Temperature Dependence of Material Properties and its

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


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


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


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


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


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


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


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


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


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


[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


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


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


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]



temporal gradients


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

]



spatial gradients


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

Documents

Temperature Dependence of Material Properties and its