ML19254D223
| ML19254D223 | |
| Person / Time | |
|---|---|
| Issue date: | 10/11/1979 |
| From: | Feit R NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES) |
| To: | NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES) |
| References | |
| 79011, NUDOCS 7910230146 | |
| Download: ML19254D223 (26) | |
Text
.
p ato UNITED STATES p
og#
0 NUCLEAR REGULATORY COMMisslON g
OCT 1 1 1979 g
S WASHINGTON, D. C. 20555 j
5
%..../
MEMORANDUM FOR: Fire Protection Research Review Group FROM:
Ronald Feit, Chairman Fire Protection Research Review Group
SUBJECT:
FIRE MODELS Enclosed for your use and information is a copy of "Models of Horizontal Electrical Cables and Cable Trays Exposed to a Fire Plume,"
by L. W. Hunter. This paper, which was sponsored by RES, appeared in Combustion and Flame.
/
f e
Rona d Feit, C irman Fire Protection Research Revie cup Division of Reactor Safety Rese ch
Enclosure:
As stated cc w/ encl:
S. H. Hanauer, DSS V. Benaroya, DSS R. Ferguson, PSYB F. Rowsome, PAS S. Scott (2cysforPDR)
L 6.1 l'L 1189 246 7 910230 l 4 6
311 COMBUSTION AND FLAME 35: 311-322(1979)
Models of Horizontal Electric Cables and Cable Trays Exposed to a Fire Plume L. W. HUNTER 1he Johns Hopkins University, Applied Physics Labora tory, Johns Hopkins Road, Laurel. Maryland 20810 Models are developed to describe horizontalinsulated cables and cable trays sxposed to a fire plume.The models also apply to cables protected by fire retardant coatings. A cable or coated cable can ignite when its surface is hot enough to generate flammable gas, unless the level of O available is insufficient for ignition.
2 Then the gas can often accumulate elsewhere and burn later. A first set of models predicts the delay time to the onset of gasification. Other models estimate the attainable mass flux of flammable gas generated by a tray of cables when the cables do not ignite directly. Longitudinal heat flow is identified as a factor tending to prevent direct ignition of single-conductor cables in the cool plumes encountered over cable-tray fires.
onset of gasification; the delay time for a tray may INTRODUCrION be predicted from a single <able model represent-Insulation on electric cables can provide a signifi-ing the most exposed cable. Other models estimate cant mass of combustible materialin power plants the attainable mass flux of flammable gas generated and telephone 4 witching buildings. Klamerus [1]
by the entire tray when the cables do not ignite di-has performed tests on stacks of horizontal,open-rectly. The formation of a fireballis clearly favored bottom trays filled with cables. The cables ignited by a large output of flammable gas. The results when exposed to intense heating from a gas burner de nonstrate that the output is large when the or an oil-spill fire. The cables did not ignite di.
throughput of plume gases is also large.
rectly when expoxd to the cooler plumes from preexisting cable fires. However, flammable gas BASIC ASSUMPTIONS then evolved that in some cases ignited elsewhere as a highly intense fireball (Fig.1). The fireball T..
Nels are formulated in terms of uncoated was observed only when the cables were laid loosely cables, but the same development applies to cmted in the trays,and not when they were tightly packed cables insofar as both consist of a cylindrical plastic or protected by shields or fire-retardant coatings.
shell around one or more metal conductors.
'Ihus the amount of plume gases that can penetrate The surface temperature at which the flammable an exposed tray played an important tole.
gas stants to evolve, denoted Trs. is a function of Models of horizontal cables, coated cables, and the chemical composition of the insulation and is trays in a fire plume have been developed by the taken to be independent of the size of the cable author and are summarized here. A cable or ccTted and the nature of the heating. It is also assumed cable can ignite when its surface is hot enough to that Trs marks the onset of chemical reactions in generate fismmable gas, unless the leve! of Os the insulation although soot and flame retardants available is insufficient for ignition. Then the gas may also evolve at this point.
