NASA/TP-2001-210398

Thermostructural Analysis of

Unconventional Wing Structures of a

Hyper-X Hypersonic Flight Research

Vehicle for the Mach 7 Mission

William L. Ko and Leslie Gong

NASA Dryden Flight Research Center

Edwards, California

October 2001
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NASA/TP- 2001-210398

Thermostructural Analysis of

Unconventional Wing Structures of a

Hyper-X Hypersonic Flight Research

Vehicle for the Mach 7 Mission

William L. Ko and Leslie Gong

NASA Dryden Flight Research Center

Edwards, California

National Aeronautics and

Space Administration

Dryden Flight Research Center

Edwards, California 93523-0273

October 2001
NOTICE

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Space Administration.

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ABSTRACT

Heat transfer, thermal stresses, and thermal buckling analyses were performed on the unconventional

wing structures of a Hyper-X hypersonic flight research vehicle (designated as X-43) subjected to

nominal Mach 7 aerodynamic heating. A wing midspan cross section was selected for the heat transfer

and thermal stress analyses. Thermal buckling analysis was performed on three regions of the wing skin

(lower or upper); 1) a fore wing panel, 2) an aft wing panel, and 3) a unit panel at the middle of the aft

wing panel. A fourth thermal buckling analysis was performed on a midspan wing segment. The unit

panel region is identified as the potential thermal buckling initiation zone. Therefore, thermal buckling

analysis of the Hyper-X wing panels could be reduced to the thermal buckling analysis of that unit panel.

"Buckling temperature magnification factors" were established. Structural temperature-time histories are

presented. The results show that the concerns of shear failure at wing and spar welded sites, and of

thermal buckling of Hyper-X wing panels, may not arise under Mach 7 conditions.

NOMENCLATURE

a

b

CL

C

P

E

E23

E33

E43

FR

FX

JLOC

k

LTA

SPAR

SS

T

Treat

rn

L,

length of rectangular plate, in.

width of rectangular plate, in.

clamped boundary condition

specific heat, Btu/lb-°F

Young's modulus, lb/in 2

two-nodes bar element

triangular combined membrane and bending element

quadrilateral combined membrane and bending element

panel edge supports allowing free in-plane motion (free)

panel edge supports with no in-plane motion (fixed)

joint location (node)

thermal conductivity, Btu/hr-ft-°F

Lockheed Thermal Analyzer

Structured Performance and Resizing

simply supported boundary condition

temperature, °F

average temperature for material properties, °F

temperature at node n

peak temperature of dome-shaped temperature distribution, °F

panel boundary heat sink temperature, °F

uniform temperature distribution, °F
TPATH

TPS

t

VIEW

( )c,-

a

c

7/

C

)vo

V

P

o-f

o-_r

o-x

o-y

rf

_'m_

Dryden computer simulation program

thermal protection system

time counted from the air-launching of Pegasus booster rocket from B-52, sec.

computer program to compute view factors, see equation (1)

critical buckling value at buckling

coefficient of thermal expansion, in/in-°F

emissivity

= (ro)cr/(ru)cr,BUckling temperature magnification factor ofthefirst kind = buckling

temperature (To)cr of dome-shaped temperature loading (fixed or free support condition)

divided by the buckling temperature (T,,)c r of uniform temperature loading (fixed

support condition).

eigenvalue associated with uniform temperature loading

eigenvalue associated with dome-shaped temperature loading

Poisson's ratio

= (To)cr/(To)cr [ T s = 0 Buckling temperature magnification factor of the second

kind = buckling temperature (To)cr of dome-shaped temperature loading case with any heat

sink temperature T s _ 0 (free support condition) divided by the buckling temperature (To)cr

of dome-shaped temperature loading case with zero heat sink temperature T s = 0 (free

support condition)

density, lb/in 3

uniaxial tensile failure stress, lb/in 2

ultimate tensile strength, lb/in 2

chord-wise stress, lb/in 2

yield strength, lb/in 2

sheer failure stress, lb/in 2

maximum shear stress, lb]in 2

INTRODUCTION

Hypersonic flight vehicles are subjected to severe aerodynamic heating during flights. To maintain

structural integrity at these high temperatures, the vehicle structural design concepts for high Mach

number vehicles are different from those of low Mach number aircraft. The vehicle structure may be

called "hot" structures or "warm" structures, depending on the operating temperature range. The hot

structures are fabricated with high-temperature materials and are capable of operating at elevated

temperatures exceeding 1000 °F. Typical hot structural components are carbon/carbon composite

2
structures,hat-stiffened panels fabricated with either monolithic titanium alloys or metal-matrix

compositematerials,andhoneycombsandwichpanelsfabricatedwith high-temperaturematerialssuchas

Titanium,or nickel-basedInconel® (Inco Alloys International,Inc., Huntington,WestVirginia) alloys.

Thewarm structuresarefabricatedwith light-weightmaterialssuchasaluminumandmustbe insulated

sothat the sub-structuraltemperatureswill not exceedthe operatingtemperaturelimit of 350 °F. The

spaceshuttleorbiteris agoodexampleof warm structure.Theentirevehicleis protectedwith athermal

protection system (TPS) to shield the aluminum substructurefrom overheatingbeyondthe warm

temperaturelimit (ref. 1).

An exampleof a recenthot structureis thenew hypersonicflight researchvehiclecalledHyper-X

(designatedastheX-43 vehicle),which hasunconventionalwing structureswith irregular-shapedwing

panels(describedin thefollowing section).

Temperaturedistributions in the hot structuresare, in general,not uniform becauseof cooler

substructuresuchassparsandribs.Thenonuniformityof the structuraltemperaturedistributioninduces

thermalstresses.Excessthermalstressescouldcausevehiclewing panelsto buckleandcreep,andcould

alsocausethe skinandsparweld sitesto losebondingintegrity.A uniform temperaturefield inducesno

thermal stressesin structuresfabricatedwith materialsthat have the samecoefficient of thermal

expansion.Thermalbucklingproblemsareof greatconcernfor bothhot andwarm structures,andhave

beenextensivelystudiedby Ko (refs. 2-11).Thosepastthermal buckling studieswere conductedon

rectangular-shapedhoneycombsandwichand hat-stiffenedpanels,andnot on irregular-shapedpanels

suchastheHyper-X wing panels.

To fully understandthethermostructural_erformanceof theunconventionalHyper-Xwing structures

undernominalMach7 aerodynamicheating, heattransferanalysis,thermalstressanalysis,andthermal

bucklinganalysismustbeperformed.Thisrequirescomplexthree-dimensionalmodelingof theHyper-X

wing structures.However,without goingthroughcomplexmodelingof theentirewing structure,onecan

usea simplemethodto quickly approximatethepanelbucklingtemperaturesof wing panels.Thisreport

presentstheresultsof heattransferanalysisandthermalbuckling analysisof wing structuresusingsuch

anapproximationmethod,anddiscusseshow theHyper-Xwing structureswouldperformundernominal

Mach7 heating.

Use of tradenamesor namesof manufacturersin this documentdoesnot constitutean official

endorsementof suchproductsor manufacturers,eitherexpressedor implied,by theNationalAeronautics

andSpaceAdministration.

