PD CEN/TR 16988:2016
Estimation of uncertainty in the single burning item test
Standard number:  PD CEN/TR 16988:2016 
Pages:  58 
Released:  20160831 
ISBN:  978 0 580 90291 8 
Status:  Standard 
PD CEN/TR 16988:2016
This standard PD CEN/TR 16988:2016 Estimation of uncertainty in the single burning item test is classified in these ICS categories:
 17.200.01 Thermodynamics in general
1.1 General
The measuring technique of the SBI (single burning item) test instrument is based on the observation that, in general, the heats of combustion per unit mass of oxygen consumed are approximately the same for most fuels commonly encountered in fires (Huggett [12]). The mass flow, together with the oxygen concentration in the extraction system, suffices to continuously calculate the amount of heat released. Some corrections can be introduced if CO _{2}, CO and/or H _{2}O are additionally measured.
1.2 Calculation procedure
1.2.1 Introduction
The main calculation procedures for obtaining the HRR and its derived parameters are summarized here for convenience. The formulas will be used in the following clauses and especially in the clause on uncertainty.
The calculations and procedures can be found in full detail in the SBI standard [1].
1.2.2 Synchronization of data
The measured data are synchronized making use of the dips and peaks that occur in the data due to the switch from ‘primary’ to ‘ main’ burner around t = 300 s, i.e. at the start of the thermal attack to the test specimen. Synchronization is necessary due to the delayed response of the oxygen and carbon dioxide analysers. The filters, long transport lines, the cooler, etc. in between the gas sample probe and the analyser unit, cause this shift in time.
After synchronization, all data are shifted so that the ‘main’ burner ignites  by definition  at time t = 300 s.
1.2.3 Heat output
1.2.3.1 Average heat release rate of the specimen (HRR _{30s})
A first step in the calculation of the HRR contribution of the specimen is the calculation of the global HRR. The global HRR is constituted of the HRR contribution of both the specimen and the burner and is defined as
[Formula removed.]
where
HRR _{total} (t)  is the total heat release rate of the specimen and burner (kW); 
E′  is the heat release per unit volume of oxygen consumed at 298 K, = 17 200 (kJ/m3); 
V _{ D } _{298} (t)  is the volume flow rate of the exhaust system, normalized at 298 K (m3/s); 
x _{a_O2}  is the mole fraction of oxygen in the ambient air including water vapour; 
ϕ(t)  is the oxygen depletion factor. 
φ ( t) The last two terms x _{a_O2} and [Formula removed.] express the amount of moles of oxygen, per unit volume, that have chemically reacted into some combustion gases. Multiplication with the volume flow gives the
amount of moles of oxygen that have reacted away. Finally this value is multiplied with the ‘Huggett’ factor. Huggett stated that regardless of the fuel burnt roughly a same amount of heat is released.
The volume flow of the exhaust system, normalized at 298 K, V _{D298}( t) is given by
[Formula removed.]
where
c  [Formula removed.] 
A  is the area of the exhaust duct at the general measurement section (m2); 
k _{ t }  is the flow profile correction factor; converts the velocity at the height of the bidirectional probe in the axis of the duct to the mean velocity over the cross section of the duct; 
k _{ ρ }  is the Reynolds number correction for the bidirectional probe, taken as 1,08; 
Δp(t)  is the pressure difference over the bidirectional probe (Pa); 
T _{ms} (t)  is the temperature in the measurement section (K). 
The oxygen depletion factor ϕ( t) is defined as
[Formula removed.]
where
xO_{2} (t)  is the oxygen concentration in mole fraction; 
xCO_{2} (t)  is the carbon dioxide concentration in mole fraction; 
Ys...Zs  mean taken over interval Y s to Z s. 
The mole fraction of oxygen in ambient air, taking into account the moisture content, is given by
[Formula removed.]
where
xO_{2} (t)  is the oxygen concentration in mole fraction; 
H  is the relative humidity (%); 
p  is the ambient pressure (Pa); 
Tms(t)  is the temperature in the general measurement section (K). 
