temperature dependence of material properties and its
TRANSCRIPT
Institute of Space Propulsion 1
Temperature Dependence of Material Properties and its Influence on the Thermal Distribution in Regeneratively Cooled Combustion Chamber Walls
M. Oschwald, D. Suslov, A. WoschnakGerman Aerospace CenterInstitute for Space Propulsion, LampoldshausenD-74239 Hardthausen
1st EUCASSJuly 4-7, 2005Moscow, Russia
Institute of Space Propulsion 2
conditions in regeneratively cooled LOX/GH2-engines
hot gas temperature: ≈ 3500 K
pressure: ≈ 11 MPa
heat flux: up to 80 MW/m2
LH2-temperature:
• cooling channel inlet ≈ 40 K
• cooling channel outlet ≈ 100 K
wall structure temperature:
• hot gas side ≈ 400 - 800 K
• cooling fluid side ≈ 40 - 100 K
hot gas wall temperature: ΔT=40 K ≈ 50% life time
A. Fröhlich, M. Popp, G. Schmidt, D. Thelemann. Heat Transfer Characteristics of H2/O2Combustion Chambers, AIAA 93-1826, 29th Joint Propulsion Conference, Monterey, CA, 1993
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stratification in cooling channels with high aspect ratio
HARCC-experiment
P8 test bench
LH2-cooled L42 combustor
pressures up to PC = 9 MPa
heat fluxes up to 40 MW/m2
variation of AR=1.7 ... 30
D. Suslov, A. Woschnak, J. Sender, M. Oschwald, Test specimen design and measurement technique for investigation of heat transfer processes in cooling channels of rocket engines under real thermal conditions, AIAA 2003-4613, 39th Joint Propulsion Conference, Huntsville, 2003
A. Woschnak, D. Suslov, M. Oschwald, Experimental and Numerical Investigations of Thermal Stratification Effects, AIAA 2003-4615, 39th Joint Propulsion Conference. Huntsville, 2003
HARCCsegment
L42-combustor
P8 test bench
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HARCC geometries
sector no.
width [mm]
height [mm]
aspect ratio
fin width [mm]
1 1.2 2.0 1.7 1.4 2 0.8 2.8 3.5 1.4 3 0.3 9.0 30 1.4 4 0.5 4.6 9.2 1.4
sector 4 AR=9.2
sector 3 AR=30
sector 1 AR=1.7
sector 2 AR=3.5
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temperature determination in wall structure with thermocouples
measurements at 4 axial locations• z=52mm, 85mm, 119mm, 152mm downstream
duct entrance5 radial positions• 0.7mm, 1.1mm, 1.5mm, 1.9mm, 7.5mm from
hot gas sidedetermination of surface temperature, heat flux and heat transfer coefficients by inverse method
LH2
hot gas
Pos. 1
Pos. 2
Pos. 3Pos. 4
0,0
50,0
100,0
150,0
200,0
250,0
300,0
350,0
400,0
0,0 5,0 10,0 15,0 20,0 25,0t [s]
T [K]
TC 0.7mmTC 1.1mmTC 1.5mmTC 1.9mmTC 7.5mm
cooling channel
LH2
heat flux q
TE1TE2
TE3
TE4
TE5
Institute of Space Propulsion 6
heat conduction / material properties
instationary problem:
stationary problem:
specific heat: cV ≈ 25.9 J/mol/K (Dulong-Petit, ambient temperature)
heat conductivity: λ ≈ 350 W/Km (typical Cu-alloy)
0)()(=∇⋅∇−
∂∂ T
tTcV λρ
CuCrZr-alloy
eCu
eNi
0)( =∇⋅∇− Tλ
combustion chamber wall construction
40 - 800 K
40 - 100 K
40 - 100 K
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Debye-theory of the specific heat
Debey-theory
quantum mechanics for low temperature behaviour
high temperature limit:
cv = 3R (Dulong-Petit)
low temperature limit:
cV ∝ a⋅(T/ ΘD )3
for copper: ΘD ≈ 315 K0 50 100 150 200 250 300
0
50
100
150
200
250
300
350
400
450
[J/kg/K]
temperature [K]
Copperspecific heat
cryocomp data base Debye theory, Θ
D = 315 K
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thermal conductivity at low temperatures
pure coppermaximum near 20 K
