262
7 The Role of Ventilation in Fires and Explosions
airflow to overcome backlayering, the speed of the air supplied must be greater than
the so-called critical speed (V c ).
7.7.1 Critical Speed According to NFPA 502: 2017
In Annex D of NFPA 502:2017, Kennedy’s (1996) analytical model is recommended
as a method for calculating critical speed in tunnels. This model employs Thomas’
equation (1970), as a basis, using the average temperature of the hot gases in the
fire zone. The model introduces a dimensionless constant K 1 as a function of the
Froude number (F r ) and a dimensionless factor K g in order to calculate the critical
speed in the case of tunnels with a certain slope. It is interesting to note here that its
application is limited to slopes of ±6%, and this gradient is exceeded in most mines.
The critical speed is determined by solving Eqs. 7.11 and 7.13 iteratively, as
described in the American standard NFPA 502:2017. The first step (i = 1) is to obtain
an initial value for the critical speed V c (Eq 7.13) using a temperature corresponding
to that of the fresh air, T f (i = 1) . Taking this calculated value of V c (i = 1) , we can
then obtain a new temperature T f (i = 2) , which then gives a second iteration value for
V c (i = 2) and so on until the system is stabilized.
The average temperature of the gases at the site of the fire (T f ) in degrees K is
calculated according to Eq. 7.11:
T f =
Q
ρ a C p A x V c
+ T a
(7.11)
where
• Q: Heat Release Rate (HRR) directly into the air at the location of the fire (kW).
• ρ a : Average density of the fresh air (kg m
−3 ) which is taken to be 1.204 kg m
−3
for dry air at 20 ºC and at atmospheric pressure. For other temperatures Eq. 7.12
can be used:
ρ a = 1.204
273.15 + 20
273.15 + T
(7.12)
where T is the temperature in ºC.
• C p : Specific heat of the air [kJ (kg K)
−1 ] which is taken to be 1.005 kJ (kg K)
−1
for dry air at 20 ºC and at atmospheric pressure.
• A x : Cross section of the gallery (m
2 ).
• V c : Critical speed (m s
−1 ).
• T a : Fresh air temperature (K).
The velocity (V c ) can be calculated using Eq. 7.13:
7 The Role of Ventilation in Fires and Explosions
airflow to overcome backlayering, the speed of the air supplied must be greater than
the so-called critical speed (V c ).
7.7.1 Critical Speed According to NFPA 502: 2017
In Annex D of NFPA 502:2017, Kennedy’s (1996) analytical model is recommended
as a method for calculating critical speed in tunnels. This model employs Thomas’
equation (1970), as a basis, using the average temperature of the hot gases in the
fire zone. The model introduces a dimensionless constant K 1 as a function of the
Froude number (F r ) and a dimensionless factor K g in order to calculate the critical
speed in the case of tunnels with a certain slope. It is interesting to note here that its
application is limited to slopes of ±6%, and this gradient is exceeded in most mines.
The critical speed is determined by solving Eqs. 7.11 and 7.13 iteratively, as
described in the American standard NFPA 502:2017. The first step (i = 1) is to obtain
an initial value for the critical speed V c (Eq 7.13) using a temperature corresponding
to that of the fresh air, T f (i = 1) . Taking this calculated value of V c (i = 1) , we can
then obtain a new temperature T f (i = 2) , which then gives a second iteration value for
V c (i = 2) and so on until the system is stabilized.
The average temperature of the gases at the site of the fire (T f ) in degrees K is
calculated according to Eq. 7.11:
T f =
Q
ρ a C p A x V c
+ T a
(7.11)
where
• Q: Heat Release Rate (HRR) directly into the air at the location of the fire (kW).
• ρ a : Average density of the fresh air (kg m
−3 ) which is taken to be 1.204 kg m
−3
for dry air at 20 ºC and at atmospheric pressure. For other temperatures Eq. 7.12
can be used:
ρ a = 1.204
273.15 + 20
273.15 + T
(7.12)
where T is the temperature in ºC.
• C p : Specific heat of the air [kJ (kg K)
−1 ] which is taken to be 1.005 kJ (kg K)
−1
for dry air at 20 ºC and at atmospheric pressure.
• A x : Cross section of the gallery (m
2 ).
• V c : Critical speed (m s
−1 ).
• T a : Fresh air temperature (K).
The velocity (V c ) can be calculated using Eq. 7.13: