Journal of Environmental Protection, 2011, 2, 231-242
doi:10.4236/jep.2011.23027 Published Online May 2011 (
Copyright © 2011 SciRes. JEP
Study of the Temperature Distribution in a Road
Tunnel under the Effect of Two Ventilation
Kalech Brahim, B outerra Mourad, El Cafsi Afif, Belghith Ali
LETTM, Faculty of Sciences of Tunis, University of Tunis-El Manar, Tunis, Tunisia.
Received October 18th, 2010; revised January 13th, 2011; accepted February 10th, 2011.
This paper proposes numer ical investigations carried out on a small scale tunnel model airing to study the fire -induced
smoke control by longitudinal and longitudinal-natural ventilation systems. We studied the effect of two ven tilation sys-
tems on the temperature distribution and stratification of the pollutant to estimate the efficiency of ve ntilation systems.
The flow is characterized by the temperature fields, temperature profiles and the Froude number. The numerical tool
used is FDS (version 4.0). This numerical study requires validation with an experience of literature. Good agreement
with experimental results confirms the possibility of using this code in the problem.
Keywords: Tunnel Fire, Ventilation, FDS, Stratified Flow, Temperature
1. Introduction
Generally, a tunnel fire has very complex flow structure
because it is a physical phenomenon that is affected by
tunnel geometry, inclination, ven tilation system capacity,
and wind pressure, also including chemical reaction, etc.
Efficient control of smoke propagation, therefore, is one
of the most important issues in designing tunnel ventila-
tion. A full understanding of the characteristics of smoke
propagation in tunnels is a necessity in order to proceed
with a successful design.
Thermal stratification is an important feature of fire
environment in a confined space. It has been found that
relative influence of inertia and buoyancy forces resolves
the stratified flow characteristics. In this study under-
standing the characteristics of flow is characterized by
the stratification and temperature distribution.
The ventilation system installed in a tunnel must en-
sure a safe environment under both emergency condi-
tions and normal conditions. Smoke movement should be
controlled in a fire incident. The design of ventilation
systems for road tunnels depends on various parameters,
such as the expected design fire and desired smoke clear
height. Under normal conditions, the tunnel ventilation
system design aims to prevent accumulation of vehicular
emissions to dangerous levels. For dilution ventilation,
fresh air entering the tunnel would mix with vehicle
emissions. The polluted air will be exhausted conse-
quently by the tunnel ventilation system. The volume of
fresh air required, traffic density and tunnel length are
the design parameters in normal conditions. The Ventila-
tion systems commonly installed for road tunnels are
longitudinal, semi-transverse, transverse, partial trans-
verse and natural ventilation systems. There are many
variations and combinations of systems, such as the
combination chosen in our study of longitudinal and nat-
ural systems.
The longitudinal ventilation system is characterized by
the longitudinal velocity of ventilation ‘the critical ve-
locity of ventilation’, the critical velocity is used to
represent the value of the ventilation velocity which is
just able to eliminate the back-layering, and force the
smoke to move in the downstream direction. When the
fire size is medium or large, there will be a flattening of
the flow in one side of the fire, which gives us a major
problem for user evacuation as the fire in the tunnel. In
the event of a tunnel fire, a longitudinal ventilation sys-
tem is often brought into action to create a safe route
upstream clear of smoke for evacuation and fire fighting.
If the ventilation velocity is low, the smoke produced
from the fire can travel in the upstream direction against
the direction of the ventilation air. This reversal of flow
is called back-layering. These values of the critical ve-
locity and the heat release rate have become one of the
Study of the Temperature Distribution in a Road Tunnel under the Effe ct of Two Ventilation Systems
Copyright © 2011 SciRes. JEP
prime criteria for the design of longitudinal ventilation
The natural ventilation system is based on the buo-
yancy of the smoke as the first criterion to control the
smoke, and largely depends on the thickness and temper-
ature of the smoke under the ceiling.
Numerical study, by using FDS, is performed by using
a large eddy simulation to give a quantitative description
of the temperature stratification and heat flux from a
square fire source in a ventilated tunnel. Numerical si-
mulation analyzed the effect of the aspect ratio on smoke
movement in tunnel fires and temperature distribution
under the tunnel ceiling will be studied by Sung Ryong
Lee et al. [1]. The back-layering length, the critical ven-
tilation velocity and the temperature distribution under
the ceiling i n tunnel fi res will be s tudi ed by Hu et al. [2].
