- Email: [email protected]
Fire plume air entrainment according to two competing assumptions
Twenty-first Symposium (International) on Combustion/The Combustion Institute, 1986/pp. 111-120
FIRE P L U M E A I R E N T R A I N M E N T A C C O R D I N G TO T W O C O M P E T I N G ASSUMPTIONS GUNNAR HESKESTAD Factory Mutual Research Corporation 1151 Boston-Providence Turnpike Norwood, Massachusetts 02062
Following a review of existing entrainment predictions for fire plumes, two promising predictions for the plume region above the flames are compared against extensive experimental data on plume mass flows. Both of these predictions assume self-preserving velocity profiles. However, one of them, a prediction of Cetegen et al., assumes self-preserving excess temperature profiles while the other, advanced by the author, assumes self-preserving density deficiency profiles, the two assumptions being mutually exclusive in strong fire plumes. The prediction based on self-preserving density deficiency profiles shows good consistency with the experimental plume flows, better than the prediction based on self-preserving excess temperature profiles. A simple extension of the former on dimensional arguments to the flaming region, assuming turbulent motion, is then examined against data available from a number of sources. The extension tests well against data from fire sources with diameters of 0.3 m and greater, the flames of which can be considered substantially turbulent. On the other hand, the extension overpredicts plume flows measured in the flaming region of 0.10-0.19 m diameter fire sources, which is attributed to prevalence of laminar flaming in the case of these small sources. Possible additional research is suggested.
1. Introduction Previously, the a u t h o r established an air e n t r a i n m e n t prediction for fire plumes in behalf of an N F P A (National Fire Protection Association) C o m m i t t e e e n g a g e d in revising a s t a n d a r d on heat a n d smoke v e n t i n g of buildings. 1 At the time, e n t r a i n m e n t theories available were the w e a k - p l u m e f o r m u l a t i o n of Yih 2, considered applicable far from the fire source, a s u b s e q u e n t modification proposed by T h o m a s et al. 3 to a c c o u n t for s t r o n g - p l u m e effects, as well as a n e a r - s o u r c e expression for the flaming region also p r o p o s e d by T h o m a s et al. 3 T h e new prediction a p p e a r e d simpler to use t h a n available alternatives, a n d probably m o r e accurate. Subsequently, reports began to become available from a n i m p o r t a n t investigation o n air e n t r a i n m e n t into fire p l u m e s by Zukoski a n d coworkers. 4'5'6'7 T h e i r e n t r a i n m e n t m e a s u r e m e n t s above the flames were r e p o r t e d s to fit the new prediction quite well but this c o m p a r i s o n was n e v e r published. O n the other h a n d , Cetegen et al. 7 showed that these e n t r a i n m e n t m e a s u r e m e n t s could also be r e p r e s e n t e d quite well by a form for the p l u m e mass flux originally derived for weak plumes, but appearing to be valid for s t r o n g p l u m e s also, provided
a virtual p l u m e origin was i n c o r p o r a t e d in the formulation. This p a p e r e x a m i n e s the differences between the two approaches, i.e., the "new' e n t r a i n m e n t p r e d i c t i o n a n d that attrib u t e d to Cetegen et al., a n d compares their capabilities against e n t r a i n m e n t m e a s u r e m e n t s above the flames. Mass flow m e a s u r e m e n t s in the flaming region are t h e n e x a m i n e d as an extension of the n e w e n t r a i n m e n t prediction. As b a c k g r o u n d , the two a p p r o a c h e s will first be reviewed together with others which have b e e n proposed.
2. Prediction Methods Yih
Yih's early m e a s u r e m e n t s 2 in weak plumes ( A p / p ~ l ) from a point source indicated that the velocity a n d density deficiency profiles could be considered self-preserving.* F r o m d i m e n s i o n a l analysis of t u r b u l e n t gravity convection, Yih's results c o r r e s p o n d to the following mass flow formula: = A (gg~2Q/cp 9 T~) 1/3 z 5/3,
(1)
*Self-preserving: Profiles preserve shape when normalized with centerline values and plume width.
111
112
FIRE
where A = 0.153 according to the measurements. Thomas et al.
In their work on r o o f venting, T h o m a s et al. ~ assumed that strong plume (near source) behavior can be d e d u c e d from Yih's weak plume formula, Eq.(1), by substituting the centerline value of density, P0, for the ambient value, P~: n~ = 0.153 (gpoZQ/cp 9 T~) a/3 z 5/3
(2)
The flame height, L, is given based on observations in terms of a nondimensional p a r a m e t e r Qo * ~ Q/[p~cpT~(gD) 1/2 D2]: Qo* < 1.0: L/D = 3.30 Q.fi.2/3
(8)
Qo* I> 1.0: L/D = 3.30 Qo .2/5-
(9)
For later use, Eq.(5) may be written (in SI units, which are used throughout) for standard atmospheric conditions (293 K, 760 m m Hg): rh (kg/s) = 0.076 @/3 (z_z~)5/3.
Thomas et al. p r o p o s e d that, for area heat sources, the height, z, should be measured above an "effective point source" or virtual origin located below the area source by an amount based on the 15 ~ angle o f spread of a (weak) plume suggested by Taylor et al.9: z~ = - 1.5,4//9.
(3)
Thomas et al. 3 also considered e n t r a i n m e n t in the flaming region of large fires. Invoking the Ricou-Spaulding assumption on entrainment velocity 1~ and assuming the u p w a r d velocity in the flame varies with z 1/2 the authors obtain: n~ = 0.096 p=(gpfl/p~) 1/2 Wjz 3/2.
(4)
Here, 9~ is the gas density in the flames and W/ is the fire perimeter. Cetegen et al.
Assuming that profiles of velocity and excess t e m p e r a t u r e are self-preserving, Cetegen et al.6'rshowed that the weak-plume representation based on Morton's work 1', the same as Eq.(1), also pertains to strongly buoyant plumes. Note that this finding contradicts the assumption of T h o m a s et al. 3 in Eq.(2). To obtain good a g r e e m e n t with their experiments, Cetegen et al. introduced a virtual origin ("offset"), z~, from which z would be measured in the formula: rh = 0.21 (gp~2/cp 9 T~) 1/3 QI/3 (z_z,,)5/3.
(5)
For o p t i m u m a g r e e m e n t with their experiments, the authors proposed the following expressions for zv, d e p e n d i n g on whether the source fire is s u r r o u n d e d by a floor flush with the source p e r i m e t e r or m o u n t e d in the laboratory space without the flush flooring: With floor: z~ = - 0 . 5 0 D + 0.33 L
(6)
Without floor: zv = - 0 . 8 0 D + 0.33 L 9
(7)
(10)
These formulations pertain to the region above the flames, i.e., z/L /> 1. T h e authors are careful to point out that their fire plumes were produced in as quiet an atmosphere as could be maintained in their laboratory and that small ambient disturbances could provide 2 0 - 5 0 percent increases in the measured plume mass flows. Cetegen et al. 6'7 also p r o p o s e d a model for air entrainment in the flaming region, z/L < 1, incorporating an initial, essentially laminar region and a turbulent flame region. It is not clear from comparisons with the measurements what prediction accuracies one may expect from the p r o p o s e d model. "New" Entrainment Prediction
In the governing equations for strong plumes (continuity, momentum, energy), one may assume self-preserving profiles for velocity and either t e m p e r a t u r e rise or density deficiency. T e m p e r a t u r e rise, AT, and density deficiency, A 9, cannot be self-preserving simultaneously, which follows from the perfect gas law in the form: ap/A0o = (AT/ATo)/(T/To)
(11)
Only in weak plumes, where T/To = 1, can temperature rise and density deficiency profiles be self-preserving simultaneously. It is important to note that the equations of mean motion and energy for the plume can accommodate (are consistent with) either the assumption of self-preserving t e m p e r a t u r e rise 6'7 or the assumption of self-preserving density deficiency,* using the known behavior of velocity and t e m p e r a t u r e rise on the plume centerline. *In the case of assuming self-preserving density deficiency (and velocity), the integral equations balance except for a small term in the momentum equation of second order, i.e., to the accuracy of terms usually included in analyses.
FIRE PLUME AIR ENTRAINMENT A n i n t e r m e d i a t e p l u m e mass-flow f o r m u l a resulting from a s s u m i n g self-preserving density deficiency profiles (and velocity profiles) ist:
defined bv vertical t e m p e r a t u r e variations (Eq.(15)) a p p e a r predictable from>':
z,/D = - 1 . 0 2 + 0.083 QmS/D ~h = Qc[1 + (1-13/y) ATo/T~]/[Cp(13/y)
Y = ~o (u/uo)(r/b~) d(r/b~)
(13)
d(r/b,,).
(14)
Here, b,, is the p l u m e r a d i u s where u/uo = %. According to M o r t o n ' s extension 12 of the w e a k - p l u m e theory to s t r o n g plumes, the centerline t e m p e r a t u r e rise can be written:
ATo/T~ = C,T g-
1/3
(cpp~T~)-2/3Q~.2i3(z - zv) 5L3(15)
where Cr is a n o n d i m e n s i o n a l constant a n d z~, is the virtual origin. This relation has b e e n verified for both weak p l u m e s 2'13'14 a n d strong plumes15-17; in the fire plumes, ATo appears to obey Eq.(15) d o w n to the m e a n flame height 16. With substitution o f Eq.(15), Eq.(12) becomes:
-
1
[ ,,,,~ lV3
IL ~"~ j|
(i8)
ATo](12)
where Q,. is the convective heat-release rate a n d y a n d [3 are the n o n d i m e n s i o n a l constants:
(3 = fo (u/u~176
1 13
OV3(z-zo) s/:~ "
9[1 + CT(1 -- t3/3" ) (gl#2cp p~ T , ) -'2/:~
.Q~/3(z-G)-5/'~].