copper alloysphonon scattering at lattice imperfections:
reduction of thermal conductivity
R.L. Powell and W. A. Blanpied, Thermal Conductivity of Metals and Alloys at Low Temperature, NBS Circular 556, 1954
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thermal conductivity of copper alloy for L42-combustor
λ
43540537534531528525522519516513510575
0 100 200 300 400 5000
50
100
150
200
250
300
350
400
measurement DLR model: λ(T)
thermal con
ductivity [W
/K/m
]
T [K] variation of thermal conductivity in wall with thermal field
Institute of Space Propulsion 10
thermal expansion coefficient
thermal expansion due to anharmonicity of potentialexpansion coefficient vanishes at T=0dT
xdx
Tkcgxx
gxcxxU
Be
143
...)(
2
32
=
+=
+−=
α
0 50 100 150 200 250 3000.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.0
2.0x10-6
4.0x10-6
6.0x10-6
8.0x10-6
1.0x10-5
1.2x10-5
1.4x10-5
1.6x10-5
1.8x10-5
2.0x10-5
thermal expan
sion [%
]
temperature [K]
Copper (cryocomp data base) thermal expansion expansion coefficient
Nickel (cryocomp data base) thermal expansion expansion coefficient
expan
sion coe
fficient [1
/K]
0.8 1.0 1.2 1.4 1.6 1.8 2.0
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
xe
potential [a.u.]
r/σ
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[K]109876543210
-1-2-3-4-5
[K]109876543210
-1-2-3-4-5
ARH/B
sector TH2 TW [K] ΔTW [K]
Q1
Q2
Q4
Q3
Tcλ=const.
Tvλ(T)
1.7 85 380.9 385.0 4.9
3.5 90 363.3 369.4 6.1
9.1 95 349.9 358.2 8.3
30 100 343.6 352.7 9.1H/B=1.7 H/B=30
ΔTW=Tv-Tc
thermal field w/o and with temperature dependence of λ
HARCC experiment, 52 mm downstream cooling fluid inlet
Institute of Space Propulsion 12
H/B=1.7 H/B=30
ΔTW=Tv-Tc
[K]302826242220181614121086420
-2-4-6
[K]302826242220181614121086420
-2-4-6
ARH/B
sector TW [K] ΔTW [K]
Tcλ=const.
Tvλ(T)
1.7 Q1 349.0 361.3 12.3
3.5 Q2 326.6 345.7 19.1
9.1 Q4 308.3 334.6 26.3
30 Q3 297.3 327.0 29.7
thermal field w/o and with temperature dependence of λ
cooling fluid temperature: 50K
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transient thermal field: cv=c0 vs. cv=cv (T)
abc
temp320310300290280270260250240230220210200190180170160150140130120110100908070
10-4 10-3 10-2 10-1
t [s]0
50
100
150
200
250
300
350
T[K
]
a: c(T)b: c(T)c: c(T)a: c0b: c0c: c0
wall temperaturespre-cooling of structure to 40 Kinstantaneous temperature increase at t=0
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abc
temp320310300290280270260250240230220210200190180170160150140130120110100908070
10-4 10-3 10-2 10-1
t [s]100
101
102
103
104
105
106
107
dT/d
t[K
/s]
a: c(T)b: c(T)c: c(T)a: c0b: c0c: c0
transient thermal field: cv=c0 vs. cv=cv (T)
temporal gradients
Institute of Space Propulsion 15
abc
temp320310300290280270260250240230220210200190180170160150140130120110100908070
10-4 10-3 10-2 10-1
t [s]0.0E+00
2.0E+04
4.0E+04
6.0E+04
8.0E+04
1.0E+05
1.2E+05
1.4E+05
1.6E+05
grad
(T)[
K/m
]
a: c(T)b: c(T)c: c(T)a: c0b: c0c: c0
transient thermal field: cv=c0 vs. cv=cv (T)
spatial gradients
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summaryshow significant temperature dependence
cV, λ, α disappear at absolute zero
specific heat cV
thermal conductivity λthermal expansion coefficient α
α → 0 for T→ 0
• reduced thermal stress at low temperature
cV→ 0 für T→ 0
• only minor differences as compared with simulation results with cV=const.
λ → 0 for T→ 0
• increase of hot gas side wall temperature
• relevant level of increase at low cooling fluid temperature and high AR