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AIAA 98-0879

Computational AeroheatingPredictions for X-34William L. Kleb, William A. Wood, and Peter A. Gnoffo

NASA Langley Research Center,

Hampton, Virginia 23681

Stephen J. AlterLockheed Martin Engineering & Sciences,

Hampton, Virginia 23681

\\\ \

36th AIAA Aerospace SciencesMeeting and Exhibit

January 12-15, 1998/Reno, NV

For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics1801 Alexander Bell Drive, Suite 500, Reston, VA 22191-4344

https://ntrs.nasa.gov/search.jsp?R=19980021432 2018-05-23T16:49:24+00:00Z

Computational Aeroheating

Predictions for X-34

William L. Kleb.* Willianl A. Wood.* and Peter A. Gnofl'o t

NASA Langley Research Center, Hampton, Vi_yinia 2,7681

Stephen .1. Alter t

Lockheed Martin Enqineerin9 (4 Scienc_:s. Hampton, ViTyiuia 2,7681

Radiative equilibrium surface temperatures, heating rates, streamlines, surface pres-

sures, and flow-field features as predicted by the Langley Aerothermodynamic Upwind

Relaxation Algorithm (I.AI!t{A) are presented for the X-34 Technology Demonstrator. Re-

sults for two trajectory points corresponding to entry peak heating and two control surfacedeflections are discussed. This data is also discussed in the context of Thermal Protection

System (TPS) design issues. The work presented in this report is part of a larger effort to

define the X-34 aerothermal environment, including the application of engineering codes

and wind-tunnel studies.

Nomenclature

o Angle of attack. (leg

/i,_ Control surfiwe defle('tions. (leg (+down)

e Enfissivity

p Density, slug/ft :_

cr St(_fan-Boltzmann constant,

4.76 x l()-l:_Btu/ff->R 4 - .s

b "Wingsl)an. 27.7 ft

h Altitude, kft

L Overall length. 58.3 ft

M Math mmd)er

p Pressure. ll)/fl 2

q Heating rat(', Btu/fl='-s

Rc Reynol(ts Number

T TOlllt)('t'atlll'(L °F

1" Velocity. fl,/s

.r Fuselage station, f)

y Butt line station, ft

: \Vat(,rline stati(m, fl

Introduction

S early as May 1993, Orbital S(qen('es Corpora-tion (OSC) of Dulh,s, Virginia l)egan cons|tier-

ing low cost methods t() laun(:h relatively small pay-h)ads (_1,5()0 ll)s) into sI)a(:(,. 1"'-' In tit(' fall of 1993,

()SC at)l)roached NASA to inquire about an alliance

"|¢(,sear('h Engineer, Am'otherrnodyrlamics [_ran(:h, Aero-

and (;as-l)ynamics l)ivision, I(esear('h and Tet'hnology Group.

tSeni(w I(esearch Engin('er, :\er()l|wrm()(lynamics Branch,

Aero- and (;as-Dynamics l)ivisi(m, t¢osearch and Technology

(;,'oup, AIAA asso(:iat(, felh)w.

++Senior Aeronauli(:a] [':ng, ine(!r, S(!Ilior Member AIAA.

(',,pyri_zhl _)199m I,) Ih¢' An_.rican Institute ,,f Aert)ll_LIItics _tlld Astr¢l-

nauth'_. Inl_ N,, ,',q)>n'iKht i_ as_erqed in _h_' IIn0ed Ntato_ under Wille 17, I N

(',,dr 'l[l_ ITS (;,,vernn_ont h_ _L r,))alt', ft*'," ticen_(' I<, (-xetci<. a]l li_ht_

un,l,'l the <-,,p3lighl clain,,'d h,q(in f,,r i_,,v, Ilm_,'ntal purl),,_e' All ,,thai li_ht_

al(" i,,uerxe, d I) 5 Ihe c,,p3"right <,wn..t

Coast

Burnout __ "" _ Descent

Launch L-1011 / _"carrier aircraft ,,_. _

j,//_scent \

_:_¢:'_._ _ <%, RecoveryIgnition _

Landing ,

RunwayI Down range landing "'i

Fig. 1 Typical X-34 mission profile.

which would utilize the Ag(,n('y's sl)a('(, transportation

kn()wledge base, facilities, and analysis tools. Subst,-

quently. Presidential Decision Dir(,('tiv(' NSTC-4 ledNASA to announ('(' a Coot)erative Agre(,m(,nt Not|(:(':'

to buihl a small r(,usabh' lamwh vehi('h, (RLV) desig-nated X-34.124 (; This was awarded to OSC, )eam('d

with R()ckw(dl Int(wnati()nal. in th(, St)ring ()f 1995.