(16)
O n e set of profiles, m e a s u r e d in the p l u m e above a m e t h a n o l pool fire using t h e r m o c o u pies a n d a pitot tube 18, c o r r e s p o n d to the values y = 0.60 a n d 13 = 0.41. A n o t h e r set, m e a s u r e d vdth a t h e r m o c o u p l e a n d laser-Doppler anem o m e t e r m in the p l u m e above a n a t u r a l gas b u r n e r , c o r r e s p o n d to the values y = 0.69 a n d 13 = 0.42. Previously Ls, the f o r m e r pair was a d o p t e d for Eq. (16), t o g e t h e r with the value Cr = 9.1 d e t e r m i n e d by G e o r g e et al. 14 Accordingly, the p r o d u c t Cr (1-f3/y) becomes 2.9 a n d the factor 1/Cr(f3/'y) becomes 0.t61, although the value 0.196 was selected previously L* instead of 0.161 o n the basis of a particular p l u m e mass flow m e a s u r e m e n t ~8. Using the constants 2.9 a n d 0.196 a n d specializing to n o r m a l atmospheric conditions (293 K, 760 m m H g ) , Eq. (16) becomes (SI units): rh (kg/s) = 0.071 ovYs (z-z~,) 5/~ [1 + 0.026 Qg/S(z- z~,) - sis]. (17) For substantially t u r b u l e n t pool fires a n d other horizontal-surface fires a n d n o r m a l atmospheric conditions, the virtual origin, z~,,
where Q is the total heat-release rate a n d D is the diameter* of the fire source. Equation (18) should also be valid for porous fuel arrays, provided any i n - d e p t h c o m b u s t i o n is not substantial, i.e., p r o v i d e d most of the volatiles released u n d e r g o c o m b u s t i o n above the array** of the crib. 16 T h e p l u m e law for t e m p e r a t u r e , Eq.(15), ceases to be valid a p p r o x i m a t e l y at the m e a n position of the flame tip where, according to K u n g a n d Stavrianidis 15, the m e a n t e m p e r a t u r e rise may be taken as 500 K. T h e e n t r a i n m e n t relations, Eqs.(16) a n d (17), cease to be valid at the same elevation. T h e limiting elevation, z, z~,, may be calculated from Eq.(15) with C-r = 9.1, setting AT, = 500 K. For n o r m a l atmospheric conditions, the result is: ze - z~ = 0.166 Q25
(19)
where z~ may be o b t a i n e d from Eq.(18). T h e limiting elevation, z~, is analogous to the flame height, L, in the f o r m u l a t i o n of Cetegen et al. discussed in the p r e c e d i n g section. At the limiting elevation, zc the predicted p l u m e mass flow, k~, is o b t a i n e d from Eqs.(17) a n d (19):
ri~t(kg/s) = 0.0054 @(kW).
(20)
Below the limiting evaluation, the mass flow rate must decrease toward a value associated with the top of the combustible. If the combustible is a pool fire, the mass flux (vapor) at the top of the combustible is negligible c o m p a r e d to ~h~. For such fires, a s s u m i n g that the flames are substantially t u r b u l e n t so that viscous effects are not i m p o r t a n t , one expects for z ~< z~: rhA~ = fn(z/ze, zdD).
(21)
Previous considerations of the e n t r a i n m e n t data of Cetegen et al. suggested s that effects of ze/D were not i m p o r t a n t in the data set a n d that for sufficiently large fires, tile d e p e n d e n c e of rhhhe on z/ze was a p p r o x i m a t e l y linear. *or effective diameter such that -rr D'2/4 = area of fire source. **Underventilated wood cribs will meet this test, whereas weU ventilated wood cribs may not, depending on the openness
114
FIRE
Other Approaches
whereas, for the p l u m e region, their result was:
On the basis of McCaffrey's classification o f plume regimes (continuous flame region, intermittent f a m i n g region, plume region) and associated behavior o f centerline t e m p e r a t u r e and velocity 1~', a n u m b e r of attempts have been made to predict mass flows. In these cases it has been assumed that velocity and excess temperature profiles were self-preserving and of Gaussian form. McCaffrey *~ himself proposed the following expression for the plume flow in the f a m i n g region from experimental velocity and temperature profiles:
7/~ = 0.289 DI/2Q(z/Q2/5) 2.
rh =0.055 z QI,2.
(22)
Cox and Chitty 91 measured velocity and temperature profiles in the flaming region over the same source used by McCaffrey 1~. T h e y confirmed the centerline behavior observed by McCaffrev and generalized their data on velocity and t e m p e r a t u r e plume widths as ~/Q2,5 versus z/Q 2~ (where ~ is velocity or t e m p e r a t u r e plume width). On this basis they were able to establish an analytical expression for plume mass flow. McCaffrey and Cox 22 later analyzed their measurements of" plume profiles jointly and determined, on the basis of an overall energy balance, that their respective velocity widths were overestimated previously 1~'~1 because of intrinsic instrument errors. Their joint analysis produced the following mass flow formula for the f a m i n g region: r/~ = 0.053 zl3Q 04s.
(23)
Hasemi 23 concentrated on the intermittent flaming region. He derived an analytical solution with experimental constants, assuming somewhat different plume width behavior than Cox and Chitty 21. His mass flow is approximated as: r/1 = 0.043 Q[z/Q z5 - 0.037].
(24)
(26)
These formulations employ the r e d u c e d height, z/Q 2/5. Recent workaT-has suggested that a more a p p r o p r i a t e form is (z-z~.)/Q/~, where z~ is the virtual origin based on axial t e m p e r a t u r e and velocity behavior. 3. Comparison of Entrainment Predictions Above Flames The most useful of the entrainment predictions for the plume region above the flames are deemed to be the prediction of Cetegen et al., which assumes self-preserving excess temperature profiles, and the "new" prediction, which assumes self-preserving density deficiency profiles. This section will compare the two approaches. Contrasting the two predictions in their form for a normal atmosphere, Eq.(10) versus Eq.(17), it is seen that they differ primarily by the presence of the bracketed term in Eq.(17). In addition, the virtual origins are calculated differently in the two approaches. Eqs.(6-9) for the prediction in Eq.(10) and Eq.(18) for the prediction in Eq.(17).
Data Source The impressive body of mass flow data for fire plumes established by Cetegen, Zukoski and Kubota 6 will be used. In their experiments, the fire sources were placed at different clearances below a hood having a 2.4 m • 2.4 m opening and exhausted by a blower. T h e mass withdrawal rate o f fluid from the hood associated with a particular stationary level of the interface between hot gases in the hood and the cool room air u n d e r n e a t h was taken as the flow rate of plume fluid at the interface elevation. Interface heights above the b u r n e r of approximately 1.0, 1.5 and 2.3 m were used. Fire sources were circular, porous-bed burners operating on natural gas of the following three diameters: 0.10 m, 0.19 m and 0.50 m. Experiments were conducted both with and without a floor s u r r o u n d i n g the gas burners. Several gas rates were used with each burner. Convective heat fluxes o f a plume were calculated from the enthalpy flux at the exit from the hood; these fuxes scattered about 70 percent of the heatrelease rate based on the mass burning rate and the heat of combustion.
Tokunaga et al. z4 derived flow formulae for the intermittent flaming region and the plume region. They assumed equal t e m p e r a t u r e and velocity widths and the same plume width behavior with height as Hasemi z3. T h e y also allowed for a source diameter effect which was determined experimentally. For the intermittent flaming region the following result was obtained:
Results
rh = 0.070 D]2Q(z/QZS- 0.0337),
Figure 1 present the experimental mass flows, rh, for a floor a r o u n d the burners,
(25)
FIRE PLUME AIR ENTRAINMENT 1.8 1.6
115
1.8 []
1.6
[] 1.4
1.4
1.2
1.2
[]
.E "E
1c
1
a
.8
0
o
"E
[] 0
"E
.6
.6
.4
.4
.2
.2
0
4
6
8
9
.8
I
0
10
6
Z/Zt FIG. 1. Plume mass flows above flames measured by Cetegen et al. 6 (floor around burners), normalized with theoretical mass flows assuming self-preserving excess temperature profiles, Eq.(10) (rh = rDar), and virtual origins according to Eq.(6).OD = 0.10 m;&D = 0.19 m; ~ = 0.50 m. normalized with theoretical mass flows assuming self-preserving t e m p e r a t u r e profiles, raar, f r o m the f o r m u l a e p r o p o s e d by Cetegan et al., Eq.(10) (where m = ~h,~r), a n d Eq.(6). T h e abscissa is the height above the b u r n e r , z, normalized with the limiting height, z~, according to Eqs.(19) a n d (18), i.e., essentially the flame height. T h e data for the greatest {nterface heights, a p p r o x i m a t e l y 9.3 m, have been omitted for reasons to be discussed later. Figure 2 shows the same data normalized with the theoretical mass flows a s s u m i n g selfp r e s e r v i n g density deficiency profiles, ~izan, from Eqs.(17) (where ~ = map) a n d (18). C o m p a r i n g this plot to Fig. 1, it is quite a p p a r e n t that there is presently less systematic variation of n o r m a l i z e d mass flow with n o r m a l ized height in the p l u m e a n d fewer "wild" points. I n Fig. 3 the data have b e e n replotted again, n o r m a l i z i n g mass flows with theoretical values m~T a s s u m i n g self-preserving t e m p e r a t u r e profiles according to Eq.(10), b u t e m p l o y i n g virtual origins based o n axial ten'tperature variations, Eq.(18). T h e scatter a n d systematic t r e n d in this plot are even less a p p e a l i n g t h a n in Fig. 1. T h e data for the greatest interface heights, a p p r o x i m a t e l y 2.B m, were omitted from Figs. 1 - 3 o n the suspicion that they may have been influenced significantly by o v e r t u r n i n g effects in the hood, causing e n t r a i n m e n t at the interface in addition to the p l u m e e n t r a i n m e n t . For
8
10
Z/Zt
FiG. 2. Plume mass flows of Fig. 1 normalized with theoretical mass flows assuming self-preserving density deficiency profiles, Eq.(17) 0D = ,Da~), and virtual origins according to Eq.(18). (Symbols as in Fig. 1). these interface heights, the radius from the fire axis to the sides of the hood (1.2 m) ~as considerably less t h a n one half the height of the hood ceiling above the b u r n e r , smaller than the m i n i m u m ratio of 1 for no o v e r t u r n i n g indicated by the Baines a n d T u r n e r experitnents '-'5. In Fig. 1, the 2.3 m data would have tallen between n o n d i m e n s i o n a l mass flows of 0 . 9 4 1.26 ( t e n d i n g to decrease with increasing z/z,), 1.8
[]
1.6
[]
"~.4
1.2
:~~~,-A -
A
1
.E
9
9
OD
4
6
.8
"E .6
.4! .2 0
3 z/zz
8
10
FIG. 3. As Fig. 1, except virtual origins for theoretical mass flows calculated according to Eq.(18) instead of Eq.(6). (Symbols as in Fig. 1).
