Brooks, William A , Jr

Griffith, George E

Strass, H Kurt

English

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NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
TECHNICAL NOTE 4052
TWO FACTORS INFLUENCING TEMPERATURE DISTRIBUTIONS
AND THERMAL STRESSES IN STRUCTURES
By WUliam A. Brooks, Jr., George E. GrifMh,
and H. Kurt Strass
Langley Aeronautical Laboratory
Langley Field, Va.
Washington
June 1957
https://ntrs.nasa.gov/search.jsp?R=19930084868 2020-06-17T18:32:05+00:00Z
TECH LIBRARY KAFB, NM
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TECHNICAL NOTE 4052
TXO FACTORS ~LUENC~G TEMPERATURE DISTRIBUTIONS
AND THERM&G STRESSES IN swcms
By William A. Brooks, Jr., George E. Griffith,
The influence of
perature distribution
and H. Kurt Strass
SU4MARY
joint conductivity and internal radiation on tem-
and thermal stresses has been discussed. Joints
of poor conductivity can occur in normal fabdication procedure and
greatly alter temperature distributions and increase thermal stresses.
On the other hsmd, inte&nal radiation tends to make the temperature
distributions more uniform and thereby relieves thermal stress.
INTRODUCTION
Thermal stresses are unquestionably an hportant
the design of supersonic aticraft. Such stresses ere
by nonuniform temperature distributions - the greater
consideration in
usually produced
the tqerature
variation within the structure, the lsrger the thermal stresses. The
present paper deals briefly with two factors which may affect the tem-
perature distribution, and thus the thermal stresses, within a structure;
these two factors are joint conductivity and internal radiation. h
order to indicate some of the effects of these two factors without
unnecessary structural complications, the basic structure considered
consists of a length of skin with an integral or am attached web. b
addition to theoretical results, experhnental data were obtained by
heating the structure either aerodynsmicall.yor by laboratory radiant-
heat sources.
SYMEXIS
a coefficient of thermal e~ansion
c spectiic heat
E modulus of elasticity
2E
h
hj
k
M
q
t
T
To
T1
T2
Taw
T
w
0
emissivity
heat-transfer coefficient
joint conductivity coefficient
thermal conductivity
Mach number
heating rate
skin thickness
temperature
initial temperature
maximum skin temperature
mintium web temperature
equilibria temperature
time
specific weight
thermal stress
NAL!ATN4052
—
.-
b
—
“
Subscripts:
RC radiation and conduction
c conduction
Maximum
DISCUSSION
—
Simple Drbegral Structure
Consider first the simplest possible type of skin-web combination,
one without joints and without internal radiation effects. Figure 1
shows such a structure, a symmetrical integra~ H-section with a flange
(or ~kin) of thickness t symmetricallyheated at a constant rate q;
l
*
NACA TN 4052 3
l
within this structure heat transfer tskes place by conduction only. The
actual temperature T minus the initial temperature To, multiplied by
4 the material thermal conductivity k and divided by the heating rate q
and skin thickness t, is plotted against a time parsmeter in which -r
is the elapsed time, c the specific heat, and w the specific weight.
The choice of these dhensionless parameters makes it possible to present
on the sane plot the results for a given cross section of different
materials subjected to different heating rates. The calculated results,
shown by the solid lines, are obtained by a shple analysis assuming
constant material thermal properties and no heat losses. Point 1, which
is fa%hest frcm the heat sink tiforded by the web, will be the hottest
point in the structure, whereas point 2, which is farthest fran the heat
source, will be the coolest. As a consequence of asszzningno heat losses
and a constant heat input, the average temperature of the structure is
proportional to the mass of the section and varies linearly with time.
In order to check the theory, three tests were @e involving constant
heating rates of 5, 16, smd 41 Btu/ft2-sec. Each test is represented
by a different symbol, amd the experimental temperatures are plotted fcm
various times until the maximum skin temperature reached 4500 F. The
parameters me such that the data for the highest heating rate, shown by
the dismonds, appear at the extreme lower end of the curves, whereas the
data for the lowest heating rate extend the full length of the curves.
The test results sre in fairly gocd agreement with the +.heory;any dis-
crepancy is due largely to the assumption of constant thermal properties
. used in the theory.
At any point in the structure, the thermal stress is proportional
to the difference between the average temperature and the temperature
of’the point in question. When multiplied by the appropriate material
properties, these differences can be converted into thermal stresses,
such as shown in figure 2.
