, * * RM017-6. REIG_CH. Xno.. Ansust 19770

8. Bushno11_ D.M.. R.A. $ones. sad $.r. Hnftnsn, ''Heat Transfer and Pressure Distributions on Spherioslly Blunted 250 hlt-AnIle Cone _t Naoh 8 and

Ansle8 ot Attaok up to 90o, ' ' NASA TN 1)-4792, Ootober 1968.

9. Wa_nbrod, J.D.. V.R. Nsrtindole, and R.L Nstt_hevs_ ''Host Transfer Rate

Neasuroment8 on North AJnertoan Rookwell Orbiter (161B) st Noninel Maoh

Nunber of 8. '° DMS-I_H-1177. Vol. IZl. J_DC, Deoenber 1971.

10. Es_es. R.H.. T.D. Buohanen, and J.D. wa_nbr©d, '*Host Trsnstur Xnvesttsatto_ of the HoDonnell-Douslas Doits gt_, Orbiter st 8 Nominal Hash Number

of 10.$.*' DMS-DR-1206, CR-120.024. Vol, 1. _J)C, May 1972.

11. Eaves, R.H.. T.D. Buohenan, _.D. Warnbrod, and C.B. 7ohnson, *SHoat .

Transfer In-.osttsotion of TWo Lansley Reseuroh Center Delta Win8 Contijuraalone st 8 Hseh Nunber ot 10.5." DNS-DR-1224, C_-120, 03_, Vol. 1, _DC,

.o Maroh 197_,

12. Nstthevs. R.E., V.R. Nartindalo, and $.D. Vernbrod. "Hoot Transfer Hate

Distribution on North _erioan Ro©L_e11 Delta Win| Orbiter Deto_nined by

Phase Chsnse Point Teohni_e st Ms oh Nnnber of 8, _' DHS-DR-12$1,

CR-120.048, Vol. I, /_,DC. Msto_, _972 :_

121 !'

I{

....,-. ,-. _. ............... _. ....... _._-=_ ........ ._...-
13. Nut,. r.w., O.L. Donnernsn. end A.C. Hsnsfieldm ''Test 11,cults iron

HASA/Roeho11 Interns,lena1 Spsae Shuttle Orbiter Tests (0B-8411. IB-102,

011-105) ,' ' AEDC-TSR-YS_-V42, August 2979.

14. Dunsvmnt. 3.C., 'WZnvosttgstion of Best Trsnsfor end Pressures on Highly

Swept Fist tnd Dihedtsled Dolts Wings st 14seh Numbers ot 6.8 end 9.6 end _

Angle of Atteok to 90'," LsRC NASA TKZ-688. 3us lP62.

|$. Pond, $.B., end P.O. JleCorntek. feShuttle Reentry Aerodynsmte Besting

Test," Lockheed Xtsetlo end Spsce Compsny, Huntsville, AL. LNSC-BREC

D22SSS5, l)eoenber 2971.

_ 16. Newnsnn, R.D. end P.G. Rentroe. *'Eyeing,ion of the Best T_snsfer sad

Plow Fields About Bigh2y Swept De2ts Wings in Byporsonte Flow.''

Wrtght-Pstterson Air Fetes Bess. JLSDTDR 64-76. April 2964.

'L

')

-i

i '

I

.)

• 122

(