116
FIRE
and in Fig. 2 they would have fallen between 1.03-1.32 (with only slight tendency to decrease with increasing z/ze), i.e., tending to be high in both cases. Data for conditions without a floor a r o u n d the b u r n e r (not included in Figs. 1-3) were limited to the 0.19 m and 0.50 m diameter burners. For the 0.19 m burner, effects of a floor were generally small6,v. On the other hand, for the 0.50 m burner, the plume flows were reported r as approximately 30 percent higher without a floor than with a floor. Excluding the data obtained with the 2.3 m interface height for the same reasons as before, in Fig. 2 all the data without a floor would have fallen in the range of normalized mass flows 0.78-1.33 (with the 2.3 m interface-height data included, the u p p e r limit would be pushed to
1,42.) On the strength of the comparison between Figs. 1 and 2 or between Figs. 3 and 2, it can be said that the e n t r a i n m e n t prediction assuming self-preserving density deficiency profiles provides a better fit to experimental data than the prediction based on self-preserving excess temperature profiles. It is clear, however, that the absence of a s u r r o u n d i n g floor may affect entrainment, as may disturbances in the ambient flow field being e n t r a i n e d ]
4. Entrainment in Flaming Region Consider first the limiting height, ze. This height is practically equivalent to the mean (luminous) flame height, L, correlated by Heskestad 16'26. For normal ambient conditions and common combustibles (values of H jr near 3100 kJ/kg), the flame height correlation gives26: L = - 1.02 D + 0.230
Q2/5.
(27)
Using the expression for the virtual origin in Eq.(18), Eq.(27) can be written: L = z~, + 0.147
Q2/5.
(28)
Asssuming a c o m m o n value for the convective fraction, QJQ = 0.7, Eq.(28) can be written: L = z~, + 0.170
Qj/5
(29)
which is practically the same as the expression for ze from Eq.(19). Equation (20) is a representation of the plume mass flow at the limiting height (mean flame height) in terms of the convective heat
flux. For fire sources with the specific convective fraction, Q/Q = 0.7, Eq.(20) can be written: ~he = 0.0038 Q = 0.0038 (srhj) (Hc/s)
(30)
where s is the mass stoichiometric ratio, air to volatiles, s~h!representing the mass stoichiometric air requirements for complete combustion. Adopting the typical value His = 3100 kJ/kg, Eq.(30) becomes rhe ~ 12 (~z/).
(31)
Hence, at the mean flame height, the mass flow in the plume is some 12 times the mass stoichiometric ratio. Considering that the mass stoichiometric ratio (s) is typically on the order of ten, the mass contributed to the plume by the fuel 0hf) is on the order of one percent of the plume mass flow at the level of the flame tip. Hence, the fuel contribution can be neglected, consistent with the form of Eq.(21). The objective here is to test Eq.(21) on available measurements in the flaming region and develop explicit forms, if possible. T h e most important data source is again Cetegen et al. 6, who used a modification of their technique for measuring mass flows above the flames. Because of the high gas temperatures associated with flames reaching well into the hot-gas layer in the hood, mass flow rates in the plumes at the interface were deduced from the fuel flow rates and concentrations of carbon dioxide in a gas sample taken from the smoke hood and completely oxidized. All these measurements were made without a floor s u r r o u n d i n g the burners. Important measurements are also available from other sources. Thomas et al. 2r used thistledown as a tracer to measure the flow of air toward ethyl alcohol and wood fires of 0.91 m diameter and a square "town gas" fire 0.30 in on the side. They presented mass air flows through a cylindrical surface of 0.68 m radius concentric with the flame as a function of height above the fire base, which may be interpreted as plume mass flow as function of height. McCaffrey ~5 determined mass flows above a 0.3 m square, porous refractory b u r n e r supplied with natural gas, using profiles of velocity d e t e r m i n e d with a bidirectional flow probe and temperature determined with a thermocouple. Yumoto and Koseki 28 b u r n e d heptane floated on water in a 0.30 m diameter vessel and measured horizontal inflow velocities with a bidirectional flow probe at different heights in a cylindrical surface of the same radius as the vessel. From these data they
FIRE PLUME AIR ENTRAINMENT d e t e r m i n e d total mass inflow as function of height, which they a s s u m e d equal to total mass flow in the p l u m e as f u n c t i o n of height. Beyler's c o m p r e h e n s i v e e x p e r i m e n t s 29 i n c l u d e d e n t r a i n m e n t m e a s u r e m e n t s for flames from 0.13 m a n d 0.19 m d i a m e t e r gas b u r n e r s (propane a n d propene). He e m p l o y e d a t e c h n i q u e similar to that used by Cetegen et al. 6'7 for regions above the flames, i.e., placing the b u r n e r s u n d e r a h o o d exhausted by a blower a n d stabifizing the hot-gas interface within the h o o d at a k n o w n distance above the b u r n e r . For the 0.19 m b u r n e r , the p l u m e mass flows correlated well with the e q u a t i o n (using the "FC layer" interface definition29): rh(kg/s) = 0.073 [z(m) + 0.06] 125
(32)
over the heat-release r a n g e 8 . 2 - 3 1 . 5 kW. T h e mass flows for the 0.13 m b u r n e r were sensitive to the heat release rate, which also covered the r a n g e 8 . 2 - 3 1 . 5 kW. Fig. 4 is a collection o f p l u m e mass flows for V 1.4
V V
1.2
V
o/
Vo ~f
.g
V
.8 0
.E
/
.6
zI~f ~
.4
117
the larger b u r n e r s , 0.3 to 0.9 m in diameter, plotted in the coordinates ~h/rh~ versus z/z~ suggested by Eq.(21), where th is the m e a s u r e d mass flow a n d z is the m e a s u r e m e n t height. Equation (20) was used to calculate d~ and Eqs.(19) a n d (18) were used to calculate z~, a s s u m i n g Qc/Q = 0.7 in all cases. In the case of square b u r n e r s , the effective source diameter was calculated on an equal source-area basis. T h e plot correlates most of the data quite well along the straight line:
hz/h~ = z/z~.
(33)
T h e data of McCaffrey 15 plots a little high, which can be a t t r i b u t e d to excessive axial velocities indicated by his bidirectional flow probe away from the p l u m e axis 22. For the e x p e r i m e n t s in this figure, the ratio z~/D r a n g e d from 0.7 to 2.3; n o effect of z(/D has been observed in this range. Fig, 5 collects p l u m e flow data for a smaller source diameter, 0.19 m. Most of the data plot below the line d e f i n e d by Eq.(32). T h e divergence from the data from the larger b u r n e r s in Fig. 4 can probably be attributed to a significantly greater prevalence of l a m i n a r flaming n e a r the source for the smaller b u r n e r s 6'7. T h e generally higher values of ze/D associated with the smaller b u r n e r (1.8-6.0) are not believed to have been i m p o r t a n t . Figure 6 shows the results for the smallest b u r n e r s , 0 . 1 0 - 0 . 1 3 m in diameter, where the associated z~/D values r a n g e d from 3 to 10. Again, one may suspect that the deviation from the line d e f i n e d by Eq.(33) is associated with l a m i n a r flaming effects (or viscous effects). A s s u m i n g the validity of Eq.(33) for essentially fully t u r b u l e n t flames, the following expression is o b t a i n e d for rh in the flaming region (z <- ze) with the aid of Eqs.(19) a n d (20) a n d taking Qc/Q = 0.7 (SI units):
/
rh(kg/s) = 0.0054 QS(0.166 Qc25 + z_~.)
/
0
/ 0
I .2
I .4
I .6
I .8
I 1
Z//Zl
FIG. 4. Plume mass flow rates in the flaming region for source diameters in the range 0.3-0.9 m (~hefrom Eq.(20) and ze from Eqs.(19) and (18)). o Cetegen et al. 6, 0.5 m dia natural gas (32-73 kW); VMcCaffrey 15, 0.3 m sq natural gas (10-50 kW); AYumoto and Koseki 28, 0.3 m dia heptane (52 kW); ~Thomas et alfl 7, 0.9 m dia ethanol (509 kW) and 0.3 m sq "town gas" (252 kW).
(34)
where z~, is given by Eq.(18) for fire sources which do not have substantial i n - d e p t h c o m b u s t i o n 2~ Equation (34) may be c o m p a r e d to other predictions for the flaming region, using app r o x i m a t e forms t h r o u g h o u t (e.g., setting z, = o in Eq.(34)). T h e a p p r o x i m a t e forms are (assuming Q#Q = 0.7): Eq.(34): Eq.(22): Eq.(23): Eq.(24): Eq.(25):
rh rh rh rh rh
= = = = =
0.032 0.065 0.063 0.053 0.087
o~c 3'5z o ~c o sSz ~ ~ Qc
Dl'2Q3'Sz.
(35) (36) (37) (38) (39)
118
FIRE 5. O n S e l f - P r e s e r v a t i o n
/O /
/
The improved a g r e e m e n t obtained for the plume mass flows above the flames when self-preserving density deficiency profiles are assumed rather than self-preserving excess temperature profiles seems to suggest that the former assumption is more nearly correct. It should be possible to check this conclusion in a direct m a n n e r from measurements of plume profiles. The strong-plume prediction for plume width12:
/
.8
/
/
/
.6
/ 9E
/
.4
9
oa
VCD 9
/
.2
bn = Cb,(To/T~) 1/2 (z-zv) 1
I
I
I
I
.2
.4
.6
.8
1
Z/Zl
FIG. 5. Like Fig. 4, except source diameters of 0.19 m. oCetegen et al. 6, 0.19 m dia natural gas (21-81 kW); VBeyler29, 0.19 m d i a propane (8 kW); Ado. (21-32 kW). There is surprisingly good consistency a m o n g most of these forms. It is especially gratifying to confirm a nearly unanimous, linear dependence on z, the d e p e n d e n c e observed in Fig. 4 and expected to represent fires with substantially turbulent flames (diameters of perhaps 0.3 m and greater).