HYPER-X FLIGHT RESEARCH VEHICLE

Hyper-X (designated as X-43) is a new hypersonic flight research vehicle (12 ft long, 5 ft span,

3,000 lb weight), designed to be flown at a range of Mach 7N10 (fig. 1). The underside of the vehicle

consists of an inlet ramp, a scramjet (supersonic-combustion ramjet) engine module, and an expansion

ramp. The scramjet engine is an air-breathing ramjet engine in which the airflow through the whole

engine remains supersonic. The Hyper-X scramjet engine uses hydrogen as fuel and inlet air as oxidizer

(no oxidizer is carried on board). The proposed flight trajectory of Hyper-X is shown in figure 2. The

Hyper-X rides on a winged Pegasus booster rocket, which is carried under the wing of a B-52 aircraft up

*It should be noted that the maximum Mach number reached during the nominal Mach 7 mission was 7.5.

3
to alaunchaltitudeof 17,000ft. for theMach7 missionor 43,000ft for theMach 10mission.After air

launchingfrom the B-52, the Pegasusboosterrocket will accelerateand ascendto an altitude of

approximately100,000ft, reachingthetest velocity (of Mach7 or Mach 10).After separationfrom the

boosterrocket, the cowl door of the Hyper-X scramjetengineopensto test the performanceof the

scramjetengine.Oncethecowl dooris open,fuel is injected,ignitedandburnedfor about8 seconds.The

entireeventfrom theopeningto theclosingof thecowl doorlastsfor 34seconds.

The Hyper-X wing structure is fabricated with high-temperatureHaynes 230 alloy (a

nickel-chromium-tungsten-molybdenumalloy) which has relatively low thermal expansion

characteristics.The designconceptof its wing structures(fig. 3) is entirely different from that of the

conventionalwing structures.The conventionalsparand rib systemis replacedwith multiple radial

stiffeners(spars,0.25in. wide) fanningoutfrom thepivoting wing roots.To housetheinstrumentation

insidethewing structure,upperandlower wing skins(0.090inchesthick) aredividedinto two separate

wing panels(a fore wing panelandan aft wing panel).The wing panelsarethenbutt-weldedat their

edgesto the main wing frame, and line-welded to the radial reinforcing stiffeners without using

conventionalfasteningscrewsor rivets. Becausethe edgesof the heatedwing panelsareconstrained,

potentialthermalbuckling of the wing panelsandpossibleshearingoff of the line-weldedsitesareof

greatconcern.

DESCRIPTION OF PROBLEM

Heat transfer and thermal stress analyses are to be performed on the midspan segment of the Hyper-X

wing (fig.3). A nominal Mach 7 aerodynamic heating is to be used as heat input to calculate time histories

of structural temperatures. The worst-case non-uniform temperature distribution obtained from the heat

transfer analysis is to be used for temperature loads to calculate thermal stresses in the wing segment.

Thermal buckling analysis is to be performed on the following three regions of the wing skin panels

(lower or upper): 1) the fore wing panel, 2) the aft wing panel, and 3) a unit panel at the middle of the aft

wing panel (fig. 3). In addition, thermal buckling is also to be conducted for the wing segment (fig 3).

These analyses are being done to locate the thermal buckling initiation zone.

The unit panel is used to establish buckling temperature magnification factors (1) to scale up the

buckling solution of uniform temperature loading for generating a buckling solution for dome-shaped

temperature loading; or (2) to scale up the buckling solution of dome-shaped temperature loading with

unheated boundary heat sinks for generating a buckling solution for the same case when the heat sinks are

heated up.

HEAT TRANSFER ANALYSIS

The finite-difference heat transfer analyses of Hyper-X wing structures are performed using the

Lockheed Thermal Analyzer (LTA). The LTA is a generalized FORTRAN program that computes

transient temperature distributions in complex structures based on an electrical analogy of capacitors and

resistors.

4
Finite-Difference Thermal Modeling

The Hyper-X wing segment selected for the heat transfer analysis is located at the wing midspan,

approximately 4.7 in. from the wing root edge (fig. 3). The chord-wise region lies between the

stream-wise distances 11.0 in. and 18.0 in. measured from the carbon/carbon leading edge, and spans

over three neighboring radial stiffeners (or spars) (fig. 3).

Two finite-difference thermal models (fig. 4) were generated for two cases of welded site skin and

spar contacts; 1) full contact, and 2) partial contact (inset of fig. 4). The two thermal models are identical

(fig. 4) except for the contact resistance between the skin panels and radial stiffeners. Each model

consists of 64 capacitors modeling Haynes ® 230 ® (Haynes International, Kokomo, Indiana) alloy. Outer

structural mold lines use a 1.5 degree half-angle for both upper and lower skins. For the full contact, the

wing skin panels are perfectly bonded to the full width (0.25 in.) of the stiffeners. For the partial contact,

the welded site is 0.040 in. wide and 0.01 in. thick. The resistance between capacitors {1 and 66}, {13

and 70}, {25 and 75}, {69 and 41}, {74 and 53}, and {79 and 65} (fig. 4) were calculated for 1) full

contact conductance, or 2) partial contact conductance representing a 0.040-inch-width contact area. The

partial contact case is a more realistic representation of the actual skin and spar welded sites. The thermal

models have a surface emissivity of e = 0.85. The external radiation view factors were calculated by

hand, but the internal radiation view factors were calculated from the VIEW program (described below).

The input thermal properties of Haynes 230 alloy are listed in Table A- 1 of the Appendix.

Internal Radiation View Factors

The internal radiation view factors were calculated from the VIEW program, which is incorporated

into the Structural Performance And Resizing (SPAR) finite-element computer program (ref. 12). Figure

5 shows the two SPAR finite-element radiation models generated for the internal view factor

computations. Each model has 63 internal radiation elements. Each of the radiation elements matches the

interior surface of each corresponding element of the finite-difference thermal model (fig. 4).

In the computations of internal radiation view factors using the VIEW program, two cases were used:

the combined case and the separate case. For the combined case, the entire wing segment was considered

as a single enclosure with obstruction at the middle spar (fig. 5-a). For the separate case, each bay was

considered independently as an enclosure without obstructions (fig. 5-b).

For case one, the radiation element numbering was started from bay 1 and continued on bay 2, (not

independently numbered for each bay). The command OBSTRUCT was used to define the obstructing

surfaces, which are the two sides of the middle spar (i. e., elements 12, 13, 14, 15, 16, 59, 60, 61, 62, 63)

(fig. 5-a). The ENCLOSURE command was used to identify the system of radiation surfaces as an

enclosure, and to correct the calculated view factors so that the sum of the view factors from each

radiation element is equal to unity. Namely, if Fij (i, j = 1, 2, 3 ..... ) is the radiation view factor defined as

the fraction of radiant heat, leaving radiation element i and incident on radiation element j, then the

ENCLOSURE command will enforce the following condition for the final values of Fij.

___Fij = 1 (1)

J

where the summation is taken overj for each given i.

5
Forcasetwo, theinternalradiationview factorswerecomputedindependentlyfor eachbayusingthe

VIEW command.For this case,theradiationelementsarenumberedindependently(startingfrom No. 1)

for each bay (fig. 5-b). Becausethere is no obstructionwithin each bay, the ENCLOSURE and

UNOBSTRUCTcommandswereused.The commandOBSTRUCTwasnot needed.The abovetwo

approaches(fig. 5-a, 5-b) gaveidentical internal view factor solutions,thusverifying the accuracyof

view factorcalculations.

Heating Profile

Figure 6 shows the preliminary flight trajectory for the Mach 7 mission of the Pegasus booster rocket

carrying the Hyper-X vehicle. The maximum Mach number of the flight trajectory turned out to be 7.5

(fig.6-c). This was the flight trajectory available at the time of this analysis and was, therefore, used to

calculate the aerodynamic heating rates. The Dryden in-house computer code called TPATH was used for

these calculations. Various parameters for inputs to the TPATH code are: time histories of altitude, angle

of attack, and Mach number (fig. 6) as well as the outer mold-line geometry of the wing cross section.