By" February 1996, how('v('r. ()SC and R()('kw('ll had

,lotormined that venture w()uhl not b(, profitab[(' and

withdrew fronl th(' agreem('nt, r' s In th(' Sl)ring ()f 1996,

NASA solicited proposals f()r a different v(qtich,, also

designat(,d X-34. ()SC was awar(]od this contra('t inJune of 1996.

The 'new X-34 ix to be a sul)orl)ital t(,chnoh)gy

demonstrator, capal)h' of flying to Math 8. r(,aching

an altitud(, of 250,000 ft, and landing autonomously

on a conv(:ntional runway. A typi('al mission profih' is

sh()wn in Fig. 1. The v(qfich' is launched fi'om ()SC's

L-1011, ignites its ti(tuid rocket ongin(', asc(,nds to alti-tude, and then coasts to a down-rang(, landingY Thev('hM(, is to serv(' as a testb('d for a multitu(h' of RLV

to(:hnologies such as composite airfram(' and prop(q-

lant tank compon(mts, low-cost avionics via GPS. and

a flush air data systetll. Ill' 11

This paper presents results us('(t to (tefine anti (h'-sign the Thermal Protection System (TPS) necessary

_A ve,'y similar mission l)rolih' 1o lhe X-15 nearly forly years

[)I'('ViOIIS. 9

OF 1 2

:\MERI('AN INSTtTI'TE OF AERONAI'TI('S AND :\STRONAI'TI('S PAI'ER 98 ()Y,7!)

for tilt, vehMe's entry into the Earth's atinosphere.

This work is part of a larger effort used to design

tile TPS, including engineering codes, are-jet facilities,

and wind-(mural studies, v' t7 The TPS is predonfi-

nat ely insulation blankets |7 of the Flexible Reusable

Surface Insulation (FRSI) class with SIRCA tiles Hi

used only on the leading edges.

NASA Langtey's aerothermal contributions con-

sisted of several focused efforts. This paper de-

scribes three b benehn|ark-quality, full-vehicle, flight

condition comlmtations using state-of-the-art Com-

tmtational Fhfid Dynamics (CFD) to ascertain TPS

temperature limits. Riley et al, r2 anchored to these

two results, expanded the trajectory envelope using

a eoutfled im,iscid-boundary layer method. Incort)o-

rating the data from this lilnited array of trajectory

points, D, rurster et a114 develol)ed a time history of

heating rates for the entire trajectory using engineer-

ing ('odes. This analysis yields the heat load tbr over

sixty points on the vehMe, providing data necessary

to (leternfilU, the appropriate TPS thickness. In attdi-

tion to the above, Berry et al |a created an extensive

database with several wind tmmel entries, investigat-

ing effects of changing Mach munber, configuration,

angle of attack. Reynolds nunlber, and control s|n'face

deflections.

The remainder of this t)aper begins with a discus-

si(m of the numerical tool and geometry emt)loyed.

and is followed by a brief discussion of the traj(wtor.v

and the sele('te(t l)oints. Next are the results, con-

sisting of: a detailed description of the dominant flow

features, a comt)arison with experinmnt in the form

of surface shear l/atterns, an(1 surface temperatures,

heating rates, and pressures. Finally. a discussion of

TPS design issues are discusse(t, followed 1)3" some ('on-

eluding remarks.

Numerical Method

In the hyl)ersonic contimmm regime, the Lan-

gley Aerothernlodynmnic Upwind Relaxation Algo-

rithm (LAURA) CFD tool is' l:) is used to describe the

aerothermodynamies of X-34. LAURA is all uI)wind-

blase(t, point-iml)licit relaxation algorithm for o))tain-

ing the numerical soh|tion to the Reynolds-averaged

Navier-Stokes equations for three-dimensional viscous

hypersonic flows in thermo-chemical nonequilibrium. '-'°

The Ul)wind-biased invis('id flux is constructed using

Roe's flux-difference-splitting '-q and Harten's entropy

fix e'' with second-order corrections based on Yee's

symmetric total-variation-diminishing scheme. 2a This

is the same computational tool that has been used

to describe the aerothern|odynamics of t)hmt body

shat)es such as Mars Pathfinder, 2'|''''_ Mars Miero-

t)robe. _6 Stardust? 7 and COMET; 2s and other vehi-

cles such as X-33. 2'° HL-20, a° Spa(:(' Shuttle, al aa and

)'An additional case which (toes not include tile all l)orti(ln

of the vehicle is also presented.

a) Lee side view. b) Wind side view.

Fig. 2 X-34 geometry.