' can often accumulate elsewhere and bum later. A The heat flux to a cable whose temperature is first set of models predicts the delay time to the below Tr, is (by assumption) independent of CopyrightC 1979 by the Combustion Institute 0010-2180/79/060311+12301.75 Published by Etsevier North Ho!!and,Inc.
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1189 247
i L W. IlUNTER 312 gggg8888888888
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- 2 88888888888888o
~
~
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DONOR FIRE 88888888888888 000000o000o000 j
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Fig.1. Upward fire spread in a stack of horizontal open-bottom trays filled with cables. Approximate dimensions are shown for the tests by Klamerus [1]. When a preexisting " donor" fire in one tray, say, no.1, spread upward through the stack, the mechanism was a leap-frog process. Flammable gas driven from no. 2 produced the fireball shown, which then ignited no. 2 from above.
chemical heats of reactions in the insulation and There is some freedom in choosing the effective heat-transfer coefficient H' and the effective gas can be written in the form temperature T,'. One choice is given by F(T) = H(T,- T) + c[Fa - aT*)
(1) where and T = cable temperature; H = a heat transfer coefficient; H' = H + 4e cT 's, (4) 8 T, = a plume gas temperature; e = emissivity of cable; D
T,' is the steady-state temperature the cable Fa = an incident radiant flux; g
g, g, o = Stefan-Eoltzmann constant.
sent. With this choice, Eq. 2 is exact near the Specifically, the first term can describe the forced steady state.
convection (usually turbulent) that occurs in a fire Cables can have one or more conductors. A plume and a gas fire ball. His description is prob-single conductor cable consists of a metal cylinder t ghtly enclosed in a hollow cylindrical she!! of i
ably adequate over the small temperature range between room temperature and the gasification plastic insulation. De core of a multiple conduc-point. For best reliability, H should be measured tor cable consists of a bundle of single conductor since there are many factors affecting it. De sec-cables. The core is wrapped with glass tape and ond term describes the radiant heat exchange.
then Jacketed in insulation. It is assumed that the For mathematical convenience, the entire flux outer shell of a multiple conductor cable makes can be approximated by a convective form, poor contact with the inner cables so that no heat flows from shell to core. With this assumption, '
F(T) = H'(T,' - T).
(2) both kinds of cable may be represented by one
}j89 2kb
313 MODELS OF CABl.ESIN A FIRE PLUME model (Fig. 2). The parameters that characterize face temperature, given that H. T, and Fa are evaluated at the stagnation point. When H. T, and the system are
" "" *"E '*** '* E 9"*"*****
T' efreetive gas tempr,ature
E" * * * " " * "
- E S"*"
Y' M
efrective heat transfer coeflicient temperature is always a maximum on the surface p0M OMe plume 4asWi-e ca e a b
uter r sus fshell Cs, Ca heat capacities of core and shell ka thermal corductivity of shell r
radial coordinate Steady Temperature t
time The steady state cable temperature determines T
temperature of cable whether gasification can ever begin. For this To room temperature application it is safe to drop any heating effects of The model directly applies to a single conductor chemical reactions in the insulation. It is sufficient cable but can also be applied to a multiple conduc-to consider a single cable in the underside of the tot cable by setting C = 0.The model also covers tray since gasification beginsin the underside,if at 1
homogeneous cylinders (set a = b to get a metal all, and the thermal contact between cables is cylinder and a = 0 to get a plastic cylinder).
poor. The hest transfer coefficient for the cable is The thermal properties of commercial cable to be evaluated on location in the tray, insulations vary widely. To obtain reliable values, The cable attabs a maximum steady tempera-direct measurements are necessary.
ture equal to T,*, provided longitudinal conduc-Angle variations in the cable are dropped. The tion can be ruled out at the center of the plume.
cable temperature T at r = b is expected to be Note that when longitudinal gradients are absent, reasonably close to the true stagnation point sur-so are radial gradients,in steady state. Under these JL,
Ce 2
k, 1
1
\\
T N~
N 4
N. N T
,g. -
s Fig. 2. Heat transfer to a cable. The symbols are defined after Eq. 4.Tre shaded re-gion is the core of the cable. For a single conductor cable, the core is a!! metal. For a multiple conductor cable, the core is a bundle of sL gle conductor cables, but Cg may be set equal to zero if it is assumed that no heat flows into the core.