The program calculates transient heating rates and surface temperatures, and also computes heat transfer

coefficients, boundary layer recovery temperatures and other parameters required to calculate the

aerodynamic heating rates. The program permits the use of different theories for calculating the heat

transfer coefficients. These theories can be properly applied at each location of interest for laminar or

turbulent flow condition, or for flows with transition. The transition condition can be input as a function

of Reynolds number and local Mach number, or prescribed at a specific time. In the present analysis, the

transition criteria used resulted in turbulent flow calculations for the entire flight profile. Local flow

conditions were calculated for an attached flow using the oblique shock theory (ref. 13). Heat transfer

coefficients were calculated using Eckert's reference enthalphy method (refs. 14, 15). Calculations were

made for the upper and lower surface of the horizontal wing. Real gas properties of air were used in all

calculations (ref. 16). Heat transfer coefficients and recovery temperatures calculated from the TPATH

code were then used as inputs to the LTA. This thermal analyzer program then calculated the heating

rates and corresponding structural temperatures for the two-dimensional thermal models.

THERMAL STRESS ANALYSIS

The SPAR finite-element computer program (ref. 12) is used in the linear thermal stress analysis of

the wing segment. The following sections discuss finite element modeling, boundary constraints, and

temperature load.

Finite Element Modeling

The wing segment selected for the thermal stress and thermal buckling analysis is located at the wing

midspan cross section where the heat transfer analysis is performed (fig. 3). The wing segment has a unit

span-wise width, and spans over three neighboring radial stiffeners (spars) in stream-wise direction. The

finite-element structural model generated for the wing segment is shown in figure 7. The wing panels and

the spars are modeled with a single row of quadrilateral combined membrane and bending elements (E43

elements). The nodal coordinates of the finite-element structural model are made coincidental with those

of the finite-difference thermal model (fig. 4). Thus, the nodal temperature output from the thermal model
canbeuseddirectly astemperatureinput to the structuralmodel.Only oneweldedsiteatthetop of the

middlespar(radialstiffener)is modeledin detailfor shearstresscalculations(insetof figure 7). Thewing

skin and sparweldedsite is modeledwith E43 elementswhoselower boundariesareconnectedto the

middle spar (E43) elementthrough triangular membraneand bendingelements(E33 elements).To

simulatetheeffectof stream-wisethermalexpansionrestraintresultingfrom the coolerwing frame,the

nodesof thethreeradial stiffenersareinterconnectedwith two nodes(E23barelements).Thesizeof the

finite-elementstructuralmodelfor thewing segmentis listedin Table 1.

Table1. Numberof joint locationsandelementsof

wing-segmentfinite-elementmodel.

Item Number

JLOC 166

E23elements 20

E33elements 8

E43elements 95

Thetemperature-dependent materialpropertiesof Haynes230 usedfor input to the structuralmodel

arelistedin theAppendix.

Boundary Constraints

The wing-segment model is allowed to expand freely in all directions. The span-wise edges of the

wing panels are constrained to have zero slopes in the span-wise direction to simulate the effect of

continuity to neighboring regions.

Temperature Load

The structural temperature distribution at time t = 89 sec (from launch of the Pegasus booster)

obtained from the heat transfer analysis is used as thermal load input for the thermal stress analysis. Time

t = 89 sec is the instant when the difference between the upper and lower skin peak temperatures reaches

a maximum. As will be seen later, this structural temperature distribution over each bay is arch-shaped.

7
THERMAL BUCKLING ANALYSIS

The SPAR program is also used for the linear thermal buckling analysis of the wing panels. The

following sections discuss material property iterations, finite element modeling, boundary conditions,

temperature load, and buckling temperature.

Material Property Iterations

In thermal buckling analysis, when high accuracy buckling solutions are sought, the material

property iteration process is required. This iteration process is described in great detail in ref. 17.

Initially, the buckling temperature is still unknown and, therefore, the material properties at a certain

assumed temperature (usually room temperature) are first used as input. Once the first-iteration buckling

temperature is calculated, the material properties corresponding to the first calculated buckling

temperature are input to the second iteration of eigenvalue calculations. This material iteration process

(updating material properties) must continue until the temperature used for the input material properties

converges with the final buckling temperature. In the present buckling study, the material iteration

process (averaging 5 - 7 iterations) for each case was terminated when the assumed material temperature

approached the calculated buckling temperature with less than 0.5 percent error.

Finite Element Modeling

The wing-segment model (fig. 7) is also used for thermal buckling analysis. Figure 8 shows the three

finite-element models (called the fore panel model, the aft panel model, and the unit panel model)

generated respectively for the fore wing panel, aft wing panel, and the unit panel located at the middle of

the aft wing panel (fig. 3). All the wing panels are modeled with E43 elements. The boundary heat sinks

and radial stiffeners are modeled with E23 bar elements. The sizes of these three wing finite-element

models are listed below.

Table 2. Number of joint locations and elements of wing-panel

finite-element models.

Fore panel model Aft panel model Unit panel model

JLOC 3116

E23 elements 350

E43 elements 3000

2419 984

276 126

2320 920
Boundary Conditions

Different supportconditionslistedbelowareconsideredfor comparativestudiesof how thebuckling

temperatureschangewith thesupportconditions.

Table3. Definition of supportconditions.

PanelBoundaries PanelandStiffenerWeldedSites

SS-SS simply supported simplysupported

SS-CL simply supported clamped

CL-SS clamped simplysupported

CL-CL clamped clamped

Basedonthefactthatthe Hyper-Xwing panels(fig. 4-b)areline-welded,the SS-SSconditionlisted

in Table3couldbetheclosestto theactualsupportconditionof theHyper-X wing panels.

Temperature Load

The thermalload inputsusedareuniform temperatureloading and dome-shaped(or arch-shaped)

temperatureloading.

Uniform Temperature Loading

Because the actual temperature distributions over the entire wing surfaces are not available, uniform

temperature loading will be analyzed first. Figure 9(a) shows an example of a typical uniform

temperature loading case for the unit panel. The uniform nodal temperature input is chosen to be

T = T u = 1 °F. The eigenvalue )vc (scaling factor) calculated from the SPAR program will then give the

buckling temperature (Tu)cr. Namely,

(Tu)cr = Xc x I°F (2)

This buckling solution is for the uniform temperature loading over the wing panels with fixed

supports, and is not the actual case. This buckling solution is the simplest fundamental case, and can

show the location of the weakest bay, where thermal buckling is likely to take place. When the panel

boundaries can have free in-plane motion (free supports), the uniform temperature loading case obviously

can not induce thermal buckling.

Dome-Shaped Temperature Loading

Hot structural panels are usually fastened to the cooler substructures (of relatively large mass) that

function as heat sinks. Thus, even under a uniform surface heat flux, the temperature distribution over the

9
hotpanelswill not beuniform, but dome-shaped(ref. 18).This is thetypical behaviorof hot structural

panels.

For the wing segment,the calculateddome-shapedtemperaturedistribution obtained from the

wing-segmentheattransferanalysisis usedasthetemperatureloadinput.

For the two-dimensionalwing panels,temperaturedistribution over the wing surfacemust be

calculatedfrom heattransferanalysisby themodelingof onecompletewing structure.In orderto avoid

thatcomplexity,thefollowing quick approximationmethodwill beused.

