," OSyo , oC yo N94- 25122

Thermophysical Property Sensitivity Effects in Steel Solidification

Tony OverfeltSpace Power Institute

Auburn University231 Leach Science Center

Auburn, AL 36849

The simulation of advanced solidification processes via digital computer techniques has gained

widespread acceptance during the last decade or so. Models today can predict transient temperature

fields, fluid flow fields, important microstructural parameters, and potential defects in castings.

However, the lack of accurate thermophysical property data on important industrial alloys threatens to

limit the ability of manufacturers to fully capitalize on the technology's benefits. This paper describes

a study of the sensitivity of one such numerical model of a steel plate casting to imposed variations in

the data utilized for the thermal conductivity, specific heat, density, and heat of fusion. The sensitivity

of the data's variability is characterized by its effects on the net solidification time of various points

along the centerline of the plate casting. Recommendations for property measurements are given andthe implications of data uncertainty for modelers are discussed.

Simulation results can only be as good as the boundary conditions/heat transfer coefficients

applied and the thermophysical properties used, i.e., density, specific heat, latent heat, and thermal

conductivity. Several other authors have investigated the important effects of interracial heat transfer

coefficients and found a strong dependency of the evolution of the thermal field on these coefficients.

However, few modelers cite more than a passing concern for the lack of thermophysical data ,and the

uncertainty inherent in the data that is available. Depending on the source of thcrmophysical property

data, considerable errors may be present. For example, the data for the thermal conductivity of

tungsten reported in the literature exhibits as much as 300% scatter even though many data sets are

reported to be accurate to within 1% or less! In addition, the data for a great many complex alloys ofindustrial interest are simply unavailable.

The casting chosen for this study is the solidification of a horizontal steel plate in green sand

with a riser at one end as shown in Figure 1. This is the same geometry investigated by Minakawa etal I in their study of the feeding of porosity. The nominal properties used were identical to those of

Minakawa et al and are shown in Table I. The thickness of the plate is 25 mm and the the length is 200

ram. Centeriine shrinkage has been observed to occur in the region indicated in Figure 1.2 The

assumptions made by Minakawa et al were repeated here. (1) The mold is instanteously filled withmolten metal at the pouring temperature. (2) The thermal contact resistance at the metal-sand mold

interface is negligible. (3) Segregation is neglected. (4) The latent heat is released uniformly between

the liquidus temperature and the solidus temperature irrespective of cooling rate effects.

The model was tested by comparing calculations of the plate centerline temperatures with the

measured temperatures of Bishop and Pellini. 2 Excellent agreement was found in the temperaturerange between the solidus and the liquidus.

The effects of various uncertainties upon the predicted solidification times due to uncertainties

in the steel's thermal conductivity, specific heat, latent heat and density are shown in Figures 2, 3, 4,and 5 respectively. A comparison of these effects is presented in Figure 6 where the solidification

times of the node at 57.1 mm from the plate edge are shown. Increasing the thermal conductivity valueof the steel by 100% only decreased the time to solidify by about 13%. An error of +50% in the

specific heat of the steel would cause an increase in the predicted time to freeze of -25%, whereas a

35

https://ntrs.nasa.gov/search.jsp?R=19940020640 2020-06-07T16:23:56+00:00Z

+50%errorin thelatentheatwouldincreasethe predicted solidification time by 55%. The sensitivity

of the model is even greater to variations in the density used. The predicted solidification time

increased by 90% with a +50% error in the steel's density.

In terms of the molten steel's properties, the model investigated was most sensitive to

uncertainties in the steel's density and least sensitive to it's thermal conductivity. The approximate

sensitivity coefficients are:

_rf 0.084 min i_Tf min_--K-= W/m°K''_' _-_= 5"2X10"5 I--_g'

_T__.f=8.76X103 rain and _l'f 2.88X10. 3 rain

% J/kg °K' _-'p"- _.

Although high temperature molten alloys are experimentally difficult, many techniques exist for

determining most of these properties required to accuracies of the order of :!:5% or better. However,

there is little agreement on standard techniques, little publicly available data on most common industrial

alloys, and apparently little incentive for researchers to worry about the absolute validity of the data

they use. Inaccurate data leads to inaccurate results and can stop a development program in its tracks.

All investigators should strive to critically assess the amount of uncertainty in the data that they use and

to quantify the expected effects of that uncertainty in their results. The maturation of computer

modeling from a research tool to a design tool demands no less.

Conclusions

1. The sensitivity of computer solidification models to uncertainties in thermophysical properties can

be readily assessed by straightforward variation of their values in a one-at-a-time manner.

2. Large errors in some of the input thermophysical properties can lead to corresponding large errors

in computer models' predictions.

3. For variations up to :_5% in the thermophysical properties, the relative importance of the input

properties is: densitystee I > latent heatstee 1 > specific heatstee I > thermal conductivitystee 1.