Reentry-F/4

For all of the results containe(t within, the LAURA

(:ode was run assuming air to behave as a perfect gas

and the fllll Navier-Stokes equations were slightly sim-

plified via tile thin-layer assumption (see Ref. 35 for

rationale). Furthermore, for nearly all the results pre-

sente(t, the flow was assumed to be flllty turbulent, us-

ing the Balwin-Lomax algebraic turlmlence too(tel :)'_''c

modified with a (tamping term according to Gupta et

a136 as implemented by Cheatwood. 37 However, se-

l(wte(l lanfinar results are also I)resented to I)ound the

l)rot)lem.

The wall-tenq)erature I)oundm'y condition is st)e('-

ifie(t as the radiation-equilibrium, wall temperature

accor(ling to the Stefan-Boltzniaml relation,

q = a_T '1. (l)

The radiat ive-equilibrimn wall teml)erature, T, is cou-

t)le(l during the solution procedure with the wall heat-

ing rate, q, where e is the surface emissivity d an(t a is

the Stefen-Boltzmmm constant.

This tout)led solution l)r()cedure between wall ten>

perature an(t wall heating rate yields ac('urate temt)er-

ature and heating rates I)ecause of the good insulation

features of the s(,lect(,d TPS blankets.

Geometry

Tile X-34 geometrical descriptioI! used in this study

is designated X0001215 as received fron! OSC in hfitial

Gral)hics Exchange St)ecifl(:ation (IGES) format. Fig-

ure 2 shows the X-34 geometry as modeled. Overall,

the vehicle is similar to the St)ace Shuttle, having a

cranked delta wing planform and vertical tail. Note,

however, that the fllselage transitions to rectangular

(:ross section approximately nfidway I)ack an(1 that the

wing ternfinates before reaching the aft end of the ve-

hicle. The vehMe is to weigh 45,000 lbs with fllll tirol

and have a wingspan, b, of 27.7 ft and an overall length,

L, of 58.3 ft.

The coordinate axes are defined in the typical body-

oriente(1 nlanner: :r running longitudinally, y along the

starboard wing, and z defiue(l by the right-hand rule,

pointing Ul)ward with the origin located at the nose. (`

('A higher-order turbulence nlodet (e.g., Sl)alart-Alhnaras or_-w) which may be more appropriale for the massively separatedflow on the lee side of the vehicle, was no! available in LAHtA

at the tinle of this study.

dA constan( enfissivity of 0.8 was used for all surfaces."OSC uses a ditferent origin lo(:ation.

2 OF 12

AMERI('AN INSTI'FUTE OF AEIIONAIITICS AND ASTRONAIrTI(_S PAPER 98 0879

Small modifications were made to the original ge-

ometry to allow more tractable grid generation and

facilitate obtaining the CFD solutions. These modifi-

cations consisted of the following:

• Backward or fl>rward facing steps created 1)y TPS

material interfaces such as that caused by tile

wing leading edge SIRCA tiles and tile trail-

ing AFRSI blankets were not preserved as sharp

steps. The surfac(' grid lines were mapped onto

the stepped surface, but no attempt was made to

align them with the discontinuities. As a result,

tile sharp steps are replaced by ramps.

• The span-wise gaps between tile elevens and the

body and the oh.wens and tile ailerons were filled

in as solid surfaces. Any other gaps or surface

irregularities have not been nto(Med. Past oxpe-

rience has shown that when elevens and ailerons

are slaved to move together as is the case for

the hypersonic portion of the x-a4's flight pro-

fih,. that th(, eff(_cts of tim gap b(,tw(!('n them is a

highly localized t)h(!noraenon as shown by Berry

et al.13 However, filling th(' gap between the body

and the elm'on has a larger (effect because it chan-

nels flow onto the aft portion of the vehicle which

would normally have pass('d through to th(" h'('-

si(to wak(!.

• Th(> lower, aft portion of the tail surfac(! ov(>r-

hanging the hack (>f the vehicle was clipped off to

provide a continuous sup(:rsonic outflow boundary

condition.

• The vehich' wake and base region including th('

engine nozzle and lee-side of the body flap were

neither ntodcled xlor eomput('d.

The surfac(! and volulIte nlcshes were gener-

ated using ICEMCFD, 3s GRIDTOOL, 39 GRIDGEN, IO

3DXlAGGS, |1 and VC:M _ as described by Alter. _3 A

typical full-vehicle grid including the body flap and

wing wake has a total of 70 blocks and 9 nfillion grid

points.

Trajectory Cases

Figure 3 shows stagnation-point heating rates, hot-

wall, for a 7.1 l inch radius sphere f as predicted by Fay

and Ridd(,ll theory for three different X-34 trajoetori('s

provided by OSC. The X10047(11 trajectory was used

by Pahner et a115 att(t Miles et al t6 to predict the

heating environment to be encountered by the nose

cap and wing leading edge SIRCA tiles. The X 1004601

traj(_ctory was used as the reference, heating trajectory

for the overall TPS design per OSC's request. Tim

actual flight trajectory is anticipated to be closer to

Xl003904.