Becausethecoolersparsfunctionasheatsinks,thecalculatedtemperaturedistributionovereachbay

is expectedto bedome-shapedbasedonpasthot structuralexperiments(ref. 18).By observation(fig. 3),

theunitpanelthathasthelargestareacomparedwith othersub-panelsmustbethe weakestsub-panelin

resisting thermal buckling. Therefore, buckling analysis of the entire wing panels under actual

temperatureloadingcan thenbe reducedto the analysisof the unit panelthat is underdome-shaped

temperatureloadingto obtainapproximatebuckling solutions.

As will beseenshortly,the stream-wisedistribution of paneltemperatureovereachbayexhibitsan

arch-shapedcurve (a crosssectionalshapeof a dome surface) because of the existence of heat sinks

(cooler radial stiffeners). Such an arch-shaped curve is very similar to part of the sine curve. Therefore,

for the two-dimensional case, dome-shaped temperature distribution could be a good approximation of

the actual surface temperature distribution over any unit panel that is supported by boundary heat sinks.

For a rectangular plate with length a and width b, the dome-shaped temperature distribution (with

peak temperature T O and boundary heat sink temperature Ts) may be ideally described by the following

equation.

. a:x KY

T(x,y) = T s + (T O - Ts) sin-- sin--

a b

(3)

which gives a sine × sine surface lifted by an amount T s.

Equation (3) may be applied directly to the irregular-shaped unit panel by simply distorting the

boundaries and mesh of the finite-element model generated for the rectangular plate to form the irregular

boundaries and mesh of the unit panel model. Thus, the nodal temperatures T(x,y) calculated from

equation (3), will automatically provide the nodal temperatures for the unit panel model. Figure 9(b)

shows the dome-shaped temperature loading over the unit panel calculated from equation (3). For the

Hyper-X case, the ratio of averaged heat sink temperature Ts to the wing panel maximum temperature T O

is roughly Ts/T o = 0.54 at time t = 89 sec.

For the dome-shaped temperature load input to the SPAR program for the eigenvalue calculations, the

peak temperature T o = 1 °F was used. The heat sink temperature T s was allowed to vary over the range

Ts/T o = 0-1 (i.e., Ts/T o = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.54, 0.6, 0.7, 0.8, 0.9, 1.0; with

Ts/T o = 0.54being the Hyper-X case). The buckling temperature (To)cr for the dome-shaped

temperature loading case is then obtained from

(To)cr = /_o × l°F (4)

10
where/_ois theeigenvaluecalculatedfrom theSPARprogramfor thedome-shapedtemperatureloading

case.The reasonfor using the wholerangeof Ts/T o = 0 - 1 is to study the effect of the heat sink

temperature Ts on the panel buckling temperature (To)cr. Keep in mind that the panel buckling

temperature (To)cr will increase with the increasing heat sink temperature Ts as a result of relaxation of

the thermal expansion constraint exerted on the unit panel by the boundary heat sink.

Buckling Temperature Magnification Factors

As will be seen shortly, the buckling temperature (To)cr for the dome-shaped temperature loading

case is much higher than the buckling temperature (Tu)cr of the uniform temperature loading case (with

fixed supports). Therefore, a buckling temperature magnification factor of the first kind rl defined below

(To)cr

- (5)

(Tu)cr

will be used to indicate how many times the buckling temperature (To)cr of the dome-shaped temperature

loading case (free or fixed supports) is magnified from the buckling temperature (Tc)cr of the uniform

temperature loading case with fixed supports (fundamental case).

In reality, the wing panel attempts to expand under heating, but its expansion is resisted by the cooler

boundary substructures (heat sinks) which expand less. This boundary constraint is the cause of thermal

buckling of the wing panels. Such substructure constraints will gradually relax as the substructures are

heated up, resulting in a higher panel buckling temperature. In order to find out how the heat sink

temperature T s affects the panel buckling temperature (To)cr for the dome-shaped temperature loading

case with free supports, another buckling temperature magnification factor of the second kind _ defined

below

(To)cr

= (Zo)crlw = °

(6)

will be used to indicate how many times the buckling temperature (To)cr for the dome-shaped temperature

loading case with free support (SS or CL) is magnified when the heat sink temperature T s increases from

T s = 0 (no heat sink thermal expansion) to a certain non-zero value T s _ 0 (with heat sink thermal

expansion).

RESULTS

The results of the heat transfer analysis, thermal stress analysis, and thermal buckling analysis of the

Hyper-X wing structure subjected to Mach 7.5 heating (the nominal Mach 7 mission) are presented in the

following sections.

11
Heat Transfer

Figure 10 shows the time histories of nodal temperatures {T13(t), T70(t)} at nodes {13, 70} of the

middle spar upper welded site (fig. 4) for the full and partial contact cases. The nodal temperature

difference (T13 - T70 ) is slightly higher for the partial contact case, and it reached a maximum value of

(T13 - T70 ) = 150°F at approximately t = 83 sec. into the flight profile.

Figure 11 shows the time histories of nodal temperatures {T53(t), T74(t)} at nodes {53, 74} of the

middle spar lower welded site (fig. 4) for the two cases of contact conditions. Although the nodal

temperature difference (T53 - T74 ) at the lower weld site is less severe than (T13 - T70 ) of the upper weld

site, it is still substantial. For the partial contact case, the lower welded site nodal temperature difference

(T53 - T74 ) reached a maximum value of (T53 - T74 ) = 130 °F at approximately t = 123 sec into the

flight profile.

Shown in figure 12 are temperature time histories at locations down the middle spar and along the

upper skin panel. The temperature gradient along the skin panel (between capacitor 13 and 14) appears to

be greater than the temperature gradient from capacitor 13 to 70, but the distance between the two

capacitors is longer. The temperature gradient per inch between capacitor 13 and 70 is actually larger.

Temperature time histories on the upper skin panel can be seen in figure 13. The temperature gradient

between capacitor 13 and 15 is higher than the gradients between capacitors 13 and 17 or 13 and 19.

Distance between capacitors 13 and 15, 15 and 17, and 17 and 19 is 0.5 inches apart. Figure 14 shows

nodal temperature time histories for node 7 of bay 1 upper skin and node 46 of bay 1 lower skin. Note

that AT = T 7 - T46 reached a maximum value, AT = 546 °F at t = 89 sec. As can be seen in the next

figure, node 7 and node 46 are respectively the peak temperatures of the upper and lower skins.

Figure 15 shows the chord-wise distributions of the upper and lower skin temperatures at t = 89 sec

into the flight profile. These temperature distributions were calculated from the thermal model with

partial contact at the spar and skin weld sites. As can be seen from figure 15, the temperature distributions

are steepest near the spars (heat sinks). Note that the panel temperature distribution over each bay is

arch-shaped. This is the typical behavior of hot structural panels supported by the boundary heat sinks.

The structural temperatures at typical points of the wing segment at t = 89 sec are listed in Table 4. The

upper and lower wing skin temperatures listed are the peak temperatures of each bay.

Table 4. Structural temperatures at typical points of wing segment; t = 89 sec, °F

Fore Baylskin Middle Bay 2 skin Aft

weld site (peak) weld sim (peak) weld site

Upper 675 1,153 748 1,127 638

Lower 479 607 476 592 418

Notice that the designed flight trajectory caused the Hyper-X upper skin temperatures to be

significantly higher than the lower skin temperatures. This implies that buckling is more critical for the

upper wing panels than the lower wing panels. The panel temperature distributions of figure 15 and the

12
associatedspartemperatures(not shown)were usedastemperatureinputsto the structuralmodel for

thermalstressandthermalbucklinganalysesof thewing segment.