Since we are interested in the HRR contribution of the specimen only, the HRR contribution of the burner should be subtracted. An estimate of the burner contribution HRR _{burner}( t) is taken as the HRR _{total}( t) during the base line period preceding the thermal attack to the specimen. A mass flow controller ensures an identical HRR through the burners before and after switching from primary to the main burner. The average HRR of the burner is calculated as the average HRR _{total}( t) during the base line period with the primary burner on (210 s ≤ t ≤ 270 s):
[Formula removed.]
where
HRRav_burner  is the average heat release rate of the burner (kW); 
HRRtotal(t)  is the total heat release rate of specimen and burner (kW). 
HRR of the specimen
In general, the HRR of the specimen is taken as the global HRR, HRR _{total}( t), minus the average HRR of the burner, HRR _{av_burner}:
For t > 312 s:
[Formula removed.]
where:
HRR(t)  is the heat release rate of the specimen (kW); 
HRRtotal(t)  is the global heat release rate of specimen and burner (kW); 
HRRav_burner  is the average heat release rate of the burner (kW). 
During the switch from the primary to the main burner at the start of the exposure period, the total heat output of the two burners is less than HRR _{av_burner} (it takes some time for the gas to be directed from one burner to the other). Formula (24) gives negative values for HRR( t) for at most 12 s (burner switch response time). Such negative values and the value for t = 300 s are set to zero, as follows:
For t = 300 s:
[Formula removed.]
For 300 s < t ≤ 312 s:
[Formula removed.]
where
max.[a, b]  is the maximum of two values a and b. 
Calculation of HRR _{30s}
In view of the calculation of the FIGRA index, the HRR data are smoothened with a ‘flat’ 30 s running average filter using 11 consecutive measurements:
[Formula removed.]
where
HRR _{30s}(t)  is the average of HRR(t) over 30 s (kW); 
HRR(t)  is the heat release rate at time t (kW). 
1.2.3.2 Calculation of THR(t) and THR _{600s}
The total heat release of the specimen THR( t) and the total heat release of the specimen in the first 600 s of the exposure period (300 s ≤ t ≤ 900 s), THR _{600s}, are calculated as follows:
[Formula removed.]
[Formula removed.]
whereby the factor 1 000 is introduced to convert the result from kJ into MJ and the factor 3 stands for the time interval inbetween 2 consecutive measurements,
and where
THR(t _{a})  is the total heat release of the specimen during the period 300 s ≤ t ≤ t _{a} (MJ); 
HRR(t)  is the heat release rate of the specimen (kW); 
THR_{600s}  is the total heat release of the specimen during the period 300 s ≤ t ≤ 900 s (MJ); (equal to THR(900)). 
1.2.3.3 Calculation of FIGRA _{0.2MJ} and FIGRA _{0.4MJ} (Fire growth rate indices)
The FIGRA is defined as the maximum of the ratio HRR _{av}( t)/( t − 300), multiplied by 1 000. The ratio is calculated only for that part of the exposure period in which the threshold levels for HRR _{av} and THR have been exceeded. If one or both threshold values are not exceeded during the exposure period, FIGRA is equal to zero. Two combinations of threshold values are used, resulting in FIGRA _{0,2MJ} and FIGRA _{0,4MJ}.

The average of HRR, HRR _{av}, used to calculate the FIGRA is equal to HRR _{30s}, with the exception of the first 12 s of the exposure period. For data points in the first 12 s, the average is taken only over the widest possible symmetrical range of data points within the exposure period:
[Formula removed.]
[Formula removed.]
[Formula removed.]
[Formula removed.]
[Formula removed.]
[Formula removed.]

Calculate FIGRA _{0,2MJ} for all t where:
(HRR _{av}( t) > 3 kW) and (THR( t) > 0,2 MJ) and (300 s < t ≤ 1 500 s);
and calculate FIGRA _{0,4MJ} for all t where:
(HRRav( t) > 3 kW) and (THR( t) > 0,4 MJ) and (300 s < t ≤ 1 500 s);
both using:
[Formula removed.]
where:
FIGRA  is the fire growth rate index 
HRR _{av}( t )  is the average of HRR( t ) as specified in a) (kW); 
As a consequence, specimens with a HRR _{av} not exceeding 3 kW during the total test have FIGRA values FIGRA _{0,2MJ} and FIGRA _{0,4MJ} equal to zero. Specimens with a THR not exceeding 0,2 MJ over the total test period have a FIGRA _{0,2MJ} equal to zero and specimen with a THR not exceeding 0,4 MJ over the total test period have a FIGRA _{0,4MJ} equal to zero.