(40)
is consistent with known centerline behavior o f excess t e m p e r a t u r e (or density deficiency) and velocity, and either self-preservation assumption 8'3~ T h e plume width, b,,, and associated coefficient, Cb,,, may apply to the velocity profile (b~, Cb~), excess t e m p e r a t u r e profile (bA~-,CHAT) or density deficiency profile (ba~, CbA~). Regardless of the self-preservation assumption one expects to see constant Cb~ in all plumes, weak and strong. However, d e p e n d i n g on whether excess temperature or density deficiency is self-preserving, either ChATor Chap will be constant, but not both. The a u t h o r has examined a n u m b e r of measurements 2'13-15'17-19'21'31'32 for the degree of constancy o f Cb,,, ChAT and Cba~, but has not been able to establish convincing conclusions because of great scatter in the data, including uncertainties about the location of the virtual origin, z~,.
/ / / /
.8
/
6. C o n c l u s i o n s
x5
/ / /
.6
/ / /
//
0(3
9 E .4 /
.2
/
~Q~)
///z~
"r.)
~
A~Z2 0
/
0
I
1
I
I
I
.2
.4
.6
.8
1
Z/ZL
FIG. 6. Like Fig. 4, except source diameters in range 0.10-0.13 m. oCetegen et alJ~, 0.10 m dia natural gas (21-52 kW); ABeyler29, 0.13 rn dia propane (8-32 kW).
1. For the plume above the flames, the entrainment prediction assuming self-preserving density deficiency profiles, Eqs.(17) and (18), provided better consistency with measurements than the prediction of Cetegen et al. assuming self-preserving excess t e m p e r a t u r e profiles, Eqs.(10) and (6-9). 2. An extension of the prediction assuming self-preserving density deficiency profiles to the flaming region tested well against plume flows measured in the flaming region for fire diameters of 0.3 m and greater, i.e., whenever the flames could be considered substantially turbulent. For the data set examined and involving fire diameters in the range 0.3-0.9 m along with flame-height to diameter ratios in the range o f 0.7-2.3, plume flows in the flaming region (z ~< ze, where ze is given by Eq.(19)) were consistent with Eq.(34). For fire
FIRE PLUME AIR ENTRAINMENT diameters of 0 . 1 0 - 0 . 1 9 m, the e x p e r i m e n t a l p l u m e flows t e n d e d to be lower than given by Eq.(34), attributed to prevalence of l a m i n a r f l a m i n g for these small fire sources. 3. Additional investigation of the flaming r e g i o n would be desirable with respect to possible effects of the flame-height to d i a m e t e r ratio. F u r t h e r m o r e , special considerations are n e e d e d for fire sources with substantial ind e p t h combustion. Effects o f a m b i e n t air currents are also of great i m p o r t a n c e , especially in the context of r o o m fires.
Nomenclature A .4/ b~ Cb~ CT cp D g H, L rh n~/ rhr ")aT rhap Q Q,. QY~ r s T AT u Wf z ze z~, [3 ~/ p Ap cr
nondimensional constant (-) area of fire source (m 9) (n=u, AT, Ap), p l u m e radius where nln,, = q2 (m) (n=u, AT,Ap), coefficients related to p l u m e width ( - ) coefficient related to p l u m e t e m p e r a t u r e (-) specific heat o f air (kJ/kg- K) fire d i a m e t e r (m) acceleration o f gravity (m/s 2) heat of c o m b u s t i o n (kJ/kg) m e a n flame height (m) p l u m e mass flow rate (kg/s) mass b u r n i n g rate (kg/s) n/ at ze (kg/s) predicted -/ a s s u m i n g self-preserving excess t e m p e r a t u r e profiles (kg/s) predicted rh a s s u m i n g self-preserving density deficiency profiles (kg/s) (total) heat release rate (kW) convective heat release rate (kW) Q/[p~cpT~(gD)l/2D 2] ( - ) radius (m) mass stoichiometric ratio, air to volatiles (-) t e m p e r a t u r e (K) T-T~, excess t e m p e r a t u r e (K) axial velocity (m/s) fire p e r i m e t e r (m) height above fuel surface (m) limiting elevation; elevation z in p l u m e c o r r e s p o n d i n g to ATo = 500 K (m) location, z, of virtual origin (m) n o n d i m e n s i o n a l constant; see Eq.(14) ( - ) n o n d i m e n s i o n a l constant; see Eq.(13) ( - ) density (kg/m ~) 9~ - P, density deficiency (kg/m 3) p l u m e radius in Gaussian profiles (m)
Subscripts fl o ~r
flames centerline ambient
119 REFERENCES
1. Guide /'or Smoke and Heat Venting, NFPA 204M-1982, Appendix A, National Fire Codes, Vol. 15, p. 204M-31, National Fire Prevention Association, 1983. 2. YIH, C-S.: Proc. U.S. National Coug. App. Mech., p 941, 1952. 3. THOMAS, P.H., HINKLEY, P.L., THEOBALD, C.R. AND SIMMS, D.L.: lnvesttgations Into the Flow oJ Hot Gases in Roof Venting, Fire Research Technical Paper No. 7, Deparnnent of Scientific and Industrial Research and Fire Offices Comminee, Joint Fire Research Organization, London: H.M. Stationary Office, 1963. 4. ZUKOSKLE.E., KUBOTA,T. AXD CETEGE*', B.: Fire Safety J. 3, 107 (1980/81). 5. ZUKOSKI, E.E., KUBOTA, T. AND CETEGEN, B.: Entrainment in the Near Field oJ Fire Plumes, California Institute of Technology, Daniel and Florence Guggenheim Jet Propulsion Center, Grant G8-9014, 1981. 6. CETEGEN, B.M., ZVKOSKL E.E. AXD KUBOTA,T.: Entrainment and Flame GeometU oj Fire Plumes, California Institute of Technology, Daniel and Florence Guggenheim Jet Propulsion Center, Grant G8-9014, 1982. 7. CETEC,EY, B.M., ZUKOSKL E.E. AN'DKUBOTA,T.: Comb. Sci. and Tech. 39,305 (1984). 8. HESKESTAD,G.: Fire Safety J. 7,25 (1984). 9. TAYLOR, G.I., MORTOX, B.R. AND TURNER,J.S.: Proc. Roy. Soc. A 234, 1 (1956). 10. RIcou, F.P. AND SPALDING, D.B.: J. Fluid Mech 11,21 (196t). 11. MORTON,B.R.: J. Fluid Mech 5, 151 (1959). 12. MORTON,B.R.: Tenth Symposium (International) on Combustion, p 973, The Combustion Institute, 1965. 13. YOKOL S.: Stud)' on the Prevention of Fire-Spread Caused b3"Hot Upward Current, Building Research Institute, Ministry of Construction, Japan, Report No. 34, 1960. 14. GEORGE, W.K., ALPERT, R i . AND TAMANIMI,F.: Int. J. Heat Mass Transfer 20, 1145 (1977). 15. McCAFFREY,B.J.: Purely Buoyant Diffusion Flames: Some Experimental Results, Center tot Fire Research, National Bureau of Standards, NBSIR 79-1910, 1979. 16. HESKESTAD, G.: Eighteenth Symposium (International) on Combustion, p 951, The Combustion Institute, 1981. 17. KUNG, H.C. AND STAVRIANIDIS, P.: Nineteenth Symposium (International) on Combustion, p 905, The Combustion Institute, 1982. 18. HESKESTAD,G.: Optimization of Sprinkler Fire Protection, Progress Report No. 9: Fire Plume Simulator, Factory Mutual Research Corporation Report 18792, 1974. 19. You, H.Z.: An Investtgation of Fire Plume Impinge-
120
FIRE
me~t on a Horizontal Ceiling, Ph.D. Thesis, The 20. 21. 22.
23,
Pennsylvania State University, 1981. HESKESTAD, G.: Fire Safety J. 5, 109 (1983). Cox, G. ANt~CHITTV, R.: Combustion and Flame 39, 191 (1980). MCCAFFREY, B.J. AND COX, G.: Entrainment and Heat Flux of Buoyant Diffusion Flames, U.S. Department of Commerce, National Bureau of Standards, NBSIR 82-2473, 1982. HASE-',~I, Y.: Characterization of the Intermittent
Flaming Region of the Upward Current Above Diffusion Flames, Building Research Institute, Ministry of Construction, Japan, Research Paper No. 95, 1982. 24. TOKUNAGA,T., SAKAI, ~1~.,KAWAGOE,K., TANAKA, T. AND HASEMI, Y.: Fire Science and Technology 2, 117 (1982). 25. BAINES, W,D. AND TURNER, J.S,: J. Fluid Mech 37, 51 (1969).