L W. IlUNTER 314 conditions, gasification would eventuill/ occur if and Jo andIs are the Bessel functions. As N-+ 0 at fixed P. Eq. 8 reduces to the radially isot!.armal T,' > Tr.
A useful test for longitudinal conduction in a result (Eq. 5), since xs -+ (2N)%, but the other realistic cable can be derived by considering a roots are bounded away from zero. Equation 8 was evaluated numerically and is plotted in Fig. 3.
homogeneous and radially isothermal cylinder, To apply Fig. 3 to a composite cable, k is again The plume temperature is a square wave of tength evaluated in the most conducting phase that can J. 'Ihe cylinder attains its maximum temperature at be heated by the plume. Gasification would even-the midpoint of the plume,where tually occur if T> Tr.
T,' - T (5)
"t T,' - To Whether a cable can ignite when heated by a fire
- * (y H'
va I-6) plume is difficult to predict quantitatively. Ig.
niton requires both gasification and O. The gasi-2 f cation is confined to the interior of the plume if It follows that longitudinal conduction has a plume is not hot enouA ne 0 Iml here is negligible effect if usually too small to support cable combustion. Ig.
nition can only occur near the edges of the plume (7)
P > S, where Os can intermix from the surrounding air.1 The important trends are revealed by the radially in which case e-8* < 0.01.
isothermal cylinder in the square-wave plume. The Equation (7) may be applied to a realistic com-posite conductor by evaluating k in the most con-steady temperature is ducting. hase that can be heated by the plume.
T This phase is metalin a single <onductor cable and
= 1
- cosh P
(11) insulation in a multiple-conductor cable. By as-T,' - To
\\ l/
sumption, in a multiple. conductor cable, heat does Figure 4 shows the longitudinal profiles. One trend not reach the core.
is that as P decreases,the Og from the surrounding If longitudinal conduction cannot be ruled out, air must penetrate further into the plume to en-then radial conduction may also be important. At counter surface temperatures in excess of a given the midpoint of a square wave plume, the surface Tr,. Thus longitudinal conduction tends to pre-temperature of a homogeneous cylinder with vent direct ignition of an exposed cable.
radial gradientsis given by The effects oflongitudinal conduction are less important when T,' is high. In Eq. I1, Tincreases T '- T I
linearly with T,' at all positions.When gasification
= 2N [ M + x,2 is occurring. T still increases with T,'(though not 8
7,, - To
,.s linearly), and it is expected that when T,' is high
,*p j
enough, T may exceed Trg, even at the edge of the (8)
I (2N)ua plume, and direct ignition may be more likely.
X exp where Delay Times bH, (9)
The delay time required toiniti:te gasification de-
- "T' termines whethe Gammable gas evolves within the Xs s@aMd lignition t :..oletable in the wake on an Oa-rich gas -
burner, [2]. Then ignition occurs in the center of the N/o(x.) = x,Is(x,),
(10) wake at the onset of fla:nmable$as generation.
\\\\
315 MODELS OF CABLESIN A FIRE PLUME 0.95 10 10 0.8
- T -T en
- T' D!i. 2.0 s
e T -- T.
