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PRESSURE LOSSES DUE TO THE LEAKAGE IN THE AIR DUCTS
- A SAFETY PROBLEM FOR TUNNEL USERS ?
Pucher Karl, Graz University of Technology, Austria
E-Mail: [email protected]
Pucher Robert, University of Applied Sciences Wien, Austria
ABSTRACT
There is a requirement in Austria to suck off an exhaust volume of at least 120m3/s at the end
of an exhaust duct in case of fire (RVS 9.261). To fulfil this, the leakage volume must be
known for a not tight exhaust duct. The paper shows how the leakage volume can be
calculated.
1.
INTRODUCTION
30 years ago many long motorway tunnels where planed in Austria. For instance: the 6,4 km
long Tauerntunnel, the 5,4 km long Katschbergtunnel, the 7 km long Pfändertunnel and the 10
km long Plabutschtunnel. All these tunnels where planed for two tubes. But the traffic amount
at that time was low and the car emission was very high. Therefore only one tube was built
and equipped with a transverse ventilation system.
The traffic amount was growing in the last 30 years very much. Also the philosophy about
the fire in a road tunnel was changed totally after the bad fire disaster in the Mont Blanc and
Tauerntunnel. Small exhaust hoods with an area of 0,5m2 where installed every 12m in the
exhaust ducts of these tunnels. The idea was to suck up the smoke in case of fire to the false
ceiling and extracted it over a long part of the exhaust duct. The advantage of this solution
was thought to have a smoke free bottom zone on the one hand and a not extreme hot smoke
in the exhaust duct because of mingling with fresh air on the other hand. Leakage of fresh air
into the exhaust duct was therefore no big problem.
But now we think it is better to suck off the smoke directly near the fire place into the
exhaust duct through large adjustable exhaust dampers (open area ~12m2) to avoid smoke
propagation in the tunnel. The adjustable smoke dampers are installed every 100m. In normal
case of operation all dampers are a little bit open, so that the same amount of exhaust air can
be sucked off through each damper. But in case of fire only this damper will be opened fully
which is closed by the fire place and all others will be closed. So a concentrated smoke
extraction is possible. There is a requirement in the new Design Guidelines Tunnel
Ventilation that the exhaust fan must be able to suck off 120m3/s at last at the end of a long
exhaust duct. In this case leakage air which is sucked into the exhaust duct between the fan
and the end of the duct has to be minimized or even prevented. If it is not possible to prevent
the leakage air in the exhaust duct we have to know it because the flow rate in the exhaust fan
will then be enlarged. Thus the power input is higher than in case of a tight exhaust duct.
Therefore we have to focus our attention on the calculation on the leakage air.
3rd International Conference ‘Tunnel Safety and Ventilation’ 2006, Graz
- 228 -
2.
CALCULATION OF THE LEAKAGE AIR
Under the assumption that the air is incompressible, the cross section of the exhaust duct is
constant and the area of the leakage strip is constant too over the whole length of the duct we
can drive the following differential equation system:
The pressure in the exhaust duct is given by the equation
λ ρ
dp a
ρ du a ²
= − a . u a ² − ka
2 dx
dx
Da 2
(1)
The velocity in the exhaust duct can be calculated with
du a
f′
=
dx
Fa
2( p v − p a ) +
ρ ⎛ Fa ⎞
2
⎜⎜ ⎟⎟ u a 2
2 ⎝ Fv ⎠
1+ ξa
(2)
and the pressure in the tunnel follows from
λ ρ
dp v
ρ du v ²
= − v uv ² − k z
)
2 dx
dx
Dv 2
(3)
The connection between uv and ua is given by
du v
F du a
=− a
dx
Fv dx
(4)
Here in is
pa(x)
[N/m2]
x
[m]
[-]
λa
λv
[ºº]
[m]
Da
Dv
[m]
ρ
[kg/m3]
[m/s]
ua
uv
[m/s]
va
[m/s]
α
[°]
f´
[m2/m]
Fa
[m]
Fv
[m]
pv
[N/m2]
ξa
[-]
ξv
ka
kv
[-]
[-]
[-]
pressure in the exhaust duct
coordinate in the exhaust duct
friction coefficient in the exhaust duct
friction coefficient in the tunnel
hydraulic diameter in the exhaust duct
hydraulic diameter in the tunnel
air density
air velocity in the exhaust duct
air velocity in the tunnel
air velocity in the leakage strip
angle under which the leakage streams into the air duct
area of the leakage strip
cross section of the air duct
cross section of the tunnel
pressure in the traffic duct
resistance coefficient for the entrance of leakage air into the air
duct
resistance coefficient for the entrance in the tunnel
is a factor which take into consideration the profile shape of ua
is a factor which take into consideration the profile shape of uv
3rd International Conference ‘Tunnel Safety and Ventilation’ 2006, Graz
- 229 3.