:The nose radius of the X0001215 configuration.

r12, _

10

q 7

(BirdS.s)6

l

II

3

2

1

100 200

5, X1004601

---x,oo,,o,...........x,oo ,o,.

".. \\

'... \\

\,

f ___--L . _ :±f i J300 400 500 600

Time (s)

Fig. 3 Stagnation-point heating (hot-wall) for

three X-34 trajectories.

Tahle 1 on tit(., next pag(" presents the free-stream

conditions and control surfac(' deflections for th(' ('as('s

cotnputed, g The points shown in th(' Tabh' ar(' tak('n

from tile X1004601 trajectory and corr(,spond to peak

nose cap heating attd slightly th(,reafter when tit(- angh"

of attack is significantly low(:red.

Results

First. th(' d(mfinant flow fi('ld fl,atures are l)r('s('nted

and analyzed to provide a basis for the discussion of

tile results to follow. Next. a comparison with ex-

perimental data of Berry et a113 is given for Cas(- 2

conditions in the fl)rin of near-surfac(_ strvamlinos via

the oil-flow t(_chniqu('. Surfitee distributi(ms ()f t(unt)('r-

ature are presented n(-xt, followed by a samph' of the

associated heating rates and an example of the effects

of a laminar or turbulent boundary layer.

Tile results presented here are a subset of tit(- data

produced during this study; the fltll dataset is available

in Ref. 44 which also provides enlarged figures, mak-

ing some of the described Datures easier to discern.

Also note: discontinuities in the figures are a result of

block-to-block averaging errors when a block-marching

solution strategy was us('d. These errors ar_" a('sth('tic

only, th(" computational cell-c(mt('r('d valu('s ar(' gh)b-

all?" cons(,rvative and consistent across bh)ck-to-bh)ek

boundari('s.

Dominant Flow-field Features

Figure 4 on tile following page shows three

stream-wise cuts with contours of pressure non-

dimensionalized by free-stream, p, fl)r Case lb. Fig-

ure 4(a) also includes red lines indicating the location

of the other two stream-wise cuts and, in blue, the lo-

gNote: for Case 2b the solution w&s not eotnputed aft of the

wing trailing edge.

3 OF 12

AMERI(_AN INSTITUTE OF AERONAUTICS AND /\STRONAI;T|CS PAPER 98 087!)

Table 1 Free-stream conditions and control surface deflections.

Case(deg) (kft) (-) (deg) fit/s) (stug/ft a) (°F) (-)

la 0118.4 6.3 23 6490 1.42×10-" -22 16×106

lb 10

2a 0ll2.1 6 15.2 6110 1.89x10 -5 -30 21×106

2b 10

a) In the platte of wing leading edge and nose cap.

b) Vertically, along fuselage (2y/b=0.lS).

c) Vertically, along wing and strake (2y/b=0.30).

Fig. 4 Non-dimensional pressure contours for var-ious stream-wise cutting planes (Case lb).

cations of span-wise cuts that will be shown in Figs. 5

and 6 on tile next page.

As shown in Fig. 4(a), the forebody of the vehicle is

enveloped in a highly swept bow shock which intersects

with the wing-induced shock. As the flow passes the

Figure 4(b) depicts a stream-wise cut along the fuse-

lage outboard of the centerline. The wind-side bowshock is shown clearly. Also shown are the faint rem-

nants of the shock created by the deflected elevons;and, at the aft end of the vehicle, the embedded shock

due to the deflected body flap. The lee-side shock is

also apparent, although somewhat smeared due m a

highly stretched grid in this region. Toward the front,

on the lee-side, a small expansion-recompression is ev-

ident due to a TPS transition. This is followed by

a rapid expansion over the canopy region. A second,slight compression is also noticeable due to cross flow

effects fi'om the side of the fuselage. This is followed

by further expansion, until the point where the fuse-

lage transitions from a rounded cross-sectional shape

to one with a considerably smaller corner radius (see

Fig. 2(a) on page 2). At this juncture, a shock is gener-ated, which is then followed by a small expansion when

the transition is complete. The wake of the wing is re-

sponsible for the area of lowest pressure just ahead of

the tail which again raises the pressure slightly due toan embedded shock.

Figure 4((:) shows a stream-wise cut further away

from the centerline, but still well inside of the wing-

bow shock interaction. The shock generated by thedeflected control surface is readily apparent on the

wind side. Another dominant feature present is the

wake of the wing and strake which is altered by a fish-

tail shock structure emanating from the trailing edge

of the wing.

