Mechanical and Thermal Properties of Chiral...

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Mechanical and Thermal Properties of ChiralHoneycombs

Alessandro Spadoni

Massimo Ruzzene

School of Aerospace EngineeringGeorgia Institute of Technology

Atlanta, GA

USNCTAM 06 25-30 June 2006, Boulder, CO

Thermal protection systems (TPS) must fulfill multiple requirements:

• thermal

• aeroelastic

• light-weight

• damage tolerance

• maintainability (current space shuttle TPS requires 40,000 man-hours for each flight) [1]

[1] Morris, W. D., White, N. H., Ebeling, C. E.: “Analysis of Shuttle Orbiter Reliability and Maintainability Data for Conceptual Studies,” 1996 AIAA Space Program andTechnology Conference, 1996, Huntsville, AL, AIAA 96-4245.

BACKGROUND

Stainless steel honeycomb used to hold leeward ablative material.

Apollo Capsule

Early concepts of metallic heat shielding configurations developed for shuttle program [2].

Shuttle Program TPS Concepts

[2] Groninger, B.V., Shideler, J. L., Rummler, D. R.: “Radiative Metallic Thermal Protection Systems: A Status Report,” Journal of Spacecraft and Rockets, Vol. 14, No. 10,October 1977, pp. 626-631.

BACKGROUND

[3] Bouslog, S. A.; Moore, B.; Lawson, I.; and Sawyer, J. W.: “X-33 Metallic TPS Tests in NASALaRC High Temperature Tunnel.” AIAA Paper 99-1045, 37th AIAA Aerospace Sciences Meeting and Exhibit, Jan. 1999.

Improved TPS Concepts Spawned by X 33 Program

Typical X-33 metallic TPS panels [3]

A prepackaged superalloy honeycomb TPS concept [4]Latest TPS concept [5]

[4] Blosser, M. L.: “Development of Metallic Thermal Protection Systems for the Reusable Launch Vehicle,” NASA Technical Memorandum 110296

[5] Blosser, M., Chen, R., Schmidt, I., Dorsey, J., Poteet, C., and Bird, K.: “Advanced Metallic Thermal Protection System Development”, AIAA-2002-0504, 40th AIAA Aerospace Sciences Meeting and Exhibit, January 14-17, 2002, Reno, NV.

OUTLINE

• Discussion of previous work on heat transfer through honeycombs

• Development of a geometrically explicit finite-element model (FEM) for transient heat transfer

• Compare initial FEM model with analytical solutions for problem at hand

• Discussion of heat transfer modes for a refined FEM model

• Parametric analysis and comparison of chiral and hexagonal honeycombs

• Eigenvalue analysis for the estimation of flat-wise compressive strength of considered honeycombs

COMPARISON OF DIFFERENT HONEYCOMB CORES BY NASA [6]

• Temperature input (as opposed to heat flux) external radiation is neglected.• Temperature input is comparable to heating rate from space re-entry [6].• Performance of honeycomb core investigated in terms of temperature

response history.• Core and face sheet material is Inconel 617 alloy.

[6] Ko, W. L.: “Heat Shielding Characteristics and Thermostructural Performance of a Superalloy Honeycomb Sandwich Thermal Protection System (TPS) ”, NASA/TP-2004-212024

Best heat shielding performance, although cell geometry is found not to affect performance significantly[6].

Variation of hexagonal honeycomb geometry with angle

HEXAGONAL HONEYCOMB UNIT CELL GEOMETRY

= -27° = 0 ° = 30 °

Variation of chiral geometry with L/R ratio

CHIRAL HONEYCOMB AND UNIT CELL GEOMETRY

Lr2tan

Rr2sin

L/R = 0.60 L/R = 0.90

L/R = 0.95

Fourier’s Law: heat flux ,

Heat equation: Power generated per unit volume

Heat equation 1-D (no power generated):

thermal conductivity , [ W/m-k ]

thermal diffusivity [ m2/s] density , [ Kg/m3] Specific heat , [ J/Kg-K ]

Assumed solution:

Non-homogeneous boundary condition

Homogeneous b.c.’s: if and

homogeneous P.D.E

Resulting governing eq.: Non-homogeneous P.D.E

Separation of variables:

ANALYTICAL 1-D CONDUCTION MODEL

ANALYTICAL 1-D CONDUCTION MODEL (Cont’d)

Relative density

Face-sheet area imposed equal

CORRELATION OF HONEYCOMB GEMOETRIES

ANALYTICAL 1-D AND NUMERICAL CONDUCTION MODELS (NO FACE SHEETS)

Hexagonal honeycomb(ANSYS)

Chiral honeycomb(ANSYS)

Analyticalsolution

0 20 40 60 80 100200

time, [sec]

T o, [ ° K

TiTo chiralTo analyticalTo hexagonal

Material: Inconel 617

• ρ 8360 Kg/m3

• c 419 J/Kg-oK• k 13.4 W/m-oK• Homogeneous isotropic• constant material properties

As temperature input is uniform at the bottom side,No gradients are expected in the x or y directions.

Analytical 1-D conduction model exactly describes conduction in both the chiral and hexagonal honeycombs

m 109.3 ,044.0 5*

−⋅== tsρ

NUMERICAL CONDUCTION MODEL

0 10 20 30 40 50 60 70 80 90 100200

time, [sec]

T o(t), [

TiT0 analytical no face sheetsT0 chiral L/R = 0.95T0 chiral L/R = 0.60T0 hexagonal

65070075080085090095010001050110011500

T(x,t=100 sec), [°K]

oKwithout face sheetswith face sheets

• The temperature at the top face sheet is taken as the mean calculated temperature

• This is the reason for the discrepancy in output temperature history, even with same relative density

L/R = 0.95

L/R = 0.60

0 10 20 30 40 50 60 70 80 90 100200

time, [sec]

T o(t), [

Ti(t)chiral L/R = 0.60chiral L/R = 0.95Hexagonal θ = 30°

Chiral honeycomb’sTemp. history deviatesFrom that of the Hexagonalhoneycomb

NUMERICAL CONDUCTION MODEL (CONT’D)

REFINED NUMERICAL MODEL

Heat transfer through solids

Conduction

Radiation

Convection

0 10 20 30 40 50 60 70 80 90 1000

time, [sec]G

ρ (air density) 1.0 Kg/m3

β (volume expansion coefficient) = 1/Tg (acc. gravity) = 9.82 m/sµ (air dynamic viscosity) = 2x10-5 Ns/m2

[7] Gibson J. L., Ashby F. M., Cellular Solids - Structures and Properties 2nd Edition, Pergamon Press, Oxford, 1998

According to [7], convection may be neglectedif the Grashof number is smaller than 1000.

Conduction and radiation are the onlyheat transfer modes considered.

ρ*/ρs =0.043

According to [7], radiation becomes dominant as the reltive density decreases.

REFINED NUMERICAL MODEL (Cont’d)

Material: Inconel 617

• ρ 8360 Kg/m3 (constant wrt T)• Homogeneous isotropic

T, [oK] c, [J/Kg-oK] k, [W/m-oK]

293.1 419 13.4

373.1 440 14.7

473.1 465 16.3

673.2 515 19.3

873.1 561 22.5

1073.2 611 25.5

1273.2 662 28.7

[8] ANSYS Inc, Theory Reference

N radiating surfacesδij Kronecker deltaεi effective emissivityFij radiation view factorsAi area of ith surfaceQi energy loss of ith surfaceσ Stafn Boltzmann constant

r distance between Ai Ajθ angle with unit normals

Air: ε = 0.009ρ = 1.23 Kg/m3

Face sheets (Inconel 617):ε = 0.85

Honeycomb core (Inconel 617):ε = 0.85

0 10 20 30 40 50 60 70 80 90 100200

time, [sec]

T o(t), [

TiL/R = 0.60L/R = 0.65L/R = 0.70L/R = 0.75L/R = 0.80L/R = 0.85L/R = 0.90L/R = 0.95

0 10 20 30 40 50 60 70 80 90 100200

time, [sec]