26. HESKESTAD, G.: Fire Safety J. 5, 103 (1983). 27. THOMAS, P.H,, BALDWIN, R. AND H~:SELDEN,
A.J.M.: Tenth Symposium (International) on Combustion, p 983, The Combustion Institute, 1965. 28. Yu~oTo, T. AND KOSEKI, H.: Fire Science and Technology 2, 91 (1982). 29. BEYI~ER, C.L.: Development and Burning of a Layer
of Products of Incomplete Combustion Generated by a Buoyant Diffusion Flame, Ph.D. Thesis, Harvard University, 1983. 30. HESKESTAD, G. AND HAMADA, T.: Ceiling Flows of Strong Fire Plumes, Factory Mutual Research Corporation Report 0KOE1.RU, 1984. 31. KUNG, H.C., AND DERIS, J.: Fire Plumes with Variable Density, Factory Mutual Research Corporation Report 19722-1, 1970. 32. GENGEMBRE, E., CAMBRAY, P., KARMED, D. AND BEI~LEW,J.C.: Comb. Sci. and Tech. 41,55 (1984),
FIRE P L U M E A I R E N T R A I N M E N T A C C O R D I N G TO T W O C O M P E T I N G ASSUMPTIONS GUNNAR HESKESTAD Factory Mutual Research Corporation 1151 Boston-Providence Turnpike Norwood, Massachusetts 02062
Following a review of existing entrainment predictions for fire plumes, two promising predictions for the plume region above the flames are compared against extensive experimental data on plume mass flows. Both of these predictions assume self-preserving velocity profiles. However, one of them, a prediction of Cetegen et al., assumes self-preserving excess temperature profiles while the other, advanced by the author, assumes self-preserving density deficiency profiles, the two assumptions being mutually exclusive in strong fire plumes. The prediction based on self-preserving density deficiency profiles shows good consistency with the experimental plume flows, better than the prediction based on self-preserving excess temperature profiles. A simple extension of the former on dimensional arguments to the flaming region, assuming turbulent motion, is then examined against data available from a number of sources. The extension tests well against data from fire sources with diameters of 0.3 m and greater, the flames of which can be considered substantially turbulent. On the other hand, the extension overpredicts plume flows measured in the flaming region of 0.10-0.19 m diameter fire sources, which is attributed to prevalence of laminar flaming in the case of these small sources. Possible additional research is suggested.
1. Introduction Previously, the a u t h o r established an air e n t r a i n m e n t prediction for fire plumes in behalf of an N F P A (National Fire Protection Association) C o m m i t t e e e n g a g e d in revising a s t a n d a r d on heat a n d smoke v e n t i n g of buildings. 1 At the time, e n t r a i n m e n t theories available were the w e a k - p l u m e f o r m u l a t i o n of Yih 2, considered applicable far from the fire source, a s u b s e q u e n t modification proposed by T h o m a s et al. 3 to a c c o u n t for s t r o n g - p l u m e effects, as well as a n e a r - s o u r c e expression for the flaming region also p r o p o s e d by T h o m a s et al. 3 T h e new prediction a p p e a r e d simpler to use t h a n available alternatives, a n d probably m o r e accurate. Subsequently, reports began to become available from a n i m p o r t a n t investigation o n air e n t r a i n m e n t into fire p l u m e s by Zukoski a n d coworkers. 4'5'6'7 T h e i r e n t r a i n m e n t m e a s u r e m e n t s above the flames were r e p o r t e d s to fit the new prediction quite well but this c o m p a r i s o n was n e v e r published. O n the other h a n d , Cetegen et al. 7 showed that these e n t r a i n m e n t m e a s u r e m e n t s could also be r e p r e s e n t e d quite well by a form for the p l u m e mass flux originally derived for weak plumes, but appearing to be valid for s t r o n g p l u m e s also, provided
a virtual p l u m e origin was i n c o r p o r a t e d in the formulation. This p a p e r e x a m i n e s the differences between the two approaches, i.e., the "new' e n t r a i n m e n t p r e d i c t i o n a n d that attrib u t e d to Cetegen et al., a n d compares their capabilities against e n t r a i n m e n t m e a s u r e m e n t s above the flames. Mass flow m e a s u r e m e n t s in the flaming region are t h e n e x a m i n e d as an extension of the n e w e n t r a i n m e n t prediction. As b a c k g r o u n d , the two a p p r o a c h e s will first be reviewed together with others which have b e e n proposed.
2. Prediction Methods Yih
Yih's early m e a s u r e m e n t s 2 in weak plumes ( A p / p ~ l ) from a point source indicated that the velocity a n d density deficiency profiles could be considered self-preserving.* F r o m d i m e n s i o n a l analysis of t u r b u l e n t gravity convection, Yih's results c o r r e s p o n d to the following mass flow formula: = A (gg~2Q/cp 9 T~) 1/3 z 5/3,
(1)
*Self-preserving: Profiles preserve shape when normalized with centerline values and plume width.
111
112
FIRE
where A = 0.153 according to the measurements. Thomas et al.
In their work on r o o f venting, T h o m a s et al. ~ assumed that strong plume (near source) behavior can be d e d u c e d from Yih's weak plume formula, Eq.(1), by substituting the centerline value of density, P0, for the ambient value, P~: n~ = 0.153 (gpoZQ/cp 9 T~) a/3 z 5/3
(2)
The flame height, L, is given based on observations in terms of a nondimensional p a r a m e t e r Qo * ~ Q/[p~cpT~(gD) 1/2 D2]: Qo* < 1.0: L/D = 3.30 Q.fi.2/3
(8)
Qo* I> 1.0: L/D = 3.30 Qo .2/5-
(9)
For later use, Eq.(5) may be written (in SI units, which are used throughout) for standard atmospheric conditions (293 K, 760 m m Hg): rh (kg/s) = 0.076 @/3 (z_z~)5/3.
Thomas et al. p r o p o s e d that, for area heat sources, the height, z, should be measured above an "effective point source" or virtual origin located below the area source by an amount based on the 15 ~ angle o f spread of a (weak) plume suggested by Taylor et al.9: z~ = - 1.5,4//9.
(3)
Thomas et al. 3 also considered e n t r a i n m e n t in the flaming region of large fires. Invoking the Ricou-Spaulding assumption on entrainment velocity 1~ and assuming the u p w a r d velocity in the flame varies with z 1/2 the authors obtain: n~ = 0.096 p=(gpfl/p~) 1/2 Wjz 3/2.
(4)
Here, 9~ is the gas density in the flames and W/ is the fire perimeter. Cetegen et al.
Assuming that profiles of velocity and excess t e m p e r a t u r e are self-preserving, Cetegen et al.6'rshowed that the weak-plume representation based on Morton's work 1', the same as Eq.(1), also pertains to strongly buoyant plumes. Note that this finding contradicts the assumption of T h o m a s et al. 3 in Eq.(2). To obtain good a g r e e m e n t with their experiments, Cetegen et al. introduced a virtual origin ("offset"), z~, from which z would be measured in the formula: rh = 0.21 (gp~2/cp 9 T~) 1/3 QI/3 (z_z,,)5/3.
(5)
For o p t i m u m a g r e e m e n t with their experiments, the authors proposed the following expressions for zv, d e p e n d i n g on whether the source fire is s u r r o u n d e d by a floor flush with the source p e r i m e t e r or m o u n t e d in the laboratory space without the flush flooring: With floor: z~ = - 0 . 5 0 D + 0.33 L
(6)
Without floor: zv = - 0 . 8 0 D + 0.33 L 9
(7)
(10)
These formulations pertain to the region above the flames, i.e., z/L /> 1. T h e authors are careful to point out that their fire plumes were produced in as quiet an atmosphere as could be maintained in their laboratory and that small ambient disturbances could provide 2 0 - 5 0 percent increases in the measured plume mass flows. Cetegen et al. 6'7 also p r o p o s e d a model for air entrainment in the flaming region, z/L < 1, incorporating an initial, essentially laminar region and a turbulent flame region. It is not clear from comparisons with the measurements what prediction accuracies one may expect from the p r o p o s e d model. "New" Entrainment Prediction
In the governing equations for strong plumes (continuity, momentum, energy), one may assume self-preserving profiles for velocity and either t e m p e r a t u r e rise or density deficiency. T e m p e r a t u r e rise, AT, and density deficiency, A 9, cannot be self-preserving simultaneously, which follows from the perfect gas law in the form: ap/A0o = (AT/ATo)/(T/To)
(11)
Only in weak plumes, where T/To = 1, can temperature rise and density deficiency profiles be self-preserving simultaneously. It is important to note that the equations of mean motion and energy for the plume can accommodate (are consistent with) either the assumption of self-preserving t e m p e r a t u r e rise 6'7 or the assumption of self-preserving density deficiency,* using the known behavior of velocity and t e m p e r a t u r e rise on the plume centerline. *In the case of assuming self-preserving density deficiency (and velocity), the integral equations balance except for a small term in the momentum equation of second order, i.e., to the accuracy of terms usually included in analyses.
FIRE PLUME AIR ENTRAINMENT A n i n t e r m e d i a t e p l u m e mass-flow f o r m u l a resulting from a s s u m i n g self-preserving density deficiency profiles (and velocity profiles) ist:
defined bv vertical t e m p e r a t u r e variations (Eq.(15)) a p p e a r predictable from>':
z,/D = - 1 . 0 2 + 0.083 QmS/D ~h = Qc[1 + (1-13/y) ATo/T~]/[Cp(13/y)
Y = ~o (u/uo)(r/b~) d(r/b~)
(13)
d(r/b,,).
(14)
Here, b,, is the p l u m e r a d i u s where u/uo = %. According to M o r t o n ' s extension 12 of the w e a k - p l u m e theory to s t r o n g plumes, the centerline t e m p e r a t u r e rise can be written:
ATo/T~ = C,T g-
1/3
(cpp~T~)-2/3Q~.2i3(z - zv) 5L3(15)
where Cr is a n o n d i m e n s i o n a l constant a n d z~, is the virtual origin. This relation has b e e n verified for both weak p l u m e s 2'13'14 a n d strong plumes15-17; in the fire plumes, ATo appears to obey Eq.(15) d o w n to the m e a n flame height 16. With substitution o f Eq.(15), Eq.(12) becomes:
-
1
[ ,,,,~ lV3
IL ~"~ j|
(i8)
ATo](12)
where Q,. is the convective heat-release rate a n d y a n d [3 are the n o n d i m e n s i o n a l constants:
(3 = fo (u/u~176
1 13
OV3(z-zo) s/:~ "
9[1 + CT(1 -- t3/3" ) (gl#2cp p~ T , ) -'2/:~
.Q~/3(z-G)-5/'~].
