Comparison of algorithms to calculate plume centerline temperature and ceiling jet temperature with experiments

42 Pages·2 MB·English

by  Davis, William D.

NISTIR 6448
Comparison of Algorithms to Calculate
Plume Centerline Temperature and
Ceiling Jet Temperature with Experiments
William D. Davis
IMIST
United States Department ofCommerce
ogy Administration
Institute ofStandards and Technology
100
.1156
NO.64*18
ZooO

NISTIR 6448
Comparison of Algorithms to Calculate
Plume Centerline Temperature and
Ceiling Jet Temperature with Experiments
William D. Davis
Fire Safety Engineering Division
Building and Fire Research Laboratory
National Institute ofStandards and Technology
January 2000
U.S. Department ofCommerce
William M. Daley, Secretary
Technology Administration
Dr. Cheryl L. Shavers, Under Secretary ofCommerce for Technology
National Institute ofStandards and Technology
Raymond G. Kammer, Director

Contents
Abstract
. 1
1. Introduction 1
2. Theory 2
.
2.1 Plume Centerline Temperature 2
2.2 Ceiling Jet Algorithm 3
3. Comparison ofModel Predictions with Experiments 4
m
3.1 Ceiling height of0.58 .5
m
3.2 Ceiling height of 1.0 5
m
3.3 Ceiling Height of2.7 6
m
3.4 Ceiling Height of 10 6
m
3.5 Ceiling Height of 15 7
m
3.6 Ceiling Height of22 8
4. Summary 9
5. References 10
i