Acknowledgements

The author gratefully acknowledges the financial support of NASA's Office of Commercial

Programs through grant NAGW-1192, General Electric Aircraft Engines, Howmet Corporation, and

PCC Airfoils, Inc. This workshop presentation was based upon a paper presented at the Modeling of

Casting, Welding, and Advanced Solidification Processes-VI Conference held at Palm Coast, FL

March 21-26, 1993.

References

1. S. Minakawa, I.V. Samarasekera, and F. Weinberg, "Centerline Porosity in Plate Castings,"

MetaU. Trans. B, 16B(1985) pp. 823-829.

2. H.F. Bishop and W.S. Pellini, "The Contribution of Riser and Chill-Edge Effects to Soundness

of Cast Steel Plates," AFS Trans., 58(1950) pp. 185-197.

36

Figure 1

it)o4

<-_ .100

<---.025

.o,:su J.

.300 :.'

..................................... b ........

..................................... b ........

::::::::::::::: Centerlineshdnkage ::::[::::::::

!!!!!iiT!i!i!it!!iiii!ii!i!!ii!!i!i:,tii:,:,!!7!

:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

" " "IL .................................................... " .........

Dimensions in meters

.025

Figure 2Effects of Uncertainty in Thermal Conductivity

20 L I ! I i• • • • i • • • I , • • • • • I

I 'e- I i"_- i i i

i ' ir i+o% _ i_ 4

1

I o ........................... _+...s.O.._.......................................................................

0

0 •'•'I••''I''•'I'''•1

0 5 10 15 20Distance from plate end, cm

37

Figure 3Effects of Uncertainty in Specific Heat

.c_ 35E

,,--30

e"E 25

.mm

O_ 10

"10(1)

co 5

0 0

+100%

+50%/+25%

+0%

......._-25%_-50%

0 5 10 15 2ODistance from plate end, cm

¢..

•_- 60

E 40

30

o 20"0

o 0

Figure 4.Effects of Uncertainty ,n Latent Heat

i +100%

+50%

+25%!

+0%i i,...._I I "25%

! ! "50%

0 5 10 15Distance from plate end, cm

20

38

E 70

"-60

._E 50t

._o... 40o

300

_ 20

-5 10

o 0

Figure 5Effects of Uncertainty in Density

0

• • • • • • • • _ • • • I I | • • • •

j I +100%

t [I _i o............................................. ......... ........ ..................................... _ ........ +50 _ O

I/ t t_

/ _ .... o

_r

5 10 15Distance from plate end, cm

2O

In

2t..

¢-

P.EL

200

150

100

50

0

50

50

Figure 6

Effects of Errors in Steel Properties

! I I _lensiiy"_.'

............................!..........................................................'...............J................I/ .......-

• i I _ ........._,.e..a.,:

i i I /i /! ;

,......__ .....___ thermal conductivity___ I I . . i .... i • H • i • 1 ." ,

25 0 25 50 75Percentage error in steel property

100

39

Heat conduction is governed by the following well knownunsteady equation:

3T _- K V2T +Lf_3t pCp pCp

where T is the temperature

p is the density

cp is specific heat

Lf is the latent heat

t is time,

K is the thermal conductivity, and

the properties are independent of temp.

A simple-minded, one-at-a-time variation of the propertiesin a validated model would quickly give valuable insightinto which thermophysical properties are the dominantones governing heat flow in casting.

4O

......... THERMAL CONDUCTIVITY OF ---i i -- -r--

.......... IRON

C.Y Ho, R.W. Powell, and P.E. Liley, Thermal Conductivity of theElements: A Comprehensive Review, J. Phys. Chem. Ref. Data,Vol. 3, Supp. No. 1, American Chenical Society and AmericanInstitute of Physics, 1974, pp. 1-369.

41

Table !