///
e
!/
0.4 0.6 1.0 p
N < 0.1 0.4 0.2 O.0 o 0 1.0 2.0 3.0 t.(gt Fig. 3. Maximum steady temperature in a homogeneous cylinder. To apply this chart to a realistis cable, & is evaluated in the most conducting phase that can be heated by the plume. Gasift:ation would eventually occur if T > T,.
f 8*
- t=140 7,f y,y 6.0-SF 19 0.8 <
as' 1.0-E ES-a2 e
s e
e t
i i
e g,
-1.0
-as
-0.s
-0.4
-42 40 a2 R4 Re as 1.0 R
t Fig. 4. Longitudinal steady temperature distribution in a radially isothermal cylinder exposed to a square-wave plume of length L This chart shows qualitative trends ofim-portance to cable ignition.
f
\\\\
s
/.
s 1
316 L W. IlUNTER lifetime of the plurr.e. In a cable tray exposed to with/ defined by the plume, different cables experience different heating rates. The delay time to gasification in a fa y'Jo(aX,)-1 (aX,)-
3 tray is that for the most exposed cable. The tem-
_ 2 perature in the cable satisfies X [NYo(X,) - X, Ya(X,)]
I8 r0T Ca BT, a < r < b, (12)
-OTX, y r br br km at
_y BT H' p = { (T,'- T) at r = b, (13)
X [N/o(X,) - X,1 (X,)].
(19) 3 BT aci 0T The / and Y are Bessel functions.
at r = a, (14)
Equation 17 was evaluated numerically for Or W at some typical values of the parameters. Figure 5 T = To t t = 0.
(15) app?ies to a single-conductor cable and Fig.6, to a a
multiple-cer.ductor cable. These charts are useful Longitudinal heat flow is dropped in these equa.
for calculating the delay time to attain gasific tion.
tions, as corrections are developed later in this Other calculations for single-conductor cables are section. When these equations are applied to a presented by Jaluria [3].
single-conductor cable, the boundary condition at The trends in the delay time uNvaries are evi-r = a reflects the fact that the conductor remains dent in Figs. 5 and 6. The parameterNagain con-radially isothermal at each instant due to Ps high trols radial conduction. As N-+ 0,it may be shown thermal conductivity. By assumption,no chemical from Eqs.12-15 that heats of reaction appearin the equations since Tfs T,'- T 2H't marks the onset of reactions.
-+ exp -
(20)
The surface temperature may be written in T,, - To bC terms of N (evaluated in the shell) and three other a result that holds when the cable is radially iso-dimensionless variables:
thermal. Here C is the average heat capacity of the bH' a
C H't cable:
Na
,as
,y E iC, t* a (16) 2 2
a C + (b2 -a )C i
kg b
bCa C=
(21) b2 The explicit form of the solution (when # # 0)is Equation 20 is a useful approxhnation especially T,'- T
' 2,./n for triple-conductor cables since these cables tend T,' - To to be radially isothermal for a < r < b (see Fig. 6).
The delay time increases as b increases. One rea-
~
~
4X*4 son is that # varies roughly as b-4 (at least when (N' + Xs')-
+ (1 7K8 b is small)in a given plume at stagnation [4]. The delay time for a homogeneous cy!!Mer (a = 0)is N/o(X,)-X,I (X,)
"a shown in Fig. 7. It is seen that the delay time X
would increase as b increases, even if the flow were
_ 07.8/2)lo(aX,)-X,I (oX,)-
adjusted to keep F constant. The limit at constant
( X (17)
- may be derived from Eqs.12-15:
T,' - T f H'2 h
[N"4 t
where X,is a root of
= exp I T,,- To (kaCa jIerfcYk:C (22) f(N, o, 7, X,) = 0, (18)
This gives the temperature of a planar surface.
I S
\\ \\O\\
MODELS OF CABLES IN A FIRE PLUI.!E 3j7 7,,- 7 Th-7, 0.0 at 0.2 a3 0.4 at at a7 0.8 ag i
8 3
1 4
e s
i 1.5 1 = a57
= 2.0 1.0 2
3 0.5 N.
= 0.0001 3
0.1 0.5 1.0 0
8 I
e 0
O a5 1.0 1.5 2.0 2.',
-in
\\7;- T, /
Fig. 5. Transient heat transfer to a single conductor cable withou* longitudinal conduc-tion (f* > 5). The chart de; ermines the exposure time t neceuary to attain gasification.