Comparison ofAlgorithms to Calculate Plume Centerline Temperature
and Ceiling Jet Temperature with Experiments
William D. Davis
National Institute ofStandards and Technology
Abstract
The predictive capability oftwo algorithms designed to calculate plume centerline temperature
(Evans) and maximum ceilingjet temperature (Davis et. al.) in the presence ofa hot upper layer are
compared with measurements from a series ofexperiments. In addition, comparisons are made
using the ceilingjet algorithm in CFAST (version 3.1), the unconfined plume algorithm of
Heskestad, and the unconfined ceilingjet algorithm ofAlpert. The experiments included ceiling
heights of0.58 m to 22 m and heat release rates (HRR) of0.62 kW to 33 MW. It was shown that
the unconfined ceiling algorithms underpredicted the temperatures while the ceilingjet algorithm in
CFAST overpredicted the temperature in the presence ofa hot layer. With the combined
uncertainty ofthe measurement and the calculation roughly equal to ±20%, the algorithms ofboth
Evans and Davis et. al. consistentlyprovidedpredictions either close to orwithin this uncertainty
interval for all fire sizes and ceiling heights.
1. Introduction
Recent experiments1 have demonstrated the need for an improved predictive capability forboth
ceilingjet temperature and plume centerline temperature in draft curtained, high bay spaces when
upper layers develop. Algorithms have been developed and tested using JET2 a modified version of
,
the zone fire model LAVENT3 which are able to simulate plume centerline temperature and ceiling
,
jet temperature forthe experiments1 These algorithms have subsequently been included in CFAST
.
(version 3.1)4 in orderto test their accuracy using this platform. This study compares the predictions
ofthe algorithms for ceilingjet temperature (Davis et. al.2) and plume centerline temperature
(Evans5) with the measurements from several experiments1,6’7’8’9. Also included in the comparisons
are the ceilingjet predictions ofCFAST (version 3.1), Alpert’s unconfined ceilingjet algorithm10
and the plume centerline temperature predictions ofHeskestad’s unconfined plume algorithm11
.
The experiments selected for comparison with these models span awide range ofparameters
including ceiling height and fire size. Since this work is done in the context ofbuildings, only
experiments which formed ahot ceiling layerwere used. In most instances, comparison between
prediction and measurement is made afterthe growing fire has reached a steady-state heat release
rate (HRR). Plume centerline temperature comparisons are made for ceiling heights ranging from
m m
0.58 to 22. while ceilingjet temperature comparisons are made for ceiling heights ranging
m
from 1.0 to 22. m.
1
1
2. Theory
2.1 Plume Centerline Temperature
The analysis offire plumes is based on the solution ofthe conservation laws for mass, momentum
and energy. Early work centered on point sources and assumed that the air entrainment velocity at
the edge ofthe plume was proportional to the local vertical plume velocity12 Measurements of
.
plume centerline temperature in plumes with unconfmed ceilings led to a correlation developed by
Heskestad11 which was consistentwith theory. The correlation gives the excess temperature as a
function ofheight above a virtual point source to be
T
(1)
The virtual origin (z is given by
0)
z0=- .02D+0.083(22/5 (2)
where Q and Q are the total and the convective heat release rates, D is the fire diameter, z is the
c
height above the fire surface, and T„,, c and p„ are the temperature, heat capacity, and density ofthe
p,
ambient gas. When a hot upper layer forms, this correlation must be modified in order to predict
plume centerline temperature since the plume now includes added enthalpy by
entraining hot layer gas as it moves through the upper layer to the ceiling. Methods ofdefining a
substitute virtual source and heat release rate in orderto extend the plume into the upper layerhave
been developed by Cooper13 and Evans5 Evans’ method defines the strength Qu and location Z of
. I2
the substitute source with respect to the interface between the upper and lower layers by
+C Q™)IZ,C -VC f2
fii=[(l 1 T T (3)
4
( )
2
m
Qu=QAp.cjjs z%) (5)
where Z is the distance from the fire to the interface between the upper and lower layer, Zu is the
X1
distance from the virtual source to the layer interface, E, is the ratio ofupper to lower layer
temperature, P is an experimentally determined constant14 (P2= 0.913), Zu is the height from the
fire to the layer interface, and Cx = 9.115. The distancebetween the virtual source and the ceiling,
H
is then obtained from
2,
H H
Z +Z
2 { 7! /2 (6)
where is the location ofthe fire beneath the ceiling (see figure 1). The new values ofthe fire
source and ceiling height are then used in a standard plume correlation15 where the ambient
temperature is now the temperature ofthe upper layer. The plume excess temperature is givenby
(7)
where T is the temperature ofthe upper layer.
u
2.2 Ceiling Jet Algorithm
The ceilingjet temperature algorithm (Davis et. al.2 ) predicts the maximum temperature excess of
the ceilingjet in the presence ofa growing upper layer. The ceilingjet temperature excess as a
function ofradius forr/H > 0.18 is givenby
r=MT(V
A
(8)
p ,
r
where
*=(0.68+0.16(1 -e'^-0) (9)
,
3
H
r =0.18 10
O 7, ( )
Y=2/3-a(l -e ~yL'yj) , (ID
and a = 0.44, y; = 1.0 m, yL is the layer thickness, and ATp is the plume centerline temperature
excess as calculated using Evans’ method (equations 3 - 8). When a hot layer is not present, the
model reduces to the correlation ofAlpert5 for r/H >0.18 with the exception that the convective heat
release rate rather than the total heat release is used in the correlation.
Qc
/ \2/3
12
A T= 5.4 rH ( )
A modification was made to this algorithm in order to accommodate the low ceiling heights
m
modeled in this paper. The parameter yh whichwas given a constant value of1.0 in reference 2,
was changed to 0.1 * H such that the algorithm could handle ceiling heights from 0.58 m to 22 m.
3. Comparison ofModel Predictions with Experiments
Data from a series ofexperiments was obtained for the purpose ofcomparison with the predictions
A
ofthe algorithms described in section 2. briefdescription ofeach experiment will be included in
the sections below. The experiments will be organized according to the distance between the fire
m
source and the ceiling with the range being 0.58 to 22 m. The new algorithms for ceilingjet
temperature and plume centerline temperature using CFAST as the computational base will be
designated as DNT in the comparisons, while the present ceilingjet algorithm in CFAST, version
3.1 will be designated as v3.1.
Uncertainty intervals are provided forboth experimental measurements and model predictions. For
each experiment, the experimental uncertainties are either those given in the report or are estimated
based on the experimental data and fire type.
Computer fire models require a number ofexperimentally determined input values and the
uncertainty in each input value generates an uncertainty in the calculated result. Uncertainty
intervals for the models in this paper are based on the estimated uncertainty in the convective heat
release rate. Uncertainties in the measurement ofthe distance between the fire and the ceiling, and
the material properties ofthe walls and ceiling are neglected. The uncertainty in convective heat
release rate is equal to the combined uncertainty for the FIRR and the radiative fraction. The
uncertainty intervals for the calculations were obtained by using ahigh, middle and low estimate of
the convective heat release rate. These estimates were done eitherby varying the radiative fraction
4