Nomirml Values of thePhysical Data Used in the Calculations

Property or Parameter Units Steel Mold

Specific heat, Cp

Density of liquid, p

Density of solid, p

Thermal conductivity, k

Heat transfer coefficient, Hs

Latent heat, Lf

Liquidus temperature, T L

Solidus temperature, T s

Pouring temperature, Tp

Emissivity, e

1/kg OK 840

kg/m 3 7100

kg/m 3 7500

W/m OK 31

W/rn 2 °K

J/kg 2.7 X 105

OK 1780

°K 1736

°K 1868

- 0.45

1050

1650

1.55

20.9

S. Minakawa, I.V. Samarasekera, and F. Weinberg,1985, vol. 16B, pp. 823-829.

42

Plate Casting

3r0 3! tO

ELEMENT

MESH PLOT

TIME 0.100E+03

XMIN 0.000E+00

XMAX 0.630E+00YMIN 0.000E+00

YMAX 0.300E+00

FIDAP 6.02

17 Jul 92

16:04:29

!Plate Casting

i

I

I

TEMPERATURE

CONTOUR PLOT

-- 0. 1736E+04

-- 0. 1758E+04

MINIMUM0.29300E+03

MAXIMUM0.18303E+04

TIME 0.300E+03

XMIN 0.000E+00

XMAX 0.630E+00YMIN 0.000E+00

YMAX 0.300E+00

FIDAP 6.02

30 Jul 92

13:00:51

43

Plate CastingTEMPERATURE

CONTOUR PLOT

-- 0.1736E+04-- 0. 1758E+04

MINIMUM0.29300E+03

MAXIMUM0o17938E+04

TIME 0.600E+03

XMIN 0.000E+00XMAX 0.630E+00

YMIN 0.000E+00

YMAX 0.300E+00

FIDAP 6.02

30 Jul 9213:02:28

Plate Casting

¥

TEMPERATURECONTOUR PLOT

LEGEND

-- 0.1736E+04

-- 0.1758E+04

MINIMUM

0.29300E+03

MAXIMUM0.17804E+04

TIME 0.900E+03

XMIN 0.000E+00

XMAX 0.630E+00!YMIN 0.000E+00

YMAX 0.300E+00

FIDAP 6.02

30 Jul 92

12:58:14

Plate Casting TEMP E RA TUBE

CONTOUR PLOT

LEGEND

-- 0.1736E+04

-- 0.1758E+04

MINIMUM

0.29300E+03

MAXIMUM0.17800E+04

TIME 0.100E+04

XMIN 0.000E+00

XMAX 0.630E+00YMIN 0.000E+00

YMAX 0.300E+00

FIDAP 6.02

30 Jul 9213:06:20

1800

1780Y

s._

:= 1760L

ID

_" 1740(D

!-

1720

1700

0 200 400 600 800CoolingTime(seconds)

1000 1200

45

Effects of Uncertainty in Specific Heat

.-.= 35

_ 25g 2O

0 0Ilia mmm I

• 1+4"06_/0i

i_ +-%:

+0% :

i_ .25%I

5O_oj

mmm,

0 5 10 15 20Distancefrompl_eend, cm

Effects of Unc_talnty In Thermal Conductivity

0 • • • • • • • • • • • • • • • •

m

.c , j' +0%

l imll

• -25% _

'_ .• _+SO%

10 f5 =• ¥

_ m

• • m •0

I

I

|

• • • • • • • • • • • •

0 5 . 10 15Distance from plate end, cm

20

46

Effects of Uncertainty in Latent Heat

---- 60 .. • • , • • • •

"= 40l / I +50%4

_ 3o............. +25%

20

10-50%

0 0 -, . , I .... , . . . . i . . . ."i

0 5 10 15 20Distance from plate end, cm

Effects of Uncertainty in Density

iiii 160 .............

so8

_ 40 , _+50°/o]

_o ......o • .. • l.._.°:°I

0 5 10 15 20Distance from plate end, cm

47

Effects of Errors in Molten Steel Properties

_°i'T" Tq7lJ_; F_;LTS:].._15

_oL L 1//7 J ] .........-"- i_ II//{ I ! .......j

_°

_ "°[ ,I // f 1 i _'_L./.././..1.... l.,..l....l....:-20

-50 -25 0 25 50 75 100

Percentage error in steel property

The finite element model calculates an effective specificheat from a supplied enthalpy vs. temperature curve.

dH/dtc.p- dT/dt

Thus Cp is determined at each integration point or nodalpoint:

H(Tn)-H(T..,)Cp= T.- T..1

48

Change in Enthalpy with Different Cp's

0.75 Cp =420 J/kg C

Cp =840 J/kg C I ,

0.5 , - .... Cp =1680 J/kg C _____

0.25

0

1700 1750 1800 1850 1900

Temperature (K)

v

"!"

Change In Enthalpy with Different L f's

1

0.75

0.5

0.25

0

1700

---L =0.27 MJ/kg

--L =0.135 MJ/kg

..... L =0.54 MJ/kg

=-l-.,I.,,,l==

/'

i'

/

I

t //" /

/'/

_ .

1740 1780 1820

Temperature (K)

1860 1900

49

Effects of Errors in Sand Properties

20

15

•" 10

s® 0

-5

_-10

-20

-50

miwll

mm

|

m

mR II I II

']UUUmJllJ

K\"

gill l

!

m

.ill

• • • I l

-25 0 25 50 75

Percentage error in sand property

100

Conclusions

1. The effectsof uncertaintiesin inputdatacan bequicklyassessedby a straightforward(butcomputer intensive)approach.

1 The calculated cooling rate of the casting modelis affected by uncertainties in the thermophysicaldata in the following order of influence:

. density. latent heat

3. thermalconductivity (sand)4. specific heat5. density and specific heat (sand)6. thermalconductivity

3. Similar analyses will be useful to benchmark theimportance of properties in fluid flow analyses.

50