Thermal Stress Analysis

The calculated chord-wise thermal stresses o-x induced in the wing-segment skins under free

expansion (to simulate actual situation) are listed in Table 5.

Table 5. Chord-wise stresses crx in the wing-segment skins; free expansion, lb/in 2.

Front bay Rear bay

Upper skin -64,900 -61,364

Lower skin -37,419 -31,938

Because the chord-wise thermal expansion of the wing panels are restrained by the cooler wing frame

(heat sink), both upper and lower wing panels of each bay are under compression. Even though the

temperature distribution over the wing panel of each bay is non-uniform and arch-shaped (fig. 15), the

thermal stress induced in the wing panel of each bay is constant. This is the typical behavior of hot

structural panels.

Figure 16 shows the deformed shape of the welded site under compression from wing panels of

opposite bays, with element shear stresses indicated. The maximum shear stress Z'max is located at the

aft upper corner element of the welded site (fig.16) with the value Z'max = 38,564 lb/in 2. The

temperature at the middle spar upper welded site was calculated as T = 748°F at t = 89 sec. The

shear failure stress zf at this temperature level is approximately _)-= 54,000 lb/in 2 for Haynes 230

alloy. This value is one-half of the uniaxial tensile failure stress o)- = 108,000 lb/in2 at T = 748°F

based on Mohr's circle. Based on this current simple stress analysis, the maximum shear stress Z'max at

the weld site will reach as high as 71 percent of the shear failure stress z'f during Mach 7.5 heating.

Thermal Buckling Analysis

The results of thermal buckling analysis of the Hyper-X wing panels are presented in the following

sections. On average, about 5N7 material iterations were required to obtain acceptable buckling solutions

presented in these following sections.

Uniform Temperature Loading

Figures 17, 18, and 19, respectively, show the buckled shapes of the fore panel, aft panel and unit

panel under uniform temperature loading and under different fixed support conditions. Note that, except

for the SS-CL condition, the aft panel buckled at the unit panel region, and the buckled mode in this

region (fig. 18) is similar to the buckled mode of the isolated unit panel (fig. 19). The buckling

13
temperaturescalculatedfor thosewing panelmodelssubjectedto uniform temperatureloadingareshown

in Table6.

Table6.Bucklingtemperatureof differentwing-panelmodels

underuniformtemperatureloading;fixed supports,(T,)cl, °F.

Support

condition Forepanel Aft panel Unit panel

SS-SS 167 121 97

SS-CL 176 188 239

CL-SS 355 175 114

CL-CL 410 294 295

Thebuckling temperatureslisted in Table6 arefor the uniform temperatureloadingoverthe wing

panelandnotfor theactualtemperatureloading.Becauseof thefixedboundarysupportsandfixed panel

and stiffenerjoint site, the buckling temperaturesareamazinglylow. Note that, exceptat the SS-CL

condition,theaftpanelhaslowerbucklingstrengththanthefore panel,andthebucklingcritical regionis

locatedattheunit panelregionof theaftpanel(fig.18).

In reality, thepanelsupportsites(heatsinks)canexpandwhenheated,resultingin the reductionof

thermalstresslevelsin the wing panelsasa resultof reducedheatsink restraint.Therefore,the actual

bucklingtemperaturescouldbemuchhigherthanthevaluespresentedin Table6.

Dome-Shaped Temperature Loading

Figures 20 and 21 show, respectively, the buckled shapes of the wing segment under actual

temperature loading (fig. 15) with fixed and free stiffeners. Note that the buckling mode of the wing

segment is very similar to that of the fore panel with the CL-SS condition (fig. 17-c). The calculated

buckling temperatures of the wing segment with fixed and free supports are shown in Table 7. The

uniform temperature loading case is also included in that table for comparison.

Table 7. Buckling temperatures of wing segment panel

under actual and uniform temperature loading.

(Tu)cr , °F (To)cr , °F 77

Uniform FX 260 ..... 1.00

Actual FX ..... 389 1.50

Actual FR* ..... 1,324 5.09

* Closest to actual case

14
The wing segmentmodelhasonly onerow of E43 elementsin the span-wisedirection.Thus,the

buckling solutiontermed"actualFR" in Table7 may not be accurateenoughto representhe buckling

temperatureof the two-dimensionalwing panel. However, Table 7 can show how the "buckling

temperaturemagnificationfactor of thefirst kind" 77changeswith thethermalloadingandtheboundary

condition.Noticethat thebuckling temperaturefor the actualFR caseis magnifiedby 5.09timesfrom

theuniform FX case.

Theunit panelwasidentifiedasthepotentialthermalbucklinginitiation zonebasedontheresultsof

the uniform temperatureloadingbuckling analysis(fig. 18and Table 6). Therefore,thermal buckling

analysisof theHyper-X wing panelsmay bereducedto the thermalbuckling analysisof theunit panel

without going through complex modeling of the entire wing structure.Figures 22 and 23 show

respectively the buckled shapes of the unit panel under dome-shapedtemperature loading

(Ts/T o = 0.54, Hyper-X case) with fixed and free supports. For the fixed supports (fig. 22), the unit

panel buckled into single half-waves in two different directions, one along the radial stiffeners and the

other transverse to these radial stiffeners. But for the free support case (fig. 23), it buckled into two

half-waves along the radial stiffeners. Table 8 shows buckling temperatures of the unit panel under

dome-shaped temperature loading (Ts/T o = 0.54, Hyper-X case) with different support conditions.

The values of the 77are also listed in the table. Data given in Table 6 for the uniform temperature loading

case are also listed for comparison.

Table 8. Buckling temperatures of unit panel; Ts/T o = 0.54 (Hyper-X case).

Uniform FX Dome-shaped FX Dome-shaped FR

Support (To)cr, °F 77 (To)cr, °F 77 (To)cr, °F 77

SS-SS 97 1.00 132 1.36 1.389" 14.32

SS-CL 239 1.00 357 1.49 2,290° 9.58

CL-SS 114 1.00 147 1.29 1,411 12.38

CL-CL 295 1.00 412 1.40 2,298° 7.79

* Closest to Hyper-X case

• Approaching melting range 2,375 °F N 2,500 °F of Haynes 230 alloy

Note that for the fixed supports, by changing the temperature loading from uniform to dome-shaped, the

values of 77are in the range of 1.29 _<77_< 1.49 for all the support fixed conditions (low magnification in

thermal buckling temperatures). However, for the dome-shaped temperature loading with free supports,

the 77 values reached as high as 7.79 _<77_< 14.32 range, implying a great magnification of buckling

temperatures. The dome-shaped temperature loading with the SS-SS free support condition (closest to the

Hyper-X case) has the highest 77value (77 = 14.32) and the CL-CL case has the lowest 77value (77= 7.79).

For the SS-CL and CL-CL cases, the buckling temperatures (indicated with solid dot in Table 7)

approached the melting range 2,375°F - 2,500°F of the wing panel material. The buckling temperature

1,389 °F of the unit panel under the dome-shaped-free-SS-SS support condition (quite close to the

buckling temperature 1,324 °F of the wing segment panel), could be a reasonable approximation to the

15
actual buckling temperature of the aft wing panel of the Hyper-X. The buckling temperature 1,389 °F of

the unit panel is 1.20 times the calculated peak temperature 1,153 °F of the wing panels (fig.14). Thus, it

is unlikely that the Hyper-X wing panels will buckle during the nominal Mach 7 flight trajectory.