Span-wise cuts for Case lb are shown in Figs. 5

and 6 on the next page. h Figure 5 shows cross-flow

streamlines colored by pressure i and Fig. 6 shows Machnumber contours from 0.2 to 9.0 in increments of 0.2.

The first pair of sub-figures (5(a) and 6(a)) are takenon the forebody, .just behind the nose cap. A pair

of wind-side vortices is clearly seen near the center-line. There is no evidence of vortices on the lee side at

this axial station. The over-expansion and subsequent

compression is evident along the side of the fuselage.

A very different picture is evident in Fig. 5(b) which

shows a cross-section located near the wing trailing

hRecall, the relative vehicle locations are depicted by the bluelines in Fig. ,l(a).

wing tip the outer wing shock sweeps aftward due to iNo explicit scale is given; as with Fig. 4, blue indicates lowthe expansion, pressures while red indicates high pressures.

1 oF 12

AMERICAN [NSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 98-0879

\

i J i J I I

a) ])owil,SLl,(_,|i_ of _p}lCWiC_l] IIOSO cap (x/l, =0.0'| )

11 \

a) l)ownstroam of spherical nos_ cap (x_l. (),01).

I \ I

[ ! l lIll f I

b) Before wing t,railing edge {x/I.=0.79).

Fig. 5 Cross-flow streamlines colored by pressure

(Case lb).

f

?

t

/i

J

6.4

\

\

b) Befbre wing tr_tiling t_tge (x/l. 0.79)

Fig. 6 Mach contours (AM=0.2, Case lb).

5 OF 12

AMERI(rAN INSTITI;TE OF AERONALTICS AND ASTRONAISTIC5 PAPER 98 0879

Fig. 7 Streamlines colored by pressure in thevicinity of the body flap notch (Case la).

Fig. 8 Span-wise cross-sectional cuts showing den-sity contours along the aft of the vehicle and thebody flap (Case la).

(_(tge. There is no longer an3' evidence of the wind-

si(le vortices, and a pair of well-defined vortices sit

on the lee side of the fuselage. Small wing-tip vor-

tices are present, and the wing-strake vortices lie alongthe side of the fuselage. The source structure above

the wing at nfid-span is merely the demarcation of in-

board/outboard span-wise flow as well as the location

where the flow has either a positive or negative ver-

tical component. Also apparent is a small separation

bubble on the inboard wing lee side.On the wind side the embedded shock due to the

d('flected control surface is also clearly indicated by amerging of streamlines paralleling the deflected control

surfaces. Figure 6(b) also shows the presence of the ex-

t(msive hour-glass shaped cross-flow shock standing on

the fuselage. This shock serves to turn the flow parallelto the vehicle symmetry plane. The vertical gradients

in Math number between the cross-flow shocks (which

are not present in pressure see Fig. a(b)) are believed

to mark the entropy interface between flow that has

gone through only the bow shock and that which has

gone through both the bow and cross-flow shocks.Next, the flow field in the vicinity of the body flap is

examined with Figs. 7 and 8. Looking from the under-

side of vehicle, Fig. 7 shows the view in the vicinity of

the body flap notch r_,gion. The" vehicle ext_mds otf to

the right and the rest of the body flap continues to theleft. The back surface of the vehMe is truncated due to

the limited computational domain used to model this

region. Near-surface streanflines are shown color(_d by

pressure variation. A stream-wise-stagnation line is

clearly evident along the leading edge of the body flapnotch. This is created by the flow expanding around

the bottom, aft corner of the vehicle. In fact, as shown

by the series of span-wise cross-sectional cuts of den-

sity contours in Fig. 8, the flow is strong enough to

create an embedded shock along the leading edge of

the body flap notch. For this figure, the viewpoint is

from the top of the wing, looking aft towards the si&_

of the body flap (the body and body flap surfaces have

been removed). The first cross-section contains the aftend of the vehicle, with the following cross-sections in

the notched area, and the last cross section just after

the body flap regains its full span.

Note: since the grid topology in the notch region was

such that it was not possible to run the notch block

with the algebraic turbulence model as implemented,

this block was run using the laminar Navier-Stokes

equations. As a eonsequence, any surface wetted byflow emanating from the notch region has erroneous

surface temperatures. However, from investigations

comparing the purely laminar results and the nfixedturbulent-laminar results, the basic flow structure inthis area remains un-effected. This is fortunate since

Fig. 7 shows that there is a dividing streamline b_'-tween the flow which remains on the wind side and the

flow which travels onto the side wall and then returns

to the wind side. This serves to limit the contamina-

tion caused by the embedded laminar block.

Surface Shear Patterns Comparison withExperiment

Computer-simulated near-surface streamlines at

flight conditions are shown in Fig. 9 on the next page

for Case 2a, assuming a turbuhmt boundary layer.