In this figure thermal-stress distributions sre shown for both the
low and high heating rates of 5 and 41 13tu/ft2-secfor the times when
the maximum skin temperature reached 450° F. The skin stresses appesm
in region A and the web stresses, in region B. The solid lines represent
thermal stresses calculated fran measured temperatures shown in figure 1,
and the sy?ibolsrepresent experimental stresses obtained frcm strain-gage
readings corrected for dflferential expsnsion between the gage and speci-
men. The agreement between theory sad experiment is quite good. As
would be expected, the higher heating rate allows less time for heat to
be conducted into the web, thus provides larger temperature differ~ces
in the structure, and consequently yields lsrger thermal stresses. For
the heating rate of 41 Btu/ft2-sec the maximrm skin stress, shown at the
? extreme right, and the msxtim web stress, at the extreme left, are more
than twice the values shown for the rate of 5 Btu/ft2-see, despite the
fact that the skin temperature rise was the ssme.
.
4 NACA TN 40~2
Another significant point is that the maximum stresses are not F
related in the ssme proportion as the heating rates, which have an 8 to
1 ratio. The stresses shown here ~e those which existed when the skin
temperature T1 was 450° F. If, however, the skin taperature were not b
limited to 450° F and a comparison were made at the same value of time,
then, indeed, the stresses would be proportional to the heating rate.
It is also possible to present the stresses in a dhnensionless form
as was done for the temperatures. Figure 3 shows the dimensionless
thermal stresses at various times during the pro~ess of the three tests
at heating rates of 5, 16, and 41 Etu/ft2-sec. It is again evident that
the high-heating-rate data sre grouped at the lower end of the theoretical
curves which sre represented by the solid lines, whereas the data for the
low heating rate extend the full length of the curves. The theoretical
stresses are obtained by using the theoretical temperatures of figure 1.
The agreeknt between theory and experiment is about the ssme as that
in figure 1, and ~ discrepancy is due to the same reason.
The results of these three figures indicate that fairly accurate
temperatures and stresses can be predicted in a simple integral structure
where only conductive heat transfer need be considered snd, further, that ‘
strain-gage readings, if treated properly, can give reasonable stress
results. However, if this structure had contained any joints, greater
temperature differences would have resulted, and accurate calculations
would have beccme somewhat more difficult.
Structure With Attached Webs
In order to show sane of the effects of joints, the temperatures in
one skin-web combination of a multiweb wing, a more realistic aircraft-
‘qypestructure which contains riveted joints, will be exsmined. When
six ZO-inch-chord, multiweb wings identical in cross section - that is,
with the ssme overall size, skin thickness, material, and so forth - were
tested at sea-level conditions at a Mach number of 2 in a blowdown jet,
the results were as shown in figure 4. This figure shows the temperature
difference Tl - T2 between the maximum temperature in the skin (point 1)
and the minimum web temperature (point 2) divided by the maximum possible
skin t~~ature rise Taw
- To plotted against time. The upper dot-
dash curve gives the theoretical temperat~e-ratio drop if no heat is
conducted into the web, that is, if the joint conductivity hj is equal
to zero, and the lower dot-dash curve gives the theoretical results
for perfect joint conductivity. The experimental data for five of the
wings, indicated by the shaded axea, lie close to the curve for perfect
joint conductivity. On the other hand, the data for the sixth wing show ‘J
that the increased temperature drop is sanewhat closer to the curve for
no joint conductivity. Since the temperature distribution depends mainly .
NACA TN 4052 5
. won heat conduction within the structure, this increased temperature
difference can be attributed almost solely to a lower joint conductivity.
The much poorer thermal conductivity of the joints of the one wing, ccm-6 pared with the other five wings, was not obtained by design but rather
results fran the small variations in otherwise identical structures
expected fran normal fabrication techniques. The X-percent increase
in temperature drop of the one wing over the average of the other five
wings also resulted in a substantial increase ti thermal stress. In
fact, the wing with the largest temperature drop fluttered and then
suffered a dynamic failure; whereas, the one wing smong the other five
which was identical in every detail survived its test without dsmage.
Construction details, such as the inclusion of ribs, invalidate further
ccmnparisonwith the other models. However, it seems obvious that joint
conductivity can have an important, and sanetimes adverse, effect on the
temperature vsriation in a structure and hence on the thermal stresses
and, as a result, on the structural integrity.