Table 9 andl0, respectively, show the buckling temperatures of unit panels under simply supported

and clamped freely expandable boundaries subjected to dome-shaped temperature loading with different

heat sink temperatures. The 77and _ are also listed.

Table 9. Buckling temperatures of unit panel under dome-shaped temperature loading;

simply supported free boundaries.

Ts/T o O. 0.1 0.2 0.3 0.4 0.5 0.54* 0.6 0.7 0.8 0.9 1.0

(To)cl,°F 826 872 971 1,067 1,189 1,352 1,389 1,458 1,732 2,507e 4,866e _o

1.00 1.06 1.18 1.29 1.44 1.64 1.68 1.77 2.10 3.04 5.89 _o

77 8.52 8.99 10.01 11.00 12.26 13.97 14.32 15.03 17.86 25.85 50.16 _o

oExceeded incipient melting point 2,345 °F of Haynes 230 alloy.

*Hyper-X

Table 10. Buckling temperatures of unit panel under dome-shaped temperature loading;

clamped free boundaries.

Ts/T o O. 0.1 0.2 0.3 0.4 0.5 0.54* 0.6 0.7 0.8 0.9 1.0

(To)cr, °F 1,294 1,385 1,408 1525 1661 1,857 1,942 2,141 2,763e 4,333e 8,447e _o

1.00 1.07 1.09 1.18 1.29 1.44 1.50 1.65 2.14 3.35 6.53 _o

77 4.39 4.69 4.77 5.17 5.63 6.29 6.58 7.26 9.37 14.69 28.63 _o

•Exceeded incipient melting point 2,345 °F of Haynes 230 alloy.

*Hyper-X

The solid dot symbols in both Tables 8 and 10 indicate that the buckling temperatures have exceeded

the melting range 2,375 °F - 2,500 °F of the wing panel material. At Ts/T o = 1 for which the

dome-shaped temperature distribution degenerates into uniform (flat) temperature distribution, the

buckling temperatures reached infinity, implying that thermal buckling does not occur. Note that at

Ts/T o = 0 in Tables 9 and 10 (no heat sink thermal expansion), the buckling temperatures

{ (To)cr = 826 °F, (To)cr = 1,294 °F} for the free simply supported and free clamped cases are much

higher than the corresponding buckling temperatures {(To)cr = 132 °F, (To)cr = 412 °F} for the

fixed support cases (Table 8). This results from the fact that for the free support cases, the unheated heat

sink still can deform elastically because of the thermal expansion of the unit panel, causing the buckling

temperatures to be much higher.

16
For the simply supported case (Table 9), 77is related to 4 through

(r°)cr - 89 4 = 8.524 (7)

rI - (Tu)cr

And, for the clamped case (Table 10),77 is related to 4 through

(To)cr 1294

77 - (T)cr - 295 4 = 4.394 (8)

The simply supported case has the numerical coefficient for 4 roughly twice of that for the clamped

case (right-hand sides of equations (7) and (8)).

The data shown in Tables 9 and 10 are plotted respectively in figures 24 and 25 for easy visualization

of how the buckling magnification factors 77 and 4 increase with the increasing heat sink temperature

Ts/T o . The 77curve for the clamped free boundary case lies much below that for the simply supported

free boundary case (fig. 24). The 4 curves (fig. 25) for the simply supported and clamped free boundary

cases are quite close (Tables 9, 10). At Ts/T o = 1, the dome-shaped temperature distribution

degenerates into uniform temperature distribution, and the buckling temperatures reach infinity (i.e., no

buckling). Both figures 24 and 25 are very useful for finding the value of 77or 4 associated with heat sink

temperature Ts/T o at certain time steps after the launching.

CONCLUSIONS

Heat transfer, thermal stress, and thermal buckling analyses were performed on the Hyper-X wing

structure for the Mach 7 mission. The key results of the analyses follow.

1. The maximum temperature differential between the upper and lower skins of the Hyper-X wing

occurs at 89 sec after air launching from the B-52 aircraft. The profile of temperature distribution

over the wing panel of each bay is dome-shaped.

2. The maximum shear stress "Cmax at the welded site is estimated as "Cmax = 38,564 lb/in 2, and is

about 71 percent of the shear failure stress of the welding material.

3. By identifying the unit panel region as the potential thermal buckling initiation zone, thermal

buckling analysis of the Hyper-X wing panels may be reduced to the thermal buckling analysis of

the unit panel without going through complex modeling of the entire wing structure.

4. The estimated buckling temperature of the unit panel is (To)cr = 1,389 °F which is 1.20 times

higher than the peak temperature 1,153 °F experienced by the wing panels under Mach 7.5

heating. This unit panel buckling solution may be considered as a reasonable estimate for the

buckling temperature of the Hyper-X wing panels. This result suggests that Hyper-X wing panels

are unlikely to buckle during a Mach 7 mission.

5. "Buckling temperature magnification factor of the first kind" 77 was established to scale up the

panel buckling temperature in the uniform temperature loading case to estimate the panel buckling

temperature of the dome-shaped temperature loading case.

17
. '"Buckling temperature magnification factor of the second kind" _ was established to scale up the

panel buckling temperature in the dome-shaped temperature loading case with unheated boundary

heat sinks to generate a solution for the same case when boundary heat sinks are heated.

Dryden Flight Research Center

National Aeronautics and Space Administration

Edwards, California, April 12, 2001

18
APPENDIX

The temperature-dependent physical properties of Haynes 230 used for input to the thermal and

structural models are listed in the following tables (Haynes International, Inc., Kokomo, Indiana).

Table A-1. Thermal properties of Haynes 230.

T, °F Cp, Btu/lb °F k, Btu/hr-ft °F e

70 0.095 5.167 0.85

200 0.099 5.917 0.85

400 0.104 7.250 0.85

600 0.108 8.500 0.85

800 0.112 9.833 0.85

1000 0.112 11.083 0.85

1200 0.134 12.333 0.85

1400 0.140 13.667 0.85

1600 0.145 14.917. 0.85

1800 0.147 16.250 0.85

19
Table A-2. Material properties of Haynes 230; p = 0.324 lb/in 3.

T, °F E x 106,1b/in 2 o-r × 10 3, lb/in 2 Cry × 10 3, lb/in 2 a × 10 -6, in/in-°F v*

70 30.6 125.4 57.4 7.0 0.310

200 30.1 (122.2) (55.0) 7.1 0.311

400 29.3 (117.3) (51.3) 7.2 0.315

600 28.3 (112.3) (47.7) 7.4 0.318

800 27.3 (107.4) (44.0) 7.6 0.321

1000 26.4 102.5 40.3 7.9 0.324

1200 25.3 97.7 39.5 8.1 0.330

1400 24.1 87.7 42.5 8.3 0.332

1600 23.1 63.1 37.3 8.6 0.334

1800 21.9 35.2 21.1 8.9 0.340

2000 20.7* 19.5 10.8 9.2* 0.343

* Estimated; ()Interpolated

REFERENCES

.

.

.

.

.

20

Ko, William L., Robert D. Quinn, and Leslie Gong, Finite-Element Reentry Heat Transfer Analysis

of Space Shuttle Orbiter, NASA Technical Paper 2657, December 1986.

Ko, William L. and Raymond H. Jackson, Compressive Buckling Analysis of Hat-Stiffened Panel,

NASA TM-4310, August 1991.

Ko, William L. and Raymond H. Jackson, Shear Buckling Analysis of Hat-Stiffened Panel, NASA

TM-4644, November 1994.