The longitudinal temperature distribution under the tun-
nel ceiling at different longitudinal ventilation velocities
have been studied experimentally and numerically. [3,4].
Numerical simulations have also been tried to predict
the fire development and to investigate into the efficien-
cy of different smoke control methods in tunnels [5-7].
Experimental tests in reduced scale are performed to
study the fire characteristics, smoke movement and con-
trol of smoke in case of a tunnel fire. A semi-empirical
model has been developed to evaluate the physical cha-
racteristics of fire in tunnels by Mégret et al. [8]. Wu et
al. [9], by using a horizontal model tunnel with propane
gas burner as the fire source, studied a control of smoke
flow using longitudinal ventilation s ystem.
Experimental study of th e smoke temperature distribu-
tion along the tunnel ceiling under the effect of the lon-
gitudinal velocity of ventilation was studied bay Hu and
al [10]. Study the fire-induced smoke control by longitu-
dinal and transverse ventilation systems [11]. To under-
stand the phenomena, Vauquelin [12] studied the critical
velocity is evaluated for different channel dimensions
and for different buoyant source characteristics to deter-
minate the influence of these parameters on the critical
Hwang et al. [13] studied the critical ventilation ve-
locity and described the stratification and the temperature
distribution in tunnel fires. Hwang studied the stratifica-
tion based on the experimental study of Newman. New-
man [14] described the temperature stratification in tun-
nel fires by the Froude model is defined by the following
( )
TfF f
== 
where ΔT is a temperature difference associated with the
T is the reference temperature;
the reference flow velocity; g is the acceleration due to
is the characteristic dimension of the duct.
In this study as in the study of Hwang et al. [2] a Froude
number is used base d o n:
ref avg
ref avg
avgin in
avg in
V uu
= ≈
Three regions can be de fined:
Region I: For
; i.e., buoyancy
dominating temperature stratification .
Region II: For
0.9 10,0.121.7
≤≤≤ ≤
significant interaction of the ventilation veloc ity with the
fire-ind uc ed buoyancy occurs.
Region III: For
10 ,012
i.e., stratification
is insignificant.
Also note that Hwang and al [13] showed that the
Froude model is independent of the dimensions of the
geometric configuration.
The smoke movement has been described mainly from
equations derived by applying Froude number preserva-
tion, combined with some experimental data from a
model channel [12,15]. The approximate Froude model-
ing requires geometric similarity, and does not app ly to a
full-scale tunnel. Functional relationships have been de-
rived from laboratory-scale tests [9,15-17].
Kunsh [16] derived an expression that takes into ac-
count the effect of the aspect ratio of the tunnel cross-
section on the critical ventilation velocity.
Falin Chen [18] review the progress of research on
smoke propagation in tunnels, wherein the tests in
full-scale tunnels, the nature of fire, the smoke propaga-
tion behavior in tunnels and the longitudinal ventilation
Some full-scale tests have also been carried out in the
past years [19]: In 1992, large-scale tests were carried
out in a disused two-lane highway tunnel in Virginia,
USA with 850 m of length and 3.2% of longitudinal
slope, to assess the heat output. Afterwards, an extensive
series of experiments were conducted at HSL, Buxton in
a 366 m long and 2.56 m high tunnel with a cross-section
of 5.4 m 2, to provide data suitable for the validation of
CFD simulation. In 1994, tests were performed in a dis-
used Norwegian mine tunnel, nominally 5.5 m high, 6.5
m wide and 2.3 km in length under the EUREKA EU499
Study of the Temperature Distribution in a Road Tunnel under the Effect of Two Ventilation Systems
Copyright © 2011 SciRes. JEP
project [20]. The main objective of this series of tests
was to determine the heat output of fire in tunnels and
the velocity profile upstr eam of the fire. In the full -scale,
the transverse and longitudinal ventilation conf igurations
were studied in the Memorial Tunnel Program [21].