In figure 5 the msximum nondtiensional temperature drops have been
plotted against a dimensionless joint conductivity psrsmeter hjt/k
where hj is the thermal conductivity of the joint. Calculated results
me shown by the solid lines. h the calculations the value of 0.013 for
. ht/k, the Biot nuuiber(an index of the rate of external to internal heat
transfer), was determined by the experimental aerodynamic heat-transfer
coefficient h. The symbols fndicate data obtained frcm the tests and
. show a 6 to 1 variation h hj which appareritlycan be e~ected even
frcm good shop practice. Data obtained by Farzelay, ~ng, and Holloway
(refs. 1 and 2) cover an even wider range in hj. Although a consider-
able scatter in hj is shown by the five lowest test points, these
points are in good agreement with the theory since they lie in a region
where a fairly lsrge change in joint conductivity has little effect on
the temperature drop. Thus, the band for the five wings shown in fig-
ure 4 masks a considerable variation in hj. The B=h point, which
does not show such gocd agreement, is in a region where a small chsage
in hj can alter the temperature drop appreciably. The spread of h3
within the band shown in figure 4 is of the ssme order of _itude as
the variation frcm the top of the band to the cmve for the one wing.
If the maximum skin or web stress were plotted instead of the tem-
perature drop, a similar vsriation with hjt/k could be observed - the
lower the value of hj, the higher the themal stress, as evidenced by
the failure of the one wing.
Actual flight-test results are shown in figure 6 for a duplicate of
. one of the five wings which had very good joint conductivity. me Mach
number and altitude for the flight sre shown at the top of the figure,
The temperature difference T1 - T2 between the skin and the web
w
6center line is plotted against
rocket model, the results were
NACA TN 4052
time. When this wing was attached to a
as shown by the solid line, which lies
much closer to the calculated curve for h. = 300 Etu/ft%r-OF than
to the curve for perfect joint conductivit~. Since a value of hj = 300
would lie slightly to the left of the test point for the one wing with
the largest temperature difference shown in figure 5, the joints of this
wing would be considered poor frcm the standpoint of thermal conductivity.
.
l
In this case failure of the wing was prevented
chcrdwise rib.
Internal Radiation in an Ertegral
by the inclusion of a
Structure
As was mentioned previously, the effect of joints is to increase
the magnitude of the thermal stresses. However, if the temperatures
involved me sufficiently high, it is possible that internal radiation
—
in a structure may bring about sane thermal-stress relief. The hotter
parts of the structure transfer heat to the cooler parts by radiation
—
and thereby lessen the temperature differences. Although there is sm
increased interest in this phenomencxn,very little information can be
found on this subject.
.
Therefore, ir.order to evaluate some of the effects of internal
radiation on the temperature distribution within a multicell beam, such
as shown in figure 7, an analog solution was made to determine the
‘.
temperature distribution of sm infinitely low box whose internal surfaces
have an emissivity of 1. The procedure was to assune a constant rate of
heat input until the maxhnum skin temperature reached a prescribed limit “-
and then to maintain this skin temperature while the web temperature
approached the skin temperature.
Heat was put into both skins at the rate of 5 Btu/ft2-sec until
the maximwn skin temperature T1 reached 1,2000 F, at which time the
skin temperature was kept constant. The maximum skin temperature TI
and the mintium web temperature T2 are plotted against the in seconds.
The dashed lines are the solution when internal radiation is neglected;
the solid lines represent the case when radiation is included. In this
situation it can be seen that, when radiation is included,”steady state
is reached much more rapidly than when conduction only is considered. It
can also readily be seen that the maximum temperature difference between
the skin and the web, when conduction and rd”iation are considered, occurs
-.
at approximately 75 seconds md is about two-thirds of that when conduc-
tion only is considered.
~ order to make a preliminary survey, other heating rates and skin-
temperature levels were also investigated as shown in figure 8. Here,
w
NACA TN 4052
in order to show one of the effects of internal
the msxtiwn difference between skin temperature
7
radiation, the ratio of
end web tanp=ature for
lmth radiation and conduction to the maxtium difference for conduction
only is plotted against the skin temperature T1. For a given heating
rate, the ratio of the temperature differences will a~roach a mininnm
.—
value as the skin temperature increases. bthe case of q = 1 Btu/ft2-see,
the limit is nearly reached at a skin temperature of 1,200° F. The curve
for the highest heating rate will eventually reach the lowest limit but at
a temperature far in excess of 1,200° F. For the conditions in the figure,
radiation effects are most significant when heating rates are low and tem-
peratures ere high.