Figure 10 on the facing page shows the correspondingoil flow from a Math 10 wind-tunnel run where the

attached flow over model is assumed to be laminar, la

While Mach 6 wind tunnel results are also available,

the Mach 10 data was chosen for comparison since the

normal-shock density ratio is more comparable to the

flight condition.

Comparing wind-side flow features_ both datasets

show similar indications of wind-side vortex patterns

(refer to Fig. 5(a) on the page before) scrubbing the

boundary layer toward the centerline on the forward

quarter of the vehicle. Forced by a span-wise pressuregradient generated by the nose geometry which tran-

sitions from a spherical cross section to a rounded,

triangular shape, the wind-side flow is initially con-

verging toward the centerline. After a quarter of thevehicle, the centerline boundary layer has thickened

6OF 12

AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 98 0879

and these wind-side vortices dissipate, establishing the

streamline patterns containing an outboard compo-

nent that dominate tile surface flow over tile latter

three-fourths of the vehicle. The surface discontinu-

ity at the wing-fuselage junction gives rise to a slight

change in the streamline patterns, more visible in the

experimental results. Both datasets show a divergence

of streamlines emanating from the wing-strake joint

which is next to the bow-shock imph_gement region.

The experim(ultal streamlines at the wing trailing edge

show some localized behavior due to the elevon gaps,

not present in the computational results, which did

not model tile elevon gaps.

Side-view comparisons show very good agreement,

particularly in the forebody patterns. Both datasets

show a strong cross-flow shock location and the sep-

aration line on tile fuselage caused by the vortex em-

anating from the strake. A strong interaction region

is seen, particularly in the computational solution, on

the fitselage aft of the wing trailing edge. There is a

bleed-through effect in this region on the experimental

model due to the elevon gap, which is not modeh_d ill

tim numerical simulation.

Lee-side surface features are in good agreement

between tile datasets, showing the strong cross-flow

shock separation on the fuselage and the strake vortex

across the wing, close to the fuselage. Inboard flow is

seen ow_r nmch of the wing while the fuselage shows

outboard flow, generated by a longitudinal recircula-

tion zone. Turning and separation, with a probabh"

horse-shoe vortex, occurs in front of the vertical tail.

Further comparisons with experimental data are

available in Ref. 13.

Surface Temperatures

This section presents the surface temperatures for

all turbulent boundary-layer cases computed: Cases

la, lb, 2a, and 2b. Discussion includes the effects

of angle-of-attack variation and control surface deflec-

tions.

Case la: Figure 11 on the following page shows sur-

face temp(,rature contours ,i for Case la. Th(' wind-sid("

JNote that t.here are three contour-level legends in the figin'e, one tin" each of the lee-side, sl,arbom'd, and win<l side views;but. these same three contour level distributions are held con

stant h)r all subsequent surface temperatm'e figures to fazilitate

C{ }III parisollS.

a) Wind side. a) Wind side.

b) Starboard side. b) Starboard side.

Fig. 9

(Case 2a).

c) Lee side.

Computed near-surface

c) Lee side.

streamlines Fig. 10 Oil flow for Mach 10 conditions from

Ref. 13 ( a = 15 deg., Re_ - 1.0 x 10_;).

7OF 12

AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAI;TICS PAPER 98-0879

T C°FJ

IOOO 1100 1200 1300 1400 1500 1500 1700

b) Starboard skle.

T toF)

100 500 _aO0 700 tOO 1100 1500 1500 I00 SO0 500 700 900 1100 1300 15Q0

c) Lee side.

Fig. 11 Surface temperatures (Case la).

c) l,ee side.

Fig. 12 Surface temperatures (Case lb).

view shown in Fig. 1 l(a) shows the expected high tem-

peratures fi_r the nose stagnation region. The forebody

chines also show significant temperature elevation dueto the vehicle's forebody geometry approaching the

bow shock generated by the spherical nose cap. Also

present on Fig. ll(a) are streaks of elevated tem-

peratures crossing the wings chord-wise. This corre-

sponds to the remnants of the forebody bow shock(cf. Fig. 4(a) on page 4). Also, although not read-

ily discernible with this choice of temperature contour

levels, there is a second streak emanating from the

bow shock-wing shock interaction point just outside

of the wing/strake .juncture, raked aft from the lead-

ing edge of the wing. This second streak is readily

apparent in the experimental results of Ref. 13. The

vast acreage of the wind-side fuselage surface is in the

range of 1300-1400 °F.

Note that the outside edges of the body flap haveslightly cooler temperatures than the inboard portion.

This area of cooler temperatures is associated withnear-surface streamlines that emanate from the lead-

ing edge of the notched body flap. This is trend is

erroneous as discussed on page 6.