(16)
O n e set of profiles, m e a s u r e d in the p l u m e above a m e t h a n o l pool fire using t h e r m o c o u pies a n d a pitot tube 18, c o r r e s p o n d to the values y = 0.60 a n d 13 = 0.41. A n o t h e r set, m e a s u r e d vdth a t h e r m o c o u p l e a n d laser-Doppler anem o m e t e r m in the p l u m e above a n a t u r a l gas b u r n e r , c o r r e s p o n d to the values y = 0.69 a n d 13 = 0.42. Previously Ls, the f o r m e r pair was a d o p t e d for Eq. (16), t o g e t h e r with the value Cr = 9.1 d e t e r m i n e d by G e o r g e et al. 14 Accordingly, the p r o d u c t Cr (1-f3/y) becomes 2.9 a n d the factor 1/Cr(f3/'y) becomes 0.t61, although the value 0.196 was selected previously L* instead of 0.161 o n the basis of a particular p l u m e mass flow m e a s u r e m e n t ~8. Using the constants 2.9 a n d 0.196 a n d specializing to n o r m a l atmospheric conditions (293 K, 760 m m H g ) , Eq. (16) becomes (SI units): rh (kg/s) = 0.071 ovYs (z-z~,) 5/~ [1 + 0.026 Qg/S(z- z~,) - sis]. (17) For substantially t u r b u l e n t pool fires a n d other horizontal-surface fires a n d n o r m a l atmospheric conditions, the virtual origin, z~,,
where Q is the total heat-release rate a n d D is the diameter* of the fire source. Equation (18) should also be valid for porous fuel arrays, provided any i n - d e p t h c o m b u s t i o n is not substantial, i.e., p r o v i d e d most of the volatiles released u n d e r g o c o m b u s t i o n above the array** of the crib. 16 T h e p l u m e law for t e m p e r a t u r e , Eq.(15), ceases to be valid a p p r o x i m a t e l y at the m e a n position of the flame tip where, according to K u n g a n d Stavrianidis 15, the m e a n t e m p e r a t u r e rise may be taken as 500 K. T h e e n t r a i n m e n t relations, Eqs.(16) a n d (17), cease to be valid at the same elevation. T h e limiting elevation, z, z~,, may be calculated from Eq.(15) with C-r = 9.1, setting AT, = 500 K. For n o r m a l atmospheric conditions, the result is: ze - z~ = 0.166 Q25
(19)
where z~ may be o b t a i n e d from Eq.(18). T h e limiting elevation, z~, is analogous to the flame height, L, in the f o r m u l a t i o n of Cetegen et al. discussed in the p r e c e d i n g section. At the limiting elevation, zc the predicted p l u m e mass flow, k~, is o b t a i n e d from Eqs.(17) a n d (19):
ri~t(kg/s) = 0.0054 @(kW).
(20)
Below the limiting evaluation, the mass flow rate must decrease toward a value associated with the top of the combustible. If the combustible is a pool fire, the mass flux (vapor) at the top of the combustible is negligible c o m p a r e d to ~h~. For such fires, a s s u m i n g that the flames are substantially t u r b u l e n t so that viscous effects are not i m p o r t a n t , one expects for z ~< z~: rhA~ = fn(z/ze, zdD).
(21)
Previous considerations of the e n t r a i n m e n t data of Cetegen et al. suggested s that effects of ze/D were not i m p o r t a n t in the data set a n d that for sufficiently large fires, tile d e p e n d e n c e of rhhhe on z/ze was a p p r o x i m a t e l y linear. *or effective diameter such that -rr D'2/4 = area of fire source. **Underventilated wood cribs will meet this test, whereas weU ventilated wood cribs may not, depending on the openness
114
FIRE
Other Approaches
whereas, for the p l u m e region, their result was:
On the basis of McCaffrey's classification o f plume regimes (continuous flame region, intermittent f a m i n g region, plume region) and associated behavior o f centerline t e m p e r a t u r e and velocity 1~', a n u m b e r of attempts have been made to predict mass flows. In these cases it has been assumed that velocity and excess temperature profiles were self-preserving and of Gaussian form. McCaffrey *~ himself proposed the following expression for the plume flow in the f a m i n g region from experimental velocity and temperature profiles:
7/~ = 0.289 DI/2Q(z/Q2/5) 2.
rh =0.055 z QI,2.
(22)
Cox and Chitty 91 measured velocity and temperature profiles in the flaming region over the same source used by McCaffrey 1~. T h e y confirmed the centerline behavior observed by McCaffrev and generalized their data on velocity and t e m p e r a t u r e plume widths as ~/Q2,5 versus z/Q 2~ (where ~ is velocity or t e m p e r a t u r e plume width). On this basis they were able to establish an analytical expression for plume mass flow. McCaffrey and Cox 22 later analyzed their measurements of" plume profiles jointly and determined, on the basis of an overall energy balance, that their respective velocity widths were overestimated previously 1~'~1 because of intrinsic instrument errors. Their joint analysis produced the following mass flow formula for the f a m i n g region: r/~ = 0.053 zl3Q 04s.
(23)
Hasemi 23 concentrated on the intermittent flaming region. He derived an analytical solution with experimental constants, assuming somewhat different plume width behavior than Cox and Chitty 21. His mass flow is approximated as: r/1 = 0.043 Q[z/Q z5 - 0.037].
(24)
(26)
These formulations employ the r e d u c e d height, z/Q 2/5. Recent workaT-has suggested that a more a p p r o p r i a t e form is (z-z~.)/Q/~, where z~ is the virtual origin based on axial t e m p e r a t u r e and velocity behavior. 3. Comparison of Entrainment Predictions Above Flames The most useful of the entrainment predictions for the plume region above the flames are deemed to be the prediction of Cetegen et al., which assumes self-preserving excess temperature profiles, and the "new" prediction, which assumes self-preserving density deficiency profiles. This section will compare the two approaches. Contrasting the two predictions in their form for a normal atmosphere, Eq.(10) versus Eq.(17), it is seen that they differ primarily by the presence of the bracketed term in Eq.(17). In addition, the virtual origins are calculated differently in the two approaches. Eqs.(6-9) for the prediction in Eq.(10) and Eq.(18) for the prediction in Eq.(17).
Data Source The impressive body of mass flow data for fire plumes established by Cetegen, Zukoski and Kubota 6 will be used. In their experiments, the fire sources were placed at different clearances below a hood having a 2.4 m • 2.4 m opening and exhausted by a blower. T h e mass withdrawal rate o f fluid from the hood associated with a particular stationary level of the interface between hot gases in the hood and the cool room air u n d e r n e a t h was taken as the flow rate of plume fluid at the interface elevation. Interface heights above the b u r n e r of approximately 1.0, 1.5 and 2.3 m were used. Fire sources were circular, porous-bed burners operating on natural gas of the following three diameters: 0.10 m, 0.19 m and 0.50 m. Experiments were conducted both with and without a floor s u r r o u n d i n g the gas burners. Several gas rates were used with each burner. Convective heat fluxes o f a plume were calculated from the enthalpy flux at the exit from the hood; these fuxes scattered about 70 percent of the heatrelease rate based on the mass burning rate and the heat of combustion.
Tokunaga et al. z4 derived flow formulae for the intermittent flaming region and the plume region. They assumed equal t e m p e r a t u r e and velocity widths and the same plume width behavior with height as Hasemi z3. T h e y also allowed for a source diameter effect which was determined experimentally. For the intermittent flaming region the following result was obtained:
Results
rh = 0.070 D]2Q(z/QZS- 0.0337),
Figure 1 present the experimental mass flows, rh, for a floor a r o u n d the burners,
(25)
FIRE PLUME AIR ENTRAINMENT 1.8 1.6
115
1.8 []
1.6
[] 1.4
1.4
1.2
1.2
[]
.E "E
1c
1
a
.8
0
o
"E
[] 0
"E
.6
.6
.4
.4
.2
.2
0
4
6
8
9
.8
I
0
10
6
Z/Zt FIG. 1. Plume mass flows above flames measured by Cetegen et al. 6 (floor around burners), normalized with theoretical mass flows assuming self-preserving excess temperature profiles, Eq.(10) (rh = rDar), and virtual origins according to Eq.(6).OD = 0.10 m;&D = 0.19 m; ~ = 0.50 m. normalized with theoretical mass flows assuming self-preserving t e m p e r a t u r e profiles, raar, f r o m the f o r m u l a e p r o p o s e d by Cetegan et al., Eq.(10) (where m = ~h,~r), a n d Eq.(6). T h e abscissa is the height above the b u r n e r , z, normalized with the limiting height, z~, according to Eqs.(19) a n d (18), i.e., essentially the flame height. T h e data for the greatest {nterface heights, a p p r o x i m a t e l y 9.3 m, have been omitted for reasons to be discussed later. Figure 2 shows the same data normalized with the theoretical mass flows a s s u m i n g selfp r e s e r v i n g density deficiency profiles, ~izan, from Eqs.(17) (where ~ = map) a n d (18). C o m p a r i n g this plot to Fig. 1, it is quite a p p a r e n t that there is presently less systematic variation of n o r m a l i z e d mass flow with n o r m a l ized height in the p l u m e a n d fewer "wild" points. I n Fig. 3 the data have b e e n replotted again, n o r m a l i z i n g mass flows with theoretical values m~T a s s u m i n g self-preserving t e m p e r a t u r e profiles according to Eq.(10), b u t e m p l o y i n g virtual origins based o n axial ten'tperature variations, Eq.(18). T h e scatter a n d systematic t r e n d in this plot are even less a p p e a l i n g t h a n in Fig. 1. T h e data for the greatest interface heights, a p p r o x i m a t e l y 2.B m, were omitted from Figs. 1 - 3 o n the suspicion that they may have been influenced significantly by o v e r t u r n i n g effects in the hood, causing e n t r a i n m e n t at the interface in addition to the p l u m e e n t r a i n m e n t . For
8
10
Z/Zt
FiG. 2. Plume mass flows of Fig. 1 normalized with theoretical mass flows assuming self-preserving density deficiency profiles, Eq.(17) 0D = ,Da~), and virtual origins according to Eq.(18). (Symbols as in Fig. 1). these interface heights, the radius from the fire axis to the sides of the hood (1.2 m) ~as considerably less t h a n one half the height of the hood ceiling above the b u r n e r , smaller than the m i n i m u m ratio of 1 for no o v e r t u r n i n g indicated by the Baines a n d T u r n e r experitnents '-'5. In Fig. 1, the 2.3 m data would have tallen between n o n d i m e n s i o n a l mass flows of 0 . 9 4 1.26 ( t e n d i n g to decrease with increasing z/z,), 1.8
[]
1.6
[]
"~.4
1.2
:~~~,-A -
A
1
.E
9
9
OD
4
6
.8
"E .6
.4! .2 0
3 z/zz
8
10
FIG. 3. As Fig. 1, except virtual origins for theoretical mass flows calculated according to Eq.(18) instead of Eq.(6). (Symbols as in Fig. 1).