Figure 9 shows some preliminary experimental results. The specimen
was made of ~-
16 (
inch Inconel with the cross section as shown 2~- inch-
square cells) ad was 12 inches long. The emissivity of the internal
surfaces was about 0.8. me heating rates were approximately 5 and
2$ Btu/ft2-sec. Although there is a measurable reduction in the msximum
temperature difference, the reduction is not as large as indicated by the
idealized theoretical results.
CONCLUDING REMARKS
In summry, two factors, joint conductivity and internal radiation,
which influence temperature distribution smd therefore thermal stresses,
have been discuss~. Even normal fabrication techniques can produce
Joints of such poor conductivity as to cause the temperature differences
to increase markedly over those of an integral structure. On the other
hand, at the higher temperatures internal radiation has the effect of
making the temperature differences less severe and the thermal stresses
smaller. At the higher temperatures these two effects tend to cancel
one another.
Langley Aeronautical Laboratory,
National Advisory Committee for Aeronautics,
Langley Field, Vs., March 6, 195’7.
NACA TN 4052
.
REFERENCES
l
1. Bsrzelay, Martin E., Tong, Kin Nee, and HO11OWV, George F.: Effect
of Pressure on Thermal Conductance of Contact Joints. NACA TN 3295,
1955.
2. %rzelay, Martin E., Tong, Kin Nee, and Hollowsy, George F.: Thermal
Conductance of Contacts in Aircraft Joints. NACATN 3167, 1954.
NACA TN 4052 9
TEMPERATURES
250 r
(T-TO) $
IN RADIANTLY HEATED H-SECTION
W++J IA
o
T
-Tt
1
I ttttt ~
ru
.iJ /“ @-sEc _ /AVEr a‘“
05
1n IF a.=
04 KIXJL
— CALCULATED /Y-
r
0
4
250
h
Cwtz
Figure 1
THERMAL STRESSES IN RADIANTIY
1:4; q’ ‘Tu
40
J
FT2-SEC
— CALCULATED
20
t
u , KSI
o —
I
T, SEC
35.0
3.3
10 NACA TN 4032
THERMAL STRESSES IN RADIANTLY HEATED H-SECTION
q
E
80 -,
60 -
40 -
‘k 20 -
7iE~t
o
-20 -
-40 ~ I I I I I
o 50 100 150 200 250
~
Cwt2
Figure 3
TEMPERATURE DIFFERENCES IN 6 MU LTIWEB WINGS
‘--2’--’=././,
‘1-T2 .5
‘AW ‘TO
5 WINGS
\h.=~
J
I WING
v I J
o 6 12
TIME, SEC
Figure 4
NACA TN b052 u
VARIATION OF TEMPERATURE DIFFERENCE WITH JOINT
+= 0.013
— CALCULATED
o TEST
TAW- To
.
n
u o
—hj.~
I I J
o .1 .2
.
Figure 5
TEMPERATURE DIFFERENCE FOR MULTIWEB WING IN FLIGHT
‘:E5zz51:T’FT
.
.
160 .
~ -T2,”F 80 -
0 8 16
TIME, SEC
Figure 6
12 NACA TN 4052
TEMPERATURE HISTORIES FOR BOX BEAM WITH INTERNAL RADIATION
~= 1.0
~=5 BTU
FT2 -SEC
111
1,200- --
ml
(D@It
/ tt! ““
T,°F 640 ‘
—-- CONDUCTION
— CONDUCTION AND
RADIATION
80 I I
o 100 200
TIME, SEC
Figure 7
INTERNAL RADIATION EFFECTS FOR VARIOUS HEATING RATES
a
1.0
(T1-T2)RC~~
(T,-T~) ~ ~Ax
s
.5 t I I
o 600 1,200
Tl, OF
BTU
q,—FT2_ SEC
Iiim —.a@Itt
—
.
“
Figure 8
NACA TN 4052 13
EXPERIMENTAL
1.0
(T1‘T2)~~,MAX
(TI-T2)cMAX9
F
. .
RESULTS FOR INTERNAL RADIATION
o 600 1,200
T,, ‘F
Figure 9
NACA -Langley Field, V.L


Two factors influencing temperature distributions and thermal stresses in structures

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