T o(t), [

θ = -27.0°

θ = -18.9°

θ = -10.7°

θ = -2.6°

θ = 5.6°

θ = 13.7°

θ = 21.9°

θ = 30.0°

L/R = 0.60 L/R = 0.90 L/R = 0.95

= -27° = 0 ° = 30 °

= 0.044 , = 0.15 mm , = 12.4 mm [6]

0 10 20 30 40 50 60 70 80 90 100200

time, [sec]

T o(t), [

Ti(t)chiral L/R = 0.60chiral L/R = 0.95Hexagonal θ = -27°

Increasing θ

Increasing L/R

0 10 20 30 40 50 60 70 80 90 1000

4 x 105

time, [sec]

q z(t), [

L/R = 0.60L/R = 0.65L/R = 0.70L/R = 0.75L/R = 0.80L/R = 0.85L/R = 0.90L/R = 0.95

0 10 20 30 40 50 60 70 80 90 1000

4 x 105

time, [sec]

q z(t), [

θ = -27.0°

θ = -18.9°

θ = -10.7°

θ = -2.6°

θ = 5.6°

θ = 13.7°

θ = 21.9°

θ = 30.0°

qz = average elemental heat flux

k0 solid conductivity: interpolated givenand Inconel 617 material properties.

0 10 20 30 40 50 60 70 80 90 1001

time, [sec]

k* (t) /

k o(t)

chiral L/R = 0.60chiral L/R = 0.95Hexagonal θ = -27°

[9] Zenkert, D., The Handbook of Sandwich Construction, Engineering Materials Advisory Services , Cradley Heath, West Midlands , 1997

k* As suggested by [9]

0 10 20 30 40 50 60 70 80 90 100200

time, [sec]

T o(t),

ts = 7.6e-005, a= 0.0062 [m]

ts = 3.0e-004, a= 0.0248 [m]

ts = 5.3e-004, a= 0.0434 [m]

ts = 7.6e-004, a= 0.0620 [m]

Chiral

Hexagonal

= 0.044

EIGENVALUE BUCKLING MODEL

-25 -20 -15 -10 -5 0 5 10 15 20 250

θ, [deg]

07 , [Pa

0.6 0.65 0.7 0.75 0.8 0.85 0.9

07 , [P

-25 -20 -15 -10 -5 0 5 10 15 20 250

θ, [deg]

07 , [P

0.6 0.65 0.7 0.75 0.8 0.85 0.9

07 , [P

a= 0.0062 [m]

a= 0.0248 [m]

Hexagonal

Chiral

[7] Gibson J. L., Ashby F. M., Cellular Solids - Structures and Properties 2nd Edition, Pergamon Press, Oxford, 1998

Analytical chiral

FEM chiral

Analytical hexagonal

FEM hexagonal

= 0.044

-25 -20 -15 -10 -5 0 5 10 15 20 250

θ, [deg]

07 , [P

0.6 0.65 0.7 0.75 0.8 0.85 0.9

07 , [P

EIGENVALUE BUCKLING MODEL

-25 -20 -15 -10 -5 0 5 10 15 20 250

θ, [deg]

07 , [P

0.6 0.65 0.7 0.75 0.8 0.85 0.9

07 , [P

a= 0.0434 [m]

a= 0.0620 [m]

Analytical chiral

FEM chiral

Analytical hexagonal

FEM hexagonal

= 0.044

SUMMARY

• Developed a numerical model that predicts the transient heat transfer through the core of chiral and hexagonal honeycombs;

• Imposing same relative density and same occupied volume results in similar heat transfer behavior;

• Chiral honeycombs seem to provide a slightly better thermal performance;

• Developed a model to predict linear, flat-wise compression strength of chiral and hexagonal honeycombs

• Chiral honeycomb show significantly better flat-wise strength than the hexagonal honeycombs

• The chiral honeycomb may offer enhanced performance for thermal-protection applications

FUTURE WORK

• Investigation of postbuckling behavior of the chiral honeycomb

Mechanical and Thermal Properties of Chiral...

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