Hydrogen-combustion analyses of large-scale tests Page: 3 of 9
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II.A Burn Time
By definition, (a) burn velocity or deflagration rate will be relative to the
unburned mixture, (b) flame speed will be relative to the walls, and (c) burn
time will be the flame propagation distance divided by the flame speed. Refer-
ence 5 discusses two turbulent-burning flame speeds that can be used to compute
the burn time for pressure-pulse burning analysis: the turbulent burn velocity
with respect to the unburned mixture, S~, and the flame speed with respect to
the vessel wall FS, which is increased to account for gas expansion.
Table XI.5-1 presents the test conditions, test results and an analysis that
compares the flame speed indicated by the test with ST and FS. The comparison
of the predicted and measured flame speed indicates that the actual flame speed
for these tests is bracketed by and FS. However, it is not clear which
should be used for compartments in general because (a) geometries and flow con-
ditions are varied and complex, and (b) NTS results are test specific with ap-
plication restricted probably to geometries and flow conditions similar to those
for NTS. Note that the flame speed Increased to account for the gas expansion
(FS) should result in maximum pressure peaks for pulse burning because the time
of burning is less, which resull3 in less energy transfer to heat sinks and less
pressure-relief flow out of the compartment. The burn-time parameter has
limited significance for continuous burning.
II.B Flammability Limit b Mean Concentration at Ignition
We define the flammability limit as the local H2 concentration at the igniter
when ignition is initiated, which is different from the volumetric mean concen-
tration at ignition (XQ). XQ is related to the flammability limit and the con-
centration gradient, which depends on turbulence and scale as discussed in
Ref. 5. For example, (a) with good mixing, XQ is higher than the flammability
limit, and (b) with poor mixing, X0 could be lower than the flammability limii
because burning could occur at a high local concentration of hydrogen.
The NTS test results indicate a value of ~5% for the flammability limit based on
the fraction of hydrogen burned (for premixed tests with turbulence) vs the
hydrogen concentration as shown in Fig. XI.5-1. This plot shows that a frac-
tion-burned value of zero corresponds to a hydrogen concentration of ~5%,
thereby defining the flammability limit. This observation is confirmed by NTS
test results for the the ratio of maximum to initial pressures vs hydrogen con-
centration going to a minimum level of combustion (pressure ratio of one) at a
hydrogen concentration of ~5%, see Ref. 1.
It appears that a reasonable estimate of the moan concentration at ignition (XQ)
can be obtained from (a) the turbulent-mixture flammability limit of 4 to 5X de-
pending on the steam concentration and (b) Ref. 5 to account for the effects of
turbulence and scale (compartment size) on concentration gradient.
II.C Fraction Burned
Figure XI.5-1 shows the fraction burned (F) indicated by the NTS tests with
turbulence and compares these results with our curve, developed in Ref. 5. Note
that the main difference between the curves is the flammability limit (where F
goes to zero), which is caused probably by the high steam concentrations of the
NTS tests. The curve comparison of Fig. XI.5-1 indicates that (a) rhe frac-
tion-burned curves should be made to depend on the steam concentration, and
(b) the NTS fraction-burned dependence on XQ (i.e., the curve shape) is similar
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Gido, R.G. & Koestel, A. Hydrogen-combustion analyses of large-scale tests, article, January 1, 1986; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc1099143/m1/3/: accessed April 18, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.