116
FIRE
and in Fig. 2 they would have fallen between 1.03-1.32 (with only slight tendency to decrease with increasing z/ze), i.e., tending to be high in both cases. Data for conditions without a floor a r o u n d the b u r n e r (not included in Figs. 1-3) were limited to the 0.19 m and 0.50 m diameter burners. For the 0.19 m burner, effects of a floor were generally small6,v. On the other hand, for the 0.50 m burner, the plume flows were reported r as approximately 30 percent higher without a floor than with a floor. Excluding the data obtained with the 2.3 m interface height for the same reasons as before, in Fig. 2 all the data without a floor would have fallen in the range of normalized mass flows 0.78-1.33 (with the 2.3 m interface-height data included, the u p p e r limit would be pushed to
1,42.) On the strength of the comparison between Figs. 1 and 2 or between Figs. 3 and 2, it can be said that the e n t r a i n m e n t prediction assuming self-preserving density deficiency profiles provides a better fit to experimental data than the prediction based on self-preserving excess temperature profiles. It is clear, however, that the absence of a s u r r o u n d i n g floor may affect entrainment, as may disturbances in the ambient flow field being e n t r a i n e d ]
4. Entrainment in Flaming Region Consider first the limiting height, ze. This height is practically equivalent to the mean (luminous) flame height, L, correlated by Heskestad 16'26. For normal ambient conditions and common combustibles (values of H jr near 3100 kJ/kg), the flame height correlation gives26: L = - 1.02 D + 0.230
Q2/5.
(27)
Using the expression for the virtual origin in Eq.(18), Eq.(27) can be written: L = z~, + 0.147
Q2/5.
(28)
Asssuming a c o m m o n value for the convective fraction, QJQ = 0.7, Eq.(28) can be written: L = z~, + 0.170
Qj/5
(29)
which is practically the same as the expression for ze from Eq.(19). Equation (20) is a representation of the plume mass flow at the limiting height (mean flame height) in terms of the convective heat
flux. For fire sources with the specific convective fraction, Q/Q = 0.7, Eq.(20) can be written: ~he = 0.0038 Q = 0.0038 (srhj) (Hc/s)
(30)
where s is the mass stoichiometric ratio, air to volatiles, s~h!representing the mass stoichiometric air requirements for complete combustion. Adopting the typical value His = 3100 kJ/kg, Eq.(30) becomes rhe ~ 12 (~z/).
(31)
Hence, at the mean flame height, the mass flow in the plume is some 12 times the mass stoichiometric ratio. Considering that the mass stoichiometric ratio (s) is typically on the order of ten, the mass contributed to the plume by the fuel 0hf) is on the order of one percent of the plume mass flow at the level of the flame tip. Hence, the fuel contribution can be neglected, consistent with the form of Eq.(21). The objective here is to test Eq.(21) on available measurements in the flaming region and develop explicit forms, if possible. T h e most important data source is again Cetegen et al. 6, who used a modification of their technique for measuring mass flows above the flames. Because of the high gas temperatures associated with flames reaching well into the hot-gas layer in the hood, mass flow rates in the plumes at the interface were deduced from the fuel flow rates and concentrations of carbon dioxide in a gas sample taken from the smoke hood and completely oxidized. All these measurements were made without a floor s u r r o u n d i n g the burners. Important measurements are also available from other sources. Thomas et al. 2r used thistledown as a tracer to measure the flow of air toward ethyl alcohol and wood fires of 0.91 m diameter and a square "town gas" fire 0.30 in on the side. They presented mass air flows through a cylindrical surface of 0.68 m radius concentric with the flame as a function of height above the fire base, which may be interpreted as plume mass flow as function of height. McCaffrey ~5 determined mass flows above a 0.3 m square, porous refractory b u r n e r supplied with natural gas, using profiles of velocity d e t e r m i n e d with a bidirectional flow probe and temperature determined with a thermocouple. Yumoto and Koseki 28 b u r n e d heptane floated on water in a 0.30 m diameter vessel and measured horizontal inflow velocities with a bidirectional flow probe at different heights in a cylindrical surface of the same radius as the vessel. From these data they
FIRE PLUME AIR ENTRAINMENT d e t e r m i n e d total mass inflow as function of height, which they a s s u m e d equal to total mass flow in the p l u m e as f u n c t i o n of height. Beyler's c o m p r e h e n s i v e e x p e r i m e n t s 29 i n c l u d e d e n t r a i n m e n t m e a s u r e m e n t s for flames from 0.13 m a n d 0.19 m d i a m e t e r gas b u r n e r s (propane a n d propene). He e m p l o y e d a t e c h n i q u e similar to that used by Cetegen et al. 6'7 for regions above the flames, i.e., placing the b u r n e r s u n d e r a h o o d exhausted by a blower a n d stabifizing the hot-gas interface within the h o o d at a k n o w n distance above the b u r n e r . For the 0.19 m b u r n e r , the p l u m e mass flows correlated well with the e q u a t i o n (using the "FC layer" interface definition29): rh(kg/s) = 0.073 [z(m) + 0.06] 125
(32)
over the heat-release r a n g e 8 . 2 - 3 1 . 5 kW. T h e mass flows for the 0.13 m b u r n e r were sensitive to the heat release rate, which also covered the r a n g e 8 . 2 - 3 1 . 5 kW. Fig. 4 is a collection o f p l u m e mass flows for V 1.4
V V
1.2
V
o/
Vo ~f
.g
V
.8 0
.E
/
.6
zI~f ~
.4
117
the larger b u r n e r s , 0.3 to 0.9 m in diameter, plotted in the coordinates ~h/rh~ versus z/z~ suggested by Eq.(21), where th is the m e a s u r e d mass flow a n d z is the m e a s u r e m e n t height. Equation (20) was used to calculate d~ and Eqs.(19) a n d (18) were used to calculate z~, a s s u m i n g Qc/Q = 0.7 in all cases. In the case of square b u r n e r s , the effective source diameter was calculated on an equal source-area basis. T h e plot correlates most of the data quite well along the straight line:
hz/h~ = z/z~.
(33)
T h e data of McCaffrey 15 plots a little high, which can be a t t r i b u t e d to excessive axial velocities indicated by his bidirectional flow probe away from the p l u m e axis 22. For the e x p e r i m e n t s in this figure, the ratio z~/D r a n g e d from 0.7 to 2.3; n o effect of z(/D has been observed in this range. Fig, 5 collects p l u m e flow data for a smaller source diameter, 0.19 m. Most of the data plot below the line d e f i n e d by Eq.(32). T h e divergence from the data from the larger b u r n e r s in Fig. 4 can probably be attributed to a significantly greater prevalence of l a m i n a r flaming n e a r the source for the smaller b u r n e r s 6'7. T h e generally higher values of ze/D associated with the smaller b u r n e r (1.8-6.0) are not believed to have been i m p o r t a n t . Figure 6 shows the results for the smallest b u r n e r s , 0 . 1 0 - 0 . 1 3 m in diameter, where the associated z~/D values r a n g e d from 3 to 10. Again, one may suspect that the deviation from the line d e f i n e d by Eq.(33) is associated with l a m i n a r flaming effects (or viscous effects). A s s u m i n g the validity of Eq.(33) for essentially fully t u r b u l e n t flames, the following expression is o b t a i n e d for rh in the flaming region (z <- ze) with the aid of Eqs.(19) a n d (20) a n d taking Qc/Q = 0.7 (SI units):
/
rh(kg/s) = 0.0054 QS(0.166 Qc25 + z_~.)
/
0
/ 0
I .2
I .4
I .6
I .8
I 1
Z//Zl
FIG. 4. Plume mass flow rates in the flaming region for source diameters in the range 0.3-0.9 m (~hefrom Eq.(20) and ze from Eqs.(19) and (18)). o Cetegen et al. 6, 0.5 m dia natural gas (32-73 kW); VMcCaffrey 15, 0.3 m sq natural gas (10-50 kW); AYumoto and Koseki 28, 0.3 m dia heptane (52 kW); ~Thomas et alfl 7, 0.9 m dia ethanol (509 kW) and 0.3 m sq "town gas" (252 kW).
(34)
where z~, is given by Eq.(18) for fire sources which do not have substantial i n - d e p t h c o m b u s t i o n 2~ Equation (34) may be c o m p a r e d to other predictions for the flaming region, using app r o x i m a t e forms t h r o u g h o u t (e.g., setting z, = o in Eq.(34)). T h e a p p r o x i m a t e forms are (assuming Q#Q = 0.7): Eq.(34): Eq.(22): Eq.(23): Eq.(24): Eq.(25):
rh rh rh rh rh
= = = = =
0.032 0.065 0.063 0.053 0.087
o~c 3'5z o ~c o sSz ~ ~ Qc
Dl'2Q3'Sz.
(35) (36) (37) (38) (39)
118
FIRE 5. O n S e l f - P r e s e r v a t i o n
/O /
/
The improved a g r e e m e n t obtained for the plume mass flows above the flames when self-preserving density deficiency profiles are assumed rather than self-preserving excess temperature profiles seems to suggest that the former assumption is more nearly correct. It should be possible to check this conclusion in a direct m a n n e r from measurements of plume profiles. The strong-plume prediction for plume width12:
/
.8
/
/
/
.6
/ 9E
/
.4
9
oa
VCD 9
/
.2
bn = Cb,(To/T~) 1/2 (z-zv) 1
I
I
I
I
.2
.4
.6
.8
1
Z/Zl
FIG. 5. Like Fig. 4, except source diameters of 0.19 m. oCetegen et al. 6, 0.19 m dia natural gas (21-81 kW); VBeyler29, 0.19 m d i a propane (8 kW); Ado. (21-32 kW). There is surprisingly good consistency a m o n g most of these forms. It is especially gratifying to confirm a nearly unanimous, linear dependence on z, the d e p e n d e n c e observed in Fig. 4 and expected to represent fires with substantially turbulent flames (diameters of perhaps 0.3 m and greater).