Ko, William L. and Raymond H. Jackson, Thermal Behavior of a Titanium Honeycomb-Core

Sandwich Panel, NASA TM-101732, January 1991.

Ko, William L. and Raymond H. Jackson, Combined Compressive and Shear Buckling Analysis of

Hypersonic Aircraft Structural Sandwich Panels, NASA TM-4290, May 1991. Also published as

AIAA Paper No. 92-2487-CP, in the proceedings of the 33rd AIAA/ASME/ASCE/AHS/ASC

Structures, Structural Dynamics and Materials Conference, Dallas, Texas, April 13-15, 1992
.

.

.

.

Ko, William L., "Mechanical and Thermal Buckling Analysis of Sandwich Panels Under Different

Edge Conditions," Pacific International Conference on Aerospace Science and Technology

Conference Proceedings, Vol. H, Tainan, Taiwan, December 6-9, 1993.

Ko, William L., Mechanical and Thermal Buckling Analysis of Rectangular Sandwich Panels under

Different Edge Conditions, NASA TM-4585, April 1994.

Ko, William L., Prediction of Thermal Buckling Strengths of Hypersonic Aircraft Sandwich Panels

Using Minimum Potential Energy and Finite Element Methods, NASA TM-4643, May 1995.

Ko, William L. and Raymond H. Jackson, Combined-Load Buckling Behavior of Metal-Matrix

Composite Sandwich Panels Under Different Thermal Environments, NASA TM-4321, September

1991.

10.

11.

12.

13.

14.

15.

16.

17.

18.

Ko, William L. and Raymond H. Jackson, Compressive and Shear Buckling Analysis of Metal

Matrix Composite Sandwich Panels under Different Thermal Environments, NASA TM-4492, June

1993. Also presented in Composite Structures, Vol. 25, July 1993, pp. 227-239.

Ko, William L., Thermostructural Behavior of a Hypersonic Aircraft Sandwich Panel Subjected to

Heating on One Side, NASA TM-4769, April 1997.

Whetstone, W. D., SPAR Structural Analysis System Reference Manual, System Level 13A,Vol. 1,

Program Execution, NASA CR- 158970-1, December 1978.

Moeckel, W. E., Oblique-Shock Relations at Hypersonic Speeds for Air in Chemical Equilibrium,

NACA TN-3895, January 1957.

Eckert, Ernst R. G., Survey of Boundary Layer Heat Transfer at High Velocities and High

Temperatures, WADC TR-59-624, Wright-Patterson AFB, Ohio, April 1960.

Zoby, E. V., Moss, J. N., and Sutton, K., "Approximate Convective-Heating Equations for

Hypersonic Flows," J. Spacecraft and Rockets, vol. 18, no. 1, Jan./Feb. 1981, pp. 64-70.

Hansen, C., Frederick, Approximations for the Thermodynamic and Transport Properties of

High-Temperature Air, NASA TR R-50, 1959.

Ko, William L., Mechanical- and Thermal-Buckling Behavior of Rectangular Plates With Different

Central Cutouts, NASA/TM-1998-206542, March 1998.

Richards, W. Lance and Randolph C. Thompson, Titanium Honeycomb Panel Testing. NASA TM4768, October 1996. Also presented at Structural Testing Technology at High Temperature

Conference, Dayton, Ohio, Nov. 4-6, 1991.

21
/-

 e asus Hyper-X booste_/

Interstage / _

adapter ---1 "_

010132

Figure l. Hyper-X hypersonic flight research vehicle mated to the

launch vehicle Pegasus ® booster rocket.

100,000

Altitude,

ft

Pegasus /

booster /

rocket ---I

F Hyper-X free flight

/ /_ Experiment completion

,_=_ _ (t= 105.00sec)

_SCrar?jet e9gi ne _ u esce nt

tat(t= 1.50sec

Hyper-X booster

separation (t = 89.00 sec)

Booster burn-out

(t = 85.50 sec)

Energy

maneuvers to

reduce speed/

energy

Air launch (t = 0.0 sec) (over water)

End of flight

(t = 728.66 sec)

Distance 010133

Figure 2. Hyper-X hypersonic flight research vehicle flight trajectory.

22
Aft wing panel

Figure 3. Unconventional wing structures of Hyper-X hypersonic flight research vehicle.

23
Full contact OR _ Partial contact

 oo0,n

t T _o.o, in.

0.25 in.

__ Upper skJnJ t

/ 0.09 in.

| i

_/0.04 in.

_Spar

al stiffener)'_

0.25 in.

_,_,,. Typical welded site /_ _,

- ^ 7 8 9 10"_1_'12, 14_'_5"_6 17 18 19 20 21 22 23 24 25

1 2 3 4 b b _ " 75

_-_ Bay 1 [_]ii Bay 2 [_]77

_5; 56 57 58 59 60 61 6"2 63 64 i5

"---Fore spar Mddl _ 64 ca acitors i espar P Aft spar

010135

Figure 4. Finite-difference thermal model for Hyper-X wing segment;

welded site dimensions in inches, full contact and partial contact.

(a) Combined case.

010137

(b) Separate case.

Figure 5. SPAR finite-element models for computations of internal radiation view

factors.

24
100,000

80,000

60,000

Altitude,

ff

40,000

20,000

20

15

10

Angle

of attack, 5

deg

0

-5

-10

0

8

7

6

5

Mach 4

number

3

2

1

I I

25 50 75 100 125 50

Time from air launch, sec

010138

(a) Altitude.

Hyper-x

separation

=89.0sec--] S

I I I I

25 50 75 100 125 150

Time from air launch, sec

010139

(b) Angle of attack.

Hyper-X

separation

t = 89.0 sec

I I I

25 50 75 100 125 150

Time from air launch, sec

010140

(c) Mach number.

Figure 6. Nominal Mach 7 mission flight trajectory of the Pegasus booster rocket carrying the Hyper-X

vehicle for heating calculations.

25
.... ded

Middle spar _ \_E33 eleme\_....__ nts

\\(not to scale)

\

\

\

E23 elements I

-- Bay 1 I Bay 2

Middle spar Aft sparFore spar 010141

JLOC 166

E23 elements 20

E33 elements 8

E43 elements 95

Figure 7. SPAR finite-element structural model for Hyper-X wing segment.

26
E23 elements 350

E43 elements iiii

(a) Fore panel model.

JLOC 2419

E23 elements 276

E43 elements 2320

(b) Aft panel model.

(c) Unit panel model

JLOC 984

E23 elements 126

010144

Figure 8. Three types of finite-element models for Hyper-X wing skins.

27
7"

0_0_4_

28
4OO

3OO

2OO

1CO

0

Partial

contact

_:.... '_ Node 70 !i .e_, :_,:

0 50 83 100 150

Time from air launch, sec

010147

Figure 10. Nodal temperature time histories at the middle spar upper welded

site; nodes 13, 70.

14OO

1300 -

I I" • • I'I'I 'I"I'_

•., oo ,A,,-:..::-

1000 53-x /_./' \

900

800

Temperature,oF 700 600 - Node 53_./// i , ._:,:ii////" 500 i_

400 300 _- Partial contact--v, " _i_

200? _:.... .... "--Full . .

1O0 __;";;_' contact

o __1 I

0 50 1O0 123 50

Time from air launch, sec

010148

Figure l l. Nodal temperature time histories at the middle spar lower welded

site; nodes 53, 74.

29
1400

1300 _--13 14

1200 Middle .\ C._'-_.. 15 Node

1100 spar_ 15

1000 _ .-.................. _2;.;

X_7o ," 14 ......',_

900 72 ,, .........................................Sf. .