When a fire occurres in a tunnel, a buoyant smoke
flow is formed below the ceiling along the tunnel. The
development of a buoyant smoke layer in a tunnel can be
summ a rized into fo ur phases or re gions [22, 23]
-Impinging region of rising plume on the ceiling
-Radial spread of smoke under the ceiling after im-
-Interaction with side walls, and thus the transition re-
gion to one-dimensional spread
-One-dimensional spreading
The mechanism for the tunnel plume distribution is the
interaction of the air flow with the plume and the interac-
tion of the plume with the tunnel walls.
In a tunnel fire situation, since the fresh air is supplied
via the ventilation upstream from the fire, there would be
rapid air entertainment into the fire plume upstream
compared with the downstream area. The entrainment
rate is responsible for the flame height and the characte-
ristics of the fire plume. Heat transfer from the smoke to
the cooler ceiling can reduce the temperature and friction
force and also the smoke velocity. Ceiling area plays an
important role in the movement of the ceiling jet. The
geometry of a tunnel is an important factor affecting
growth and development of a fire.
This paper presents numerical investigations carried
out on a small scale tunnel model to study the fire-in-
duced smoke control by longitudinal and longitudin-
al-natural ventilation systems, for certain types of tunn els,
based on the criterion of flow stratification and tempera-
ture distribution.
2. Numerical Model
The Fire Dynamics Simulator (FDS) is being developed
at N IST (Nation al Institute o f Standards and Technology)
(2006) to study fire behavior and to evaluate the perfor-
mance of fire protection systems in buildings. An ap-
proximate form of Navier-Stokes equations appropriate
for low Mach number applications is used in the model.
The approximation involves the filtering out of acoustic
waves while allowing for large variations in temperature
and density. To handle sub-grid scale convective motion,
a large eddy simulation technique is used in which the
la rge -scale eddies are computed directly and the sub-grid
scale dissipative processes are modeled. Fire-driven flow
in FDS is simulated by LES turbulence model. Details on
the numerical model may be found in [24,25]. The com-
puter program can be used to analyze fire related prob-
lems, such as temperature, velocity and concentration
FDS solves flow equations numerically. The physical
equations include Navier-Stokes equations for flow
analysis, energy conservation equations for temperature
distribution, and other scalar equations for smoke and
particles transport. Governing equations are described as
follows (NIST, 2006):
Conservation of mass:
( )
+∇⋅ =
Conservation of momentum:
( )
up gf
ρ ρτ
+⋅∇+∇ =++∇⋅
Conservation of energy (see Equa tion (3)):
Conservation of species:
() ()
llll l
+∇⋅=∇ +
CFD simulation is now a practical tool in fire engi-
neering for simulating buoyancy-induced flows [26,27].
Turbulence methods commonly used in CFD are based
on the Reynolds Averaging Navier-Stokes equation
(RANS) method, Large Eddy Simulation (LES) and Di-
rect Numerical Simulation (DNS).
In this study used Large Eddy Simulation (LES) me-
thod. The application of LES techniques to fire is aimed
to extract greater temporal and spatial fidelity from si-
mulation of fire. This model explicitly calculates the
turbulent large scales and models the effects of smaller
ones using sub grid closure rules. LES of reacting flows
can resolve the instantaneous position of a large-scale
flame, so that LES captures the low-freque ncy variations
of flow parameters. The approach based on LES has a
particular advantage over the Reynolds-Averaging pro-
cedures which is that only the effects of small-scale tur-
bulence motion have to be modeled. The balance equa-
tions for LES are obtained by filtering the instantaneous
balance equations.
In predicting smoke movement by LES, two points
should be c onsidere d [24,25,28]:
-Fine enough grids; and
-A suitable Sub-grid Model (SGM) on small eddies.
The grid size should be fine enough to include the
turbulence scales associated with the largest eddy mo-
tions which can be described accurately by the SGM.
( )( )
r ll
hqqkTh DY
t Dt
+∇⋅−=−∇⋅+∇⋅ ∇+∇⋅∇
Study of the Temperature Distribution in a Road Tunnel under the Effe ct of Two Ventilation Systems
Copyright © 2011 SciRes. JEP
The ratio of the largest to the smallest eddy length scales
that can be resolved by the computation with the current-
hardware limitations giving a few million grids is about
100 [24].