(40)
is consistent with known centerline behavior o f excess t e m p e r a t u r e (or density deficiency) and velocity, and either self-preservation assumption 8'3~ T h e plume width, b,,, and associated coefficient, Cb,,, may apply to the velocity profile (b~, Cb~), excess t e m p e r a t u r e profile (bA~-,CHAT) or density deficiency profile (ba~, CbA~). Regardless of the self-preservation assumption one expects to see constant Cb~ in all plumes, weak and strong. However, d e p e n d i n g on whether excess temperature or density deficiency is self-preserving, either ChATor Chap will be constant, but not both. The a u t h o r has examined a n u m b e r of measurements 2'13-15'17-19'21'31'32 for the degree of constancy o f Cb,,, ChAT and Cba~, but has not been able to establish convincing conclusions because of great scatter in the data, including uncertainties about the location of the virtual origin, z~,.
/ / / /
.8
/
6. C o n c l u s i o n s
x5
/ / /
.6
/ / /
//
0(3
9 E .4 /
.2
/
~Q~)
///z~
"r.)
~
A~Z2 0
/
0
I
1
I
I
I
.2
.4
.6
.8
1
Z/ZL
FIG. 6. Like Fig. 4, except source diameters in range 0.10-0.13 m. oCetegen et alJ~, 0.10 m dia natural gas (21-52 kW); ABeyler29, 0.13 rn dia propane (8-32 kW).
1. For the plume above the flames, the entrainment prediction assuming self-preserving density deficiency profiles, Eqs.(17) and (18), provided better consistency with measurements than the prediction of Cetegen et al. assuming self-preserving excess t e m p e r a t u r e profiles, Eqs.(10) and (6-9). 2. An extension of the prediction assuming self-preserving density deficiency profiles to the flaming region tested well against plume flows measured in the flaming region for fire diameters of 0.3 m and greater, i.e., whenever the flames could be considered substantially turbulent. For the data set examined and involving fire diameters in the range 0.3-0.9 m along with flame-height to diameter ratios in the range o f 0.7-2.3, plume flows in the flaming region (z ~< ze, where ze is given by Eq.(19)) were consistent with Eq.(34). For fire
FIRE PLUME AIR ENTRAINMENT diameters of 0 . 1 0 - 0 . 1 9 m, the e x p e r i m e n t a l p l u m e flows t e n d e d to be lower than given by Eq.(34), attributed to prevalence of l a m i n a r f l a m i n g for these small fire sources. 3. Additional investigation of the flaming r e g i o n would be desirable with respect to possible effects of the flame-height to d i a m e t e r ratio. F u r t h e r m o r e , special considerations are n e e d e d for fire sources with substantial ind e p t h combustion. Effects o f a m b i e n t air currents are also of great i m p o r t a n c e , especially in the context of r o o m fires.
Nomenclature A .4/ b~ Cb~ CT cp D g H, L rh n~/ rhr ")aT rhap Q Q,. QY~ r s T AT u Wf z ze z~, [3 ~/ p Ap cr
nondimensional constant (-) area of fire source (m 9) (n=u, AT, Ap), p l u m e radius where nln,, = q2 (m) (n=u, AT,Ap), coefficients related to p l u m e width ( - ) coefficient related to p l u m e t e m p e r a t u r e (-) specific heat o f air (kJ/kg- K) fire d i a m e t e r (m) acceleration o f gravity (m/s 2) heat of c o m b u s t i o n (kJ/kg) m e a n flame height (m) p l u m e mass flow rate (kg/s) mass b u r n i n g rate (kg/s) n/ at ze (kg/s) predicted -/ a s s u m i n g self-preserving excess t e m p e r a t u r e profiles (kg/s) predicted rh a s s u m i n g self-preserving density deficiency profiles (kg/s) (total) heat release rate (kW) convective heat release rate (kW) Q/[p~cpT~(gD)l/2D 2] ( - ) radius (m) mass stoichiometric ratio, air to volatiles (-) t e m p e r a t u r e (K) T-T~, excess t e m p e r a t u r e (K) axial velocity (m/s) fire p e r i m e t e r (m) height above fuel surface (m) limiting elevation; elevation z in p l u m e c o r r e s p o n d i n g to ATo = 500 K (m) location, z, of virtual origin (m) n o n d i m e n s i o n a l constant; see Eq.(14) ( - ) n o n d i m e n s i o n a l constant; see Eq.(13) ( - ) density (kg/m ~) 9~ - P, density deficiency (kg/m 3) p l u m e radius in Gaussian profiles (m)
Subscripts fl o ~r
flames centerline ambient
119 REFERENCES
1. Guide /'or Smoke and Heat Venting, NFPA 204M-1982, Appendix A, National Fire Codes, Vol. 15, p. 204M-31, National Fire Prevention Association, 1983. 2. YIH, C-S.: Proc. U.S. National Coug. App. Mech., p 941, 1952. 3. THOMAS, P.H., HINKLEY, P.L., THEOBALD, C.R. AND SIMMS, D.L.: lnvesttgations Into the Flow oJ Hot Gases in Roof Venting, Fire Research Technical Paper No. 7, Deparnnent of Scientific and Industrial Research and Fire Offices Comminee, Joint Fire Research Organization, London: H.M. Stationary Office, 1963. 4. ZUKOSKLE.E., KUBOTA,T. AXD CETEGE*', B.: Fire Safety J. 3, 107 (1980/81). 5. ZUKOSKI, E.E., KUBOTA, T. AND CETEGEN, B.: Entrainment in the Near Field oJ Fire Plumes, California Institute of Technology, Daniel and Florence Guggenheim Jet Propulsion Center, Grant G8-9014, 1981. 6. CETEGEN, B.M., ZVKOSKL E.E. AXD KUBOTA,T.: Entrainment and Flame GeometU oj Fire Plumes, California Institute of Technology, Daniel and Florence Guggenheim Jet Propulsion Center, Grant G8-9014, 1982. 7. CETEC,EY, B.M., ZUKOSKL E.E. AN'DKUBOTA,T.: Comb. Sci. and Tech. 39,305 (1984). 8. HESKESTAD,G.: Fire Safety J. 7,25 (1984). 9. TAYLOR, G.I., MORTOX, B.R. AND TURNER,J.S.: Proc. Roy. Soc. A 234, 1 (1956). 10. RIcou, F.P. AND SPALDING, D.B.: J. Fluid Mech 11,21 (196t). 11. MORTON,B.R.: J. Fluid Mech 5, 151 (1959). 12. MORTON,B.R.: Tenth Symposium (International) on Combustion, p 973, The Combustion Institute, 1965. 13. YOKOL S.: Stud)' on the Prevention of Fire-Spread Caused b3"Hot Upward Current, Building Research Institute, Ministry of Construction, Japan, Report No. 34, 1960. 14. GEORGE, W.K., ALPERT, R i . AND TAMANIMI,F.: Int. J. Heat Mass Transfer 20, 1145 (1977). 15. McCAFFREY,B.J.: Purely Buoyant Diffusion Flames: Some Experimental Results, Center tot Fire Research, National Bureau of Standards, NBSIR 79-1910, 1979. 16. HESKESTAD, G.: Eighteenth Symposium (International) on Combustion, p 951, The Combustion Institute, 1981. 17. KUNG, H.C. AND STAVRIANIDIS, P.: Nineteenth Symposium (International) on Combustion, p 905, The Combustion Institute, 1982. 18. HESKESTAD,G.: Optimization of Sprinkler Fire Protection, Progress Report No. 9: Fire Plume Simulator, Factory Mutual Research Corporation Report 18792, 1974. 19. You, H.Z.: An Investtgation of Fire Plume Impinge-
120
FIRE
me~t on a Horizontal Ceiling, Ph.D. Thesis, The 20. 21. 22.
23,
Pennsylvania State University, 1981. HESKESTAD, G.: Fire Safety J. 5, 109 (1983). Cox, G. ANt~CHITTV, R.: Combustion and Flame 39, 191 (1980). MCCAFFREY, B.J. AND COX, G.: Entrainment and Heat Flux of Buoyant Diffusion Flames, U.S. Department of Commerce, National Bureau of Standards, NBSIR 82-2473, 1982. HASE-',~I, Y.: Characterization of the Intermittent
Flaming Region of the Upward Current Above Diffusion Flames, Building Research Institute, Ministry of Construction, Japan, Research Paper No. 95, 1982. 24. TOKUNAGA,T., SAKAI, ~1~.,KAWAGOE,K., TANAKA, T. AND HASEMI, Y.: Fire Science and Technology 2, 117 (1982). 25. BAINES, W,D. AND TURNER, J.S,: J. Fluid Mech 37, 51 (1969).
26. HESKESTAD, G.: Fire Safety J. 5, 103 (1983). 27. THOMAS, P.H,, BALDWIN, R. AND H~:SELDEN,
A.J.M.: Tenth Symposium (International) on Combustion, p 983, The Combustion Institute, 1965. 28. Yu~oTo, T. AND KOSEKI, H.: Fire Science and Technology 2, 91 (1982). 29. BEYI~ER, C.L.: Development and Burning of a Layer
of Products of Incomplete Combustion Generated by a Buoyant Diffusion Flame, Ph.D. Thesis, Harvard University, 1983. 30. HESKESTAD, G. AND HAMADA, T.: Ceiling Flows of Strong Fire Plumes, Factory Mutual Research Corporation Report 0KOE1.RU, 1984. 31. KUNG, H.C., AND DERIS, J.: Fire Plumes with Variable Density, Factory Mutual Research Corporation Report 19722-1, 1970. 32. GENGEMBRE, E., CAMBRAY, P., KARMED, D. AND BEI~LEW,J.C.: Comb. Sci. and Tech. 41,55 (1984),