Mechanical and Thermal Properties of Chiral...
Transcript of Mechanical and Thermal Properties of Chiral...
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
q = 0
Best heat shielding performance, although cell geometry is found not to affect performance significantly[6].
d
b
L
tc/2
tc
tc/2
tc/2
tc/2
tc
Variation of hexagonal honeycomb geometry with angle
HEXAGONAL HONEYCOMB UNIT CELL GEOMETRY
= -27° = 0 ° = 30 °
r
θ
βR
Ltc
y
x
Variation of chiral geometry with L/R ratio
CHIRAL HONEYCOMB AND UNIT CELL GEOMETRY
( )
( )
( )R
2Rsin
Lr2tan
Rr2sin
=
=
=
θ
β
β
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 ]
a
x
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
[6] Ko, W. L.: “Heat Shielding Characteristics and Thermostructural Performance of a Superalloy Honeycomb Sandwich Thermal Protection System (TPS) ”, NASA/TP-2004-212024
d
L
h
t /2
t
t /2
t /2
t /2
t
r
θ
βR
Lt
y
x
Face-sheet area imposed equal
CORRELATION OF HONEYCOMB GEMOETRIES
ANALYTICAL 1-D AND NUMERICAL CONDUCTION MODELS (NO FACE SHEETS)
980
1000
1020
1040
1060
1080
1100
1120
oK
Hexagonal honeycomb(ANSYS)
Chiral honeycomb(ANSYS)
Analyticalsolution
0 20 40 60 80 100200
300
400
500
600
700
800
900
1000
1100
1200
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
ρ
a
ts
a
ts
NUMERICAL CONDUCTION MODEL
0 10 20 30 40 50 60 70 80 90 100200
300
400
500
600
700
800
900
1000
1100
1200
time, [sec]
T o(t), [
o K]
TiT0 analytical no face sheetsT0 chiral L/R = 0.95T0 chiral L/R = 0.60T0 hexagonal
65070075080085090095010001050110011500
0.002
0.004
0.006
0.008
0.01
0.012
0.014
T(x,t=100 sec), [°K]
x, [m
]
oKwithout face sheetswith face sheets
700
750
800
850
900
950
1000
1050
1100
• 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
oK
oK
L/R = 0.60
0 10 20 30 40 50 60 70 80 90 100200
300
400
500
600
700
800
900
1000
1100
1200
time, [sec]
T o(t), [
o K]
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
0.1
0.2
0.3
0.4
0.5
0.6
0.7
time, [sec]G
r
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
REFINED NUMERICAL MODEL (Cont’d)
0 10 20 30 40 50 60 70 80 90 100200
300
400
500
600
700
800
900
1000
1100
1200
time, [sec]
T o(t), [
o K]
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
300
400
500
600
700
800
900
1000
1100
1200
time, [sec]
T o(t), [
o K]
Ti
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]
[6] Ko, W. L.: “Heat Shielding Characteristics and Thermostructural Performance of a Superalloy Honeycomb Sandwich Thermal Protection System (TPS) ”, NASA/TP-2004-212024
0 10 20 30 40 50 60 70 80 90 100200
300
400
500
600
700
800
900
1000
1100
1200
time, [sec]
T o(t), [
o K]
Ti(t)chiral L/R = 0.60chiral L/R = 0.95Hexagonal θ = -27°
Increasing θ
Increasing L/R
REFINED NUMERICAL MODEL (Cont’d)
0 10 20 30 40 50 60 70 80 90 1000
0.5
1
1.5
2
2.5
3
3.5
4 x 105
time, [sec]
q z(t), [
W/m
]
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
0.5
1
1.5
2
2.5
3
3.5
4 x 105
time, [sec]
q z(t), [
W/m
2 ]
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
1.02
1.04
1.06
1.08
1.1
1.12
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]
REFINED NUMERICAL MODEL (Cont’d)
0 10 20 30 40 50 60 70 80 90 100200
300
400
500
600
700
800
900
1000
1100
1200
time, [sec]
T o(t),
[ o K
]
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
a
ts
a
ts
a
ts
a
ts
REFINED NUMERICAL MODEL (Cont’d)
= 0.044
EIGENVALUE BUCKLING MODEL
-25 -20 -15 -10 -5 0 5 10 15 20 250
0.5
1
1.5
2
2.5
θ, [deg]
σz,
el 1
07 , [Pa
]
0.6 0.65 0.7 0.75 0.8 0.85 0.9
0
0.5
1
1.5
2
2.5
L/R
σz,
el 1
07 , [P
a]
-25 -20 -15 -10 -5 0 5 10 15 20 250
0.5
1
1.5
2
2.5
θ, [deg]
σz,
el 1
07 , [P
a]
0.6 0.65 0.7 0.75 0.8 0.85 0.9
0
0.5
1
1.5
2
2.5
L/R
σz,
el 1
07 , [P
a]
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
λ
Analytical chiral
FEM chiral
Analytical hexagonal
FEM hexagonal
= 0.044
-25 -20 -15 -10 -5 0 5 10 15 20 250
0.5
1
1.5
θ, [deg]
σz,
el 1
07 , [P
a]
0.6 0.65 0.7 0.75 0.8 0.85 0.9
0
0.5
1
1.5
L/R
σz,
el 1
07 , [P
a]
EIGENVALUE BUCKLING MODEL
-25 -20 -15 -10 -5 0 5 10 15 20 250
0.1
0.2
0.3
0.4
0.5
0.6
0.7
θ, [deg]
σz,
el 1
07 , [P
a]
0.6 0.65 0.7 0.75 0.8 0.85 0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
L/R
σz,
el 1
07 , [P
a]
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