The LES Sub-grid Model commonly used in LES was
developed originally by Smagorinsky. In LES, the eddy
viscosity was obtained by assuming that the small scales
are in equilibrium, by balancing the energy production
and dissipation [24,28]. A refined filtered dynamics
sub-grid model was applied in the FDS model to account
for the sub-grid scale motion of viscosity, thermal con-
ductivity and material diffusivity [24]. The dynamic vis-
cosity defined in FDS is
( )
ijk ijk
Cs S
= ∆
where Cs is the empirical Smagorinsky constant,
()xyz∆=δ δ δ
and the term
consists of second-order
spatial differences averaged at the grid centre. The ther-
mal conductivity
and material diffusivity
the fluid are related to the viscosity
in terms of the
Prandtl number Pr and Schmidt number Sc by:
p ijk
ijk r
( )
ijk c
Both Pr and Sc are assumed to be constant. The spe-
cific heat Cp is taken to be that of the dominant species
of the mixture [24]. The constants Cs, Pr and Sc are de-
faulted in FDS as 0.2, 0.5 and 0. 5, r e spective ly.
The Courant-Friedrichs-Lewy (CFL) was used in FDS
[24] to justify convergence. This criterion is more im-
portant for large-scale calculations where convective
transport dominates the diffusive one. The estimated
velocities are tested at each time step to ensure that the
CFL condition is satisfied [24]:
max max,,1
ijk ijkijk
δ⋅ <
The initial time step was set automatically in FDS by
the size of a grid cell divid ed by the characteristic veloc-
ity of the flow.
Default values of the initial time step is
( )
5x y zgHδδδ
are the di-
mensions of the smallest grid cell, H is the height of the
computational domain, and g is the gravitational accele-
ration [24]. During the calculation, the time step is vary-
ing and constrained by the convective and diffusive
transport speeds to make sure that the CFL condition is
satisfied [24].
The time step is eventually changed to a quasi-steady
value when the fire burns steadily. The results from a
numerical analysis are sensitive to the grid size used. In
this study we chose the time step to be sure that the CFL
condition is verified, in order to obtain a good conver-
gence. The most recent models derived to calculate the
critical ventilation velocity are those presented by
[9,16,17,29,30,] in Table 1.
This study used dimensionless velocity and dimen-
sionless heat release rate with the tunnel hydraulic height
as the characteristic length in the analysis. The study of
the fire plume showed that the critical ventilation veloc i-
ty is determined by the interaction of the fire with the
fresh air ventilation flow and the tunnel walls. The flow
behaviors should be studied in three dimensions. The
presence of the tunnel wall has a strong influence on the
fire plume distributions. The tunnel fire situation is in
principle different from the one where fire plume im-
pinges on a ceiling, in which the buoyancy force in the
ceiling flow is a function of the ceiling height. In a tun-
nel fire, the buoyancy force in the back layering is due to
the whole fire plume. Although the problem is three-di-
mensional, at the critical ventilation conditions, the flow
in the tunnel can be divided into three sections, they are
the fresh air flow section, the fire plume section and the
downstream smoke flow section. In each section, the
mean hydraulic tunnel height is the characteristic length
for the flow. Therefore it provides a basis for using the
hydraulic tunnel height as the characteristic leng th in the
dimensionless analysis study.
The following equations for dimensionless heat re-
lease rate and the critical ventilation velocity in this
12 52
QTc gH
′′ =⋅⋅⋅ ⋅
′′ =
are the dimensionless critical ven-
tilation velocity and dimensionless heat release rate.
is ambient air density,
is heat capacity
22 2
222 2
u v wuvuwvw
Sxyzxy zxzy
 
∂∂ ∂∂∂∂∂∂∂
 
=++++++ ++−∇⋅
 
 
∂∂∂∂∂ ∂∂∂∂
 
 u
Study of the Temperature Distribution in a Road Tunnel under the Effe ct of Two Ventilation Systems
Copyright © 2011 SciRes. JEP
of the hot gases,
is the ambient temperature and g
the acceleration due to gravity (g = 9.81 m/s2). The ex-
pression of
4.H AP=
. A cross-sectional area of
the tunnel a nd P is the tunnel perimeter.