T,,- 7 T - T.
,,,0 0 a t a2 as a4 a8 at a7 as as f a aet,
/
=0 ES
. e a, "8
a5 j.0 1
O a5 1.0 1.5 2.0 2.5 e
,g, \\T;-7 /
Fig. 6. Transient heat transfer to a multiple ccnductor cable without longitudi duction (l* > 5). The chart determines the exposure time t necessary to attain gasu.
tion. There is no heat transfer from the shell of insulation (a < r < b) to the cabL within.
L W. IlUNTER 318 s
5 4
3 2
a=0 N a - ===
kn s 1 c
1 0
0.1
-1 0.01
-2
-3 I
I I
I I
I I
I I
0 0.1 n2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 4
T -7 g
- T,-7, Fig. 7. Transient heat transfer to a hornogeneous cylinder (a = 0) without longitudinal conduction (l* > 5). This chart shows the trends in the delay tirne as curvature (b) varies.
interest to estimate the total mass. production rate Trends in the delay time due to longitudinal of flammable gas that can result when the cables conduction can be brought out most simply for a gasify but do not bum. TheJlammable gas is as-homogeneous and radially isothermal cylinder (a =sumed to make up a constant mass fraction Yrs of 0,N = 0). The cylinder temperature at the center all the evolved gases and soot.The gasification rate of a square-wave gas. temperature profile is given is greatest directly over the center of the plume, by near the x. axis shown in Fig. 9. Here the steady.
state bt and mass exchange rnay & convenkntly T * -- T,,._,. + 2 [' dt' e-a r' analyzed by overall balance equations. It is as.
T,' - To lo sumed that longitudinal (:-) conduction is negligi-ble in the cables near the x axis.
)
The mus flux emerging from the upper surface Xerfc(P l.
(23)
/
of the tray, on axis,is the sum Yr ~18f " +8f "
ts s
f a flux f ev Ived gases and soot and a flux of lattu rnatchu de Hux entenng It is seen that for large P this expression reduces p me gasu.
te Eq. 20. Equation 23 was evaluated numerice!!ythe underside of the tray, on axis. The arrange-and is plotted in Fig. 8. The delay time increases as ment of cables controlsif, for not a!! of the total P ume fluxif.., can penetrate the tray.
P decreases, and longitudinal conduction becomes l
fi The temperature of the gases rising through the
?nore important.
tray drops from T,(0) at the undersurface (x = 0)
Gasification Rate to T,(d) at the upper surface (x = d). The heat loss from the gas is absorbed by the cables. Incident Once it has been established that a cable ty does radiation is also absorbed. In steady state the cables begin to gasify before the plume dies out,it.s cf i
MODELS OF CABLES IN A FIRE PLUME 339 1.0 0.9 t's t 0.57 0.28 0.14 I4 j
0.8 R7 -
0.6 a5 0.4 a3 0.2 0.1 8
f e
e e
0 0
R1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 T,-Tg T'-T, Fig. 8. Transient heat transfer to a homogeneous, radially isothermal cylinder (a = 0, N = 0). This chart shows trends in the t' Ly time as longitadinal heet flow increases (l* decreases).
are radially isothermal, since r<onduction is absent where d denotes specific heat at constant pressure by assumption. Hence the heat deposited to the for the solid (s) and gas (g) phases, L is the heat of cables is spent in gasification, except for the heat gasification at gasification temperature, and T.,is radiated from the exposed upper and lower tray an average cable temperature. All the radiation surfaces, on axis. The cables in depth are in radiant terms are grouped together inda". It fo!!ows that equilibrium.
the mass flux of flammable gas is The combined mass and energy balance is
.~
,y, "
0 = M,"d,[T,(0)- To] + da"-LYrs-'Ars" Y,,@,"d,[T,(0)- 7,(d)] + da"}
-(N "
- Irs' rs ) s{ Is(d) ~ Io}
4 + d,[ 7,(d) - To } + (d. - d,)(T., - To) s
- Yrs-sAr,"(,- 0,)(T., - To),
(24)
(25) dL 8*
s'
_T,(d)_
5
~
i 5
an
% x=0 T,(0)
L-e a;
Fig. 9. The flow of plume gas and flammatde gas through an exposed cable tray.