SOME RESULTS
Figure 1 shows the result from a calculation of the pressure distribution (x = 0,pa =
2
240 N/m ) in the exhaust duct and the tunnel itself when the exhaust duct is tight. The
calculation was performed under the assumption that a volume of 120m3/s is sucked off at
the end of the duct. The air velocity in the exhaust duct and in the tunnel is then constant as
it can be seen in Figure 2.
length of the exhaust duct (m)
0
150
300
450
600
750
900
1050
1200
1350
1500
1650
0
pressure
(N/m^2)
pressure in the tunnel (fst=0m^2/m)
-200
-400
-600
exhaust duct is open
portal
-800
-1000
pressure in the tight exhaust duct (fst=0m^2/m)
-1200
Fig. 1: Pressure distribution in a tight exhaust duct and in the tunnel
16
velocity
(m/s) 14
air velocity in the tight exhaust duct (fst=0m^2/m)
12
10
8
6
portal
4
exhaust damper is open
2
length of the exhaust duct
(m)
0
0
150
300
450
600
750
900
1050
1200
1350
1500
1650
-2
air velocity in the tunnel (fst=0m^2/m)
-4
Fig. 2: Velocity distribution in a tight exhaust duct and in the tunnel.
3rd International Conference ‘Tunnel Safety and Ventilation’ 2006, Graz
- 230 Figure 3 shows the result when the exhaust duct is not tight. (f´ = 0.001m2/m). The pressure
distribution starts with the pressure of – 250N/m2 near the open exhaust damper at the end of
the exhaust duct. It can be seen that pressure in front of the exhaust fan is roughly p=1800N/m2 in comparison of p=-1100N/m2 in a tight duct.
length of the exhaust duct (m)
0
pressure
(N/m^2)
150
300
450
600
750
900
1050
1200
1350
1500
1650
0
pressure in the tunnel
(fst=0.001m^2/m)
-200
-400
-600
-800
portal
one exhaust damper is open
-1000
-1200
pressure in the not tigtht exhaust duct
(fst=0.001m^2/m)
-1400
-1600
-1800
-2000
Fig. 3: Pressure in the not tight exhaust duct (fst=0.001m^2/m)
25
velocity
(m/s)
20
air velocity in the not tight exhaust duct
15
10
exhaust damper is open
portal
5
length of the exhaust duct (m)
0
0
-5
150
300
450
600
750
900
1050
1200
1350
1500
1650
air velocity in the tunnel (fst=0.001m^2/m)
-10
Fig. 4: Velocity in the not tight exhaust duct (fst=0.001m^2/m)
The pressure behind the portal in the tunnel is only a little bit lower than in case of a tight
exhaust duct. The air velocity in the exhaust duct is growing from 13.52/s near the open
exhaust damper to 20.47/s near the exhaust fan (Fig. 4). So the flow rate in front of the fan is
181.6m^3/s in comparison to 120m^3/s in a tight exhaust duct. If we take only the pressure
losses in the exhaust ducts into our power input calculation for the exhaust fan we need
408.7kW (ŋFan~ 0.8) for the not tight duct and only 165kW for the tight duct to suck off
120m^3/s (ŋFan~ 0.8) at the end of the exhaust duct.
3rd International Conference ‘Tunnel Safety and Ventilation’ 2006, Graz
- 231 4.
CONCLUSION
The calculation showed that it is important to know the leakage volume that is sucked into the
exhaust duct between the open smoke damper and the exhaust fan. The leakage volume and
the additional pressure drop in the not tight exhaust duct enlarge the power input of the
exhaust fan to suck off 120m3/s at the end of an exhaust duct very much.
3rd International Conference ‘Tunnel Safety and Ventilation’ 2006, Graz