The geometric configuration of the field study is
shown in Figure 1(a). The longitudinal computational
domain, L=14.92 m, was divided into five segments
Figure 1(b). Segment 1 is the upstream section of the
tunnel, its length is 2.01 m and
δ0.03 mx=
. Segment 2
has a length 3.00 m and
0.02 mxδ=
. Segment 3 was
the burner section of length 2.41 m and
Segment 4 has a length 2.82 m and
0.02 mxδ=
. Seg-
ment 5 is the downstream section of the tunnel, its length
is 4.68 m and
0.03 mxδ=
. Non-uniform d istribution of
the mesh allows us to maintain a sufficient degree of
accuracy in the solution. Width, W = 0.5 m, is meshed
and height, H = 0.25 m, is meshed
The first plane of the longitudinal domain was set to
be the inlet of the ventilation flow and the last plane was
set as naturally opened with no initial velocity boundary
condition specified. The circular burner was simulated as
a square burner with different dimensions suitably to
each release rate. The side of the source varies from 0.08
to 0.26 m for 1.5 with heat release rate up to 30 kW.
These fire sizes correspond to fires of approximately 2.5
50 MW in a reality. A propane gas burner was used to
simulate the fire source, for designating a fire to pre-
scribe a Heat Release Rate Per Unit Area (HRRPUA) on
a SURF line.
A Validation of Simulations against the experimental
results available in the public literature by Wu et al. and
the model of Kunsch in Fi gure 2. The critical velo city is
plotted as a function of the heat release rate in dimen-
sionless form. In our study the critical velocity taken as
reference is that which with a back-layering does not
exceed the height Hof the tunnel to multiply by 2.25.
Figure 3 Show s that the isoclines of temperature. The
comparison between numerical values and those of the
experiment gives good agreement.
A good agreement was obtained with the simulated
current values for the temperature and the critical value
of the ventilation velocity.
3. Results and Discussion
The fire simulation is done by a plume. This problem is
complex for the presence of the longitudinal air flow.
First, the trajectory of the fluid is diverted downstream of
the flow. The problem is with geometry and characteris-
tic of the plume, the flow can take several forms. The
important parameters are the angle of inclination of the
plume and the balance between buoyancy and momen-
tum in the plume. In this study, the geometric configura-
tion as shown in Figure 4, is identical for all simulations
Table 1. The models derived to calculate the critical velocity of ventilation.
Formulae Remark Source
Thomas [29]
00 ,
p ic
Danziger&Kennedy [30]
.* 3
* .*
= <
* .*
0.35 for0.124
UQ= >
Oka&Atkinson [17]
0.4for 0.20
= ≤
0.40 for0.20
UQ= >
12 25
00 p
QTc gH
=⋅⋅⋅ ⋅
Wu&Bakar [9]
*2 3
**1 3
*2 3
1 6.13
Uc Q
(H/W) =1;
= 1.44 and
= 3.57
(H/W) =0.5;
= 1.48 and
= 3.11
Qp gH
Kunsch [16]
Study of the Temperature Distribution in a Road Tunnel under the Effe ct of Two Ventilation Systems
Copyright © 2011 SciRes. JEP
Figure 1. (a) Geometric configuration; (b) Boundary condi-
tion and mesh di st ribution.
Figure 2. Cur ve validation.
as it was previously defined in the validation, even for
the mesh, the turbulence model and boundary conditions.
In all cases by setting the velocity of longitudinal venti-
lation and the heat release rate convected. The width “d”
of opening equal to 0.04 m.
The longitudinal ventilation velocity had a large in-
fluence, on the smoke temperature distributions, as
shown in Figures 5 and 6. For these temperature fields in
Figures 5(a) and 6(a), the temperature at 0.1 m away
from the fire was higher upstream than downstream, and
were nearer at 0.15 m position. At further away positions,
they were much lower upstream than downstream.
This phenomenon should be due to their different
physics embedded for upstream positions near the fire
and far away. At the near fire position, the incoming lon-
gitudinal ventilation velocity would a ct like a barr ier, the
heat would accumulate at these positions and the local
temperature would be higher, while for the upstream
positions some further away, beyond the barrier, the
smoke front upstream would shear with the oppositely
coming longitudinal velocity, resulting in more air en-
trainment and faster temperature decrease.
At velocity of ventilation equal to 0.62 m/s, th e critical
velocity of ventilation, in Figure 5(a) the temperature
reached 700˚C at the source. In the upstream side of the
source the temperature varies from 145˚C to 290˚C and
in the downstream side of the source the temperature va-
ries from 80˚C to 145˚C. In Figure 6(a), at the source the
temperature reached 640˚C and in the downstream side
of the source the temperature varies from 90˚C to 145˚C.