\\\\
bhg
320 L W. HUNTER The gas emerging from an exposed tray mixes with Hence the gas temperature at x = d is slightlyless normal air above the tray. The formation of a than Tr,.
flammable mixture is favored by a high flux hr,",
which in turn is nearly proportional to the plume 2[Tr, - Rd)]
throughout, h,". This result explains the observed T,W Tr,-
('}
6 importance of cable placement and establishes h,"
as a useful measure ofit.
The correction term is estimated from the differ.
The gas temperature T,(0) in the last expres-ential equation (Eq. 26).
sfon is simply the plume gas temperature below The thermal penetration depth 6 in the tray the tray. To estimate T (d), consider the differen-may be correlated, Fig.10, with the mass flux of tial balance equation for T,(x) inside the tray gas through the tray. It is assumed that the heat-under the assumption that T is constant in any transfer coefficient in the definition of 6 may be horizontal plane, T= Rx),and that the concentra-estimated from the correlations suggested by tion of evolved materials is small. It may be shown McAdams [5] for heat exchangers. In Fig.10, k, that T,(x) satisfies is the thermal conductivity of the gas,,is the vis-cosity, and Pr is the Prandt1 number.
If 6 is large enough tojustif' dropping the cor-
$,"O' dx
[ T (x)- Rx)]'
(26) y b
rection term in Eq. 31 and if radiation is small compared to convection, it follows from Eq. 25 where d is the fraction of the cross. sectional area that the mass fraction of flammable gas in the flow of the tray occupied by cables. Assuming that T, emerging from the tray is independent of the flux
. aries much more rapidly than T, the solution of through the tray and hence independent of cable Eq. 26 is placement:
T,(r)- Rx)
-(x/b) 4'8 a exp (27)
T (0)- R0) 6 y,,- sg,," + Af,"
s where Yr:0 [T,(0)- Trs]
4 + 0,[ T,(0)- To] + (d. - d )(T,-7.,f Ai,"C, 6=
(28)
(32) 2e#
is a dimensionless thermal penetration depth. It This result is often sufficiently accurate for engi-follows that T,(x) -+ T(x), with T (x) > Ux),
nuring utimatn.
when E > 6.
(29)
Coatings and Shields b
" " "I When this condition is mst, gasification continues as x increases but the rate approaches 0; therefore, trays, fire can spread upward if enough heat is
" I"Y' Ex) approaches the lowest surface temperature at tuy e.
"1 nha dirudy or genentu Harn-8 which gasification can occur, namely, Tr8. Hence the temperature of the gas in depth approaches mable gas that ignites elsewhere A fire shield Tr,. Only the topmost (exposed) layer of cables against the underside of the expos ~ d tray can pre-e hu a temperature somewhat less than Tr, due t vent the fire spread [1] by blocking the heat transfu.
radiantlosses:
Fire-retardant coating; are also effective in pre-H[Tr,- Rd)] = cord)4 (30) venting upward spread [1]. To understand their
\\\\89 256
i MODELS OF CABLES IN A FIRE PLUME 321
--- CABLES STAGGERED CABLES IN LINE
/
h J
/ *'
~
/
1
/,s **
e1
-7 e
i 1
9 1
10 102 103 10'
[1-2Ws)4]-1 e
l's Fig.10. Thermal penetration depth in a cable tray (adapted from McAdams [5]).