The starboard and lee-side views (Figs. ll(b)

and 11 (c)) show the effects of several flow features pre-

viously discussed. For instance, between the canopy

and the round-to-squared fuselage transition, hmgitu-dinal low-temperature streaks are well defined, corre-

sponding to the pair of vortices located .just above the

fuselage. As mentioned previously on page 4, when

the fuselage cross-section transition is encountered, an

embedded shock is generated whk:h is indicated by the

triangular-shaped region of higher temperatures in thisarea.

Case lb: Surface temperatures for the deflected

control surface case (lb), are shown in Fig. 12. As

compared to the undeflected case, the temperatures

on the forebody are not effected by" the change dueto fact that the shock layer has supersonic flow. As

shown by Fig. 12(a) the deflected surfaces now expe-

rience 200-300 °F higher temperatures on their windsides.

For this case, the non-physical effect of having to run

the "notched" body flap region with the laminar equa-tions is more readily apparent than for the undeflected

case since the embedded body-flap-notch leading-e, dge

shock (refer to Fig. 8 on page 6) is stronger.

Although difficult to see in Figs. ll(b) and 12(b),

the wing wake is slightly larger for the deflected case.Also, the footprint of the wing fish-tail shock is at a

8oF 12

AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 98-0879

T (oF)

==

1000 1100 1200 1300 1400 1500 1800 1700

T (°F1

1000 1100 1200 1300 1400 1500 IS(X) 171110

a) Wind side.

T (I:1I

200 400 BOO O00 1000 1200 1400

a) Wind side.

T (flI

200 400 600 800 1000 1200 1400

b) Starboard side.

T (oF)

100 300 500 700 900 110013001500

b) Starbt,aM side.

T (_F)

100 300 500 700 900 1100 1300 1500

c) I,ee side.

Fig. 13 Surface temperatures (Case 2a).

c) Lee side.

Fig. 14 Surface temperatures (Case 2b).

lower angle relativ(" to the vehicle's longitudinal axis.

Case 2a: Surface temperatures for this lower-angle-

of-attack case are shown in Fig. 13. As compared with

Case 1, the wind-side temperatures are oil the order

of 250 °F lower while maintaining the" same qualita-

tive distribution, exe(!pt for the wing-shock/bow-shock

interaction occurring slightly closer to the fuselage.

Figs. late) and la(b), however, show increased heating

on the lee-side. Most notable are the nose region and

the tail leading edge. Th(_ fllselage transition area is

also slightly hotter. The wing-wake structure appears

to have higher energy as its temperature footprints are

on the order of a 100 °F higher than the higher-angle-

of-attack (:as(:. Tit(: terminating fish-tail shock also

appears stronger, refle(:ted by its more oblique angle.

Case 2b: The effects of deflecting the eleven con-

trol surface 10 deg. are shown in Fig. 14. As for Cases

la and lb, the forward portion of tit(: vehMe is not

effected by this change due to supersonic flow, and the

deflection simply results in higher wind-side tempera-

lures fur the flap (see Fig. 14(a)). However, for this

lower angle-of-attack case, there is a small area of flow

separation near the outboard end of the devon, result-

ing in slightly lower temperatures in tiffs area. This

is faintly visible in Fig. 14(a) as a sliver of blue along

90F 12

tit(' hing(- lilw b(-tw('en 70 and 80(/: st)an. Its t)r('senc('

is more clearly indicat('d by the conv(,x shape of th('

yellow-gr('en contour level on the elevens in this region.

Heating Rates

Figs. 11-14 have been presented in terms of tem-

peratures since this is tile most important quantity

to consider wh(_n ensuring that no TPS ten_p(,ratur('

lintits are violated. For the read('r, estimates of tim

corresponding heating rates can be derived from the

temperature distributions with Eq. 1 on page 2.

An example of an actual heating rate distribution is

shown in Fig. 15 on the next page k for Case 2t3. Tb("

heating-rate distributions for the ronmining cases art'

presented it). Ref. 44.

krl'|le dashed pattern of very low heating rates apparent on

the lee side of the fuselage (see I;ig. 15(c)) is due to an instabilit5' of the Baldwin-l,omax turbulence model when coupled withthe iterative, radiative equilibrium wall boundary condition in a

multiple-block context. An improved algorithm for determiningthe location of the maxiinum vorticity within the boundary layer

eliminat(yd this problenl in subsequeut runs. This particular cast,wa_ llOt re-colnputt'd due to limited resources and the fact that

most regions of interest are outside the domain of dependence.