Temperature, 800 , ... z,."

oF 700 ,'/" 13_

600 , .,' .-" ,-z

J ."". ".. j ),

500 ''" "" '" /

400 ,,,," .,' ,.'" ,-_

jy" /" j /

300 .... ," ,'/"

F/.. "" --." j" j

lOO "- ,

o

0 50 100 150

Time from air launch, sec

010149

Figure 12. Nodal temperature time histories in the vicinity of the middle

spar upper welded site.

Temperatu re,

OF

1400

1300

1200

1100

1000

900

800

700

600

500

400

300

200

100

0

0

Node

19

. ,.:.j2.'---2 k-- 222;-2 L"22---2--- -

.;_" 17

,/

.......... 15 ................. ) /"

It,, ,

t,;

,,,/.,,:;;,

t/

/," / . _ _--15

./_y_/////_---13 / /2-17rl 9

50 100 150

Time from air launch, sec

010150

Figure 13. Upper skin nodal temperature time histories near the middle spar

upper welded site.

30
1800 1700 ........................................

1600 - " _ .................

1500 7_ ,'/"......

1400 41 4243 4445 46 4748 49 5051 52 5354 5556 57 5859 60 6162 63 64 65 ,*"

1300 /'

1200 _.. 1100

Temperature, 1000 AT = 546 °F_/_'4 y/

oF 900 800 /"1

700 Node 7--_ / _"/_-- Node 46 600

200300400500100 _ ................ /I

0 50 89 100 150

Time from air launch, sec

010151

Figure 14. Nodal temperature time histories for node 7 of bay 1 upper skin

and node 46 of bay 1 lower skin.

1200

1153 ....

1100 t _ ?/_ /-Upper

skin

1000

900

Temperatu re,

OF 800

700

600 I _ /--Lower

_/_ _*'_///_"_/ skin

500 ""__Fore spa r v__ Middle spar _,/ /-Aftispar

400

0 1 2 3 4 5 6 7 8

Chord-wise distance, in.

010152

Figure 15. Chord-wise distributiuon of Hyper-X wing segment skin

temperatures; t = 89 sec, 0.04 in. web contact.

31
U.... Flow direction

_',_._' _ Compression

element

_a,_)...\/y _

"_'T/- _'°°'_- o_

Figure 16. Deformed shape of welded site with element shear

stresses indicated, lb/in2; Mach 7.5 heating (nominal Mach 7

mission).

32
(a) SS-SS condition. 010154

(b) SS-CL condition.

010155

(c) CL-SS condition.

010156

(d) CL-CL condition.

Figure 17. Buckled shapes of fore pane/ under different

conditions, uniform temperature loading. fixed

010157

support

33
010158

(a) SS-SS condition.

(Tu)cr = 188 °F

(b) SS-CL condition.

(Tu)cr = 175 °F

........ </: ////./-/.-G",

, , , , , , ' ,' .' , " ," ," ," <','<_,:d_,c_<::_:::<::<:<: : : / :" I I /L_. 010160I

(d) CL-CL condition.

Figure 18. Buckled shapes of aft panel under different fixed support

conditions, uniform temperature loading.

34
010162

(a) SS-SS condition.

010163

(b) SS-CL condition.

010164

(c) CL-SS condition.

j 010165

(d) CL-CL condition.

Figure 19. Buckled shapes of unit panel under different fixed support

conditions, uniform temperature loading.

35
(Tu)cr = 389 °F

010166

Figure 20. Buckled shape of wing segment under actual temperature loading

at t = 89 sec, fixed stiffeners.

(Tu)cr = 1,324 °F

010167

Figure 21. Buckled shape of wing segment under actual temperature loading at

t = 89 sec, free stiffeners.

36
010168

(a) SS-SS condition.

010169

(b) SS-CL condition.

010170

(c) CL-SS condition.

010171

(d) CL-CL condition.

Figure 22. Buckled shapes of unit panel under different fixed support

conditions, dome-shaped temperature loading, Ts/T o = 0.54.

37
010172

(a) SS-SS condition.

010173

(b) SS-CL condition.

j 010174

(c) CL-SS condition.

38

010175

(d) CL-CL condition.

Figure 23. Buckled shapes of unit panel under different free support

conditions, dome-shaped temperature loading, Ts/T o = 0.54.
6O

55-

50-

45-

--"-- Simply supported free boundaries

Clamped free boundaries

O0

O0 4o35

q 3O

25 Hyper-X '

20 It ./// '

15 /'

10 ___./_- I ..//J

5 ...................... 0.54

I I

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

Ts/To 010176

Figure 24. Plots of buckling temperature magnification

factors ofthefirst kind, q, as functions of boundary heat

sink temperature Ts/T o .

8

7

6

5

4

3

2

1

--"-- Simply supported free boundaries j,co

Clamped free boundaries T

/ll/i/°

-- III

Hyper-X //'

I //

I/-o.54

I I I/ I I I I

.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0

Ts/To 010177

Figure 25. Plots of buckling temperature

magnification factors of the second kind, 4, as

functions of boundary heat sink temperature Ts/T o .

39
REPORT DOCUMENTATION PAGE FormApproved

OMB No. 0704-0188

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORTTYPE AND DATES COVERED

October 2001 Technical Publication

4.TITLE AND SUBTITLE 5. FUNDING NUMBERS

Thermostmctural Analysis of Unconventional Wing Structures of a

Hyper-X Hypersonic Flight Research Vehicle for the Mach 7 Mission

6. AUTHOR(S)

William L. Ko and Leslie Gong

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

NASA Dryden Flight Research Center

RO. Box 273

Edwards, California 93523-0273

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

National Aeronautics and Space Administration

Washington, DC 20546-0001

WU 710-55-24-E8-RR-00-000

8. PERFORMING ORGANIZATION

REPORT NUMBER

H-2453

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA/TP-2001-210398

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified--Unlimited

Subject Category 39

This report is available at http://www.dfrc.nasa.gov/DTRS/

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

Heat transfer, thermal stresses, and thermal buckling analyses were performed on the unconventional

wing structures of a Hyper-X hypersonic flight research vehicle (designated as X-43) subjected to

nominal Mach 7 aerodynamic heating. A wing midspan cross section was selected for the heat transfer

and thermal stress analyses. Thermal buckling analysis was performed on three regions of the wing

skin (lower or upper); 1) a fore wing panel, 2) an aft wing panel, and 3) a unit panel at the middle of

the aft wing panel. A fourth thermal buckling analysis was performed on a midspan wing segment. The

unit panel region is identified as the potential thermal buckling initiation zone. Therefore, thermal

buckling analysis of the Hyper-X wing panels could be reduced to the thermal buckling analysis of that

unit panel. "Buckling temperature magnification factors" were established. Structural temperaturetime histories are presented. The results show that the concerns of shear failure at wing and spar welded

sites, and of thermal buckling of Hyper-X wing panels, may not arise under Mach 7 conditions.

14. SUBJECTTERMS

Buckling temperature magnification factors, Hyper-X wing,

Non-uniform temperature loading, Thermal buckling

17. SECURITY CLASSIFICATION

OF REPORT

Unclassified

NSN 7540-01-280-5500

Irregular panels,

18. SECURITY CLASSIFICATION

OFTHIS PAGE

Unclassified

19. SECURITY CLASSIFICATION

OF ABSTRACT

Unclassified

15. NUMBER OF PAGES

43

16. PRICE CODE

A03

20. LIMITATION OF ABSTRACT

Unlimited

Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102