The factor l1 - 2(e/w)1/2]-s convetk 4 " to the mass flux averaged over the minimum free ar.a in a horizontal pL.e. The heat transfer coefficient is also shown.
mechanisms, note that the analysis of uncoated C
average heat capacity of cable (Eq.
cables in the previous sections also applies to 21) coated cables, since in both cases there is a fire-d specific heat of plume and evolved e
retardant plastic shell around one or more metal gases at constant pressure conductors. Two ways in which coatings work d
depth of cables in a tray against upward fire spread are demonstrated by H
heat. transfer coefficient from plume Eq. 25: (1) coatings reduce the throughput h," of gas to a cable hot plume gases; and (2) the concentration of Yrs N'
effective heat. transfer coefficient f
of flammable gas is lower in the evolved material.
(Eq.4)
Both factors reduce the output he," of flammable Jo,Js Bessel functions gas. Coatings can also release more flame. inhibiting ks, km thermal conductivities of cable core chemicals.
and shell k = ks or ka k
thermal conductivity of plume gas g
The author benefitedfrom dixussions with R.
I length of cable heated by plume Felt, L. Klamerus, F. R. Krause, R. E. Luna, and l*
dimensionless parameter defined by R. H. Nilson. The author thanks S. Favin for Eq.6 writing computer programs and J. R. Kuttler for L
heat of pyrolysis of cable insulation checking some of the mathematics. This work k,"
mass flux of plume gas through an was supported by U.S. Nuclear Regulatory Com-exposed tray mirsion, contract No. A T(49 25-9007).
Aos,,"
mass flux oigas in plume N
dimentionless parameter defined by Eq.9 s
It Prandtl number, y, d,/k, a
inner radius of cable insulation r
radial coordinate in cable b
outer radius of cable insulation t
time C,C heat capacities of cable core and t*
dimensionless parameter defined by 2
shell Eq.16 j
l
/
L W. liUNTER 322 t eas lifetime of plume mission (1717 H Street, NW, Washington, D.C. 20555) h for inspection and copying for a fee:
To room temperature
- a. Klamerus, L. J., and Nilson, R. H. Cable tray fire T
cable temperature tests, Report SAND 77-1125C on Sandia Laboratories.
7, gas temperature Albuquerque, NM, J uly 1977.
8 Ts effective gas temperature (Eq. 3)
- b. Klamerus, L. J., A preliminary report on fire protec-Tr, cable surface temperature at onset tion research program (July 6,1977 Test), Report SAND 771424 of Sandia Laboratories, Albuquerque, of pyrolysis NM,0ctober 1977.
vertical position in cabic tray (Fig.
- c. Klamerus, L. J., A preliminary report on fire protec-x 9) tion research program fire retardant coatings tests roots cf Eq.10 for s = 1,2,
,n (December 7,1977-January 31,1978), Report SAND x,
X, roots of Eq.18 for s = 1,2,
, n 78-0518 of Sandia Laboratories, Albuquerque, NM, Ygg mass fraction of flammable gas in March 1978.
- 2. a. Hunter, L. W., Schacke, H., Grunfelder, C., and evolved gases and soot Fristrom,R.M. Cbmbust.Scf Technol. 15:41 (1977).
Yo,Yg Bessel functions
- b. Schacke, H., Hunter, L. W., Grunfelder, C., and longitudinal cable coordinate Fristrom, R. M..Sisteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, a
a 7
Ca/Ca 1977,p.1317.
8 dimensionless parameter defined by
- 3. Jaluria, Y.,J. Heat 7>ansf. 96:127 (1976), Fig. 7.
Eq. 28
- 4. Schtichting, H., Boundary 14per 77ttory, McGraw-
- s viscosity of gas Hill, New York,1960, p. 324.
Stefan-Boltzmann constant
- 5. McAdams, W. H., Hear 7)ansmfrsion, McGraw-Hill, o
p fraction of cross-sectional area of 1942,pp.226-230.
tray filled by cables REFERENCES
- 1. The following reports are available in the Public Docu-Received 30 November 1978; revised 13 February 1979 ment Room of the (J.S. Nuclear Regulatory Com-1189 258