AMERICAN INSTITUTE OF AERONAI:TICS AND ,,_tSTRONAISTI('S PAPER 98-0879

q (etuatLW

1 2 8 4. § 6 7 e 9 10111213

b) Starbom'd side.

q (eituAt'-iQ

0.1 0.2 0.4 0,6 0,9 1.4 2,! 3,3 5.2 6.0

b) Starboard side.

q (etu,_4}

0.1 0,2 0,4 10.6 0,9 1.4 2,! 3,3 5.2 iLO

c) Lee side.

Fig. 15 Heating rates (Case lb).

c) Lee side.

Fig. 16 Heating rates (Case 2h), laminar.

Boundary-Layer State

For Cases la and lb, both laminar and turbulent

boundary-layer solutions were obtained. This section

provides a brief synopsis of the effects of the boundary-

layer state, focusing on the deflected control surfaces

case, Case lb.

Figures 15 and 16 show surface heating rates for

turbulent and laminar boundary layers, respectively.

By comparing Figs. 15 and 16, it is immediately ev-

ident that the turbulent boundary-layer assumption

provides a more conservative estimate of the heating

rates than the laminar boundary layer. Overall, the

laminar heating rates tend to be half of those for the

turbulent boundary layer. However, as is also evident

if pressure distributions are examined, the qualitative

agreement is very close; signifying that most of the

heating patterns are determined by "inviscid" flow fea-

tures such as shocks and vortex cores.

TPS Considerations

As provided by OSC_ the general layout of the TPS

materials is given in Fig. 17, indicating the materials'

respective temperature limits while the TPS blanket

orientations is depicted in Fig. 18 on the facing page.

As a result of comparing the Case 2 temperature

u_( _ _ SIDE

W_DWARD

Fig. 17 Thermal protection system multi-use tem-

perature limits (°F).

distributions from Figs. 13 and 14 on the page before

and the TPS temperature limits shown in Fig. 17, the

bond line between the AFRSI and FRSI blankets on

the lec side neat" the wing leading edge was moved aft

to account for the increased exposure found at 15 degs.

angle of attack. The TPS treatment on the lee side of

10 OF 12

AMERICAN INSTITUTE OF AERONAUTICS AND ASTRONAUTICS PAPER 98-0879

J_ Leeward

Side

Acknowledgments

The authors wouhl like t() thank Gral)hic Artist

Richard Wheless of NCI Infornlation Systmns, Hamp-

ton, Virginia for generating Fig. 1 on page 1 and

Nornm Bean of Computer Sciences Corporation,

Hamilton, Virginia for generating the surface grid

database.

In addition, we would like to thank ()rbital Sciences

Corporation of Dulles, Virginia for providing the im-

petus for such an exciting project.

This paper was typeset in Donald Knuth's 10pt

Colnllllter .Modern using the free, multi-t)latform TEX

typesetting system and KM)'s aiaa t)acl,atge _r' (among

others).

Fig. 18 Thermal protection blanket layout.

the nose region was also changed fi)r this reason.

By cOral)re'ins l)redicted near-surface streamlines of

Fig. 9 on page 7, the TPS inateria[ layout in Fig. 17,and the TPS blanket orientations of Fig. 18. one can

investigate asl)ects of the TPS orientations. For ex-

mnple, Ul)On careflfllv examining thes(' figures, it is

evident that no blanket-tit:blanket or l)lanket-to-tile

gaps are aligned with the local flow.

Concluding Remarks

Radiative equilibrium surface teml)eratures, heating

rates, streamlines, surt.lce pressures, and flow-field fea-

tures as l)redi('ted by the LAITI{A (:(lilt' were i)resented

for tlt(' X-34 Technology Demonstrator. Results for

two traje('tory i)oints near I)eak heating and the (,f-

fects of control surfa(:e defter:\ions were l)r('sented for

fully turbulent flow. Laminar flow results were also

presented that illustrate tlt(' effects of the boundary-

layer state. The effects of the results on tlt(, TPS

design were also indicated. The presented results of

wall t eml)erature were use(l extensively t(i ensure that

the t emlmrature limits of the selected TPS bbmkets

will not be exceeded.

Results show that downward deflection of control

surfa('es sul)stantially increases the temt)eratures thcv

exl)erien(:e (luring flighl. Furthermore, a "n()t(qmd"

body Ha l) design (:reates an emi)edd(,d sho(:k whi(:h ('re-

ates large heating rat('s on the tal)ered t)ortion of the

body-flap si(le wall.

Tit(' effe(:t (if h)werillg tit(' angle of attack flom 23

to 15 (leg. at flight conditions was shown to substan-

tially increase tim extellt of lee-si(le heating on the

nose-canot)y region and aft of the wing leading edges.

Also shown was that using turl)u]eIH I)()undary-layer

heating results is ('onsiderat)ly more (:onservative than

using results which mo(M a fully laminar boundary

layer.

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