The highest temperature is below the ceiling and it
degrades according to the length of the tunnel. For the
mixed ventilation system the values of temperature are
highs then values of longitudinal ventilation system.
There is a bigger jump temperature values depending
on the height of the tunnel, for the mixed ventilation
system as the longitudinal ventilation system, as shown
in Figures 5(a) and 6(a), then there exists a layer of
smoke largest below the ceilin g for the mixed ventilation
system. Hence we can deduce that the flow is stratified,
at the critical velocity of longitudina l ventilation equal to
0.62 m/s, for the mixed ventilation system.
For high velocity of ventilation in Figures 5(b) and
6(b), the temperature in the upstream side of the tunnel is
the ambient temperature. Downstream of the tunnel, the
temperature is distributed over almost the entire height of
the tunnel as the recorded values are 40˚C to 90˚C in the
right before the opening and 40˚C to 160˚C in the left
before the openin g.
The temperature values are almost equal. The flow is
homogeneous, there is a mixture between air ventilation
and the smoke which is delayered (destratification) flow
and reduces the temperature values relative to the longi-
tudinal air flow at low velocity of ventilation.
With longitudinal ventilation system and at the critical
velocity of ventilation, in t he upstream side of the tunnel,
the velocity of smoke becomes zero because all the
quantity of pollutant is transported to the downstream
tunnel. During this, with the ventilation system mixed
(longitudinal-natural) a large amount of pollutants has
been convected to the upstream portion of the tunnel for
low velocity of ventilation. Has the opening to the left is
a pressure difference between the inside of tunnel and the
environment, it is an area of suction.
For the spread of smoke along the tunnel, there would
be a boundary layer in the smoke layer contacting the
tunnel ceiling. The smoke flow temperature would de-
crease along the tunnel due to the heat loss to the tunnel
ceilings through this boundary layer. It is one of the spe-
cial features of tunnel fire s, differing in that with normal
compartment fires, that the smoke layer temperature de-
cay largely when traveling down the tunnel.
Study of the Temperature Distribution in a Road Tunnel under the Effect of Two Ventilation Systems
Copyright © 2011 SciRes. JEP
Figure 3. Temperature contour at y = 0.25 m plane, showing the c onditions at the critical ventilation. (a) Q = 7.5 kW, (b) Q =
15 kW; (1-EXP) Wu and al, (2-NUM) Kalech et al.
Study of the Temperature Distribution in a Road Tunnel under the Effe ct of Two Ventilation Systems
Copyright © 2011 SciRes. JEP
Figure 4. Geometric configuration adopted for simulations.
Figure 5. Temperature contour at y = 0.25 plane or the mixed ventilation system (with opening) Q = 10.5 kW. (a) U= 0.62 m/s;
(b) =1.1 m/s.
Figure 6. Temperature contour at y = 0.25 plane for the longitudinal ventilation system Q = 10.5 kW, (a) U = 0.62 m/s; (b) =
1.1 m/s.
Study of the temperature distribution in a road tunnel under the effect of two ventilation systems
Copyright © 2011 SciRes. JEP
The vertical temperature distribution at the down-
stream side of the tunnel is shown in Figure 7. The rec-
orded values of temperature are close to average for the
two ventilation systems.
In exit of tunnel at Section 14.92 m, two temperature
profiles almost similar.
In Section 10 .3 m between the right opening and down
the tunnel, for mixed ventilatio n system, the temperature
equal to 20˚C in the floor and increases slowly until it
reaches 25˚C at a height of 0.1m, then it increases pro-
gresely until it reached 80˚C to 0.17 m and in the end it
increases sharply to reach 130˚C below the ceiling.
However, with the longitudinal ventilation system, it is
expected that the temperature reached 45˚C at 0.05 m,
70˚C at 0.1 m and 0.15 m from it would be equal to
105˚C up to the ceiling. The vertical temperature profile
for the longitudinal ventilation system does not admit an
inflection point behavior the mixed ventilation system,
compared to the mixed ventilation system, the tempera-
ture increase is progressively along the vertical direction,
i.e. the flow is homogene o us.
In Section 7.3 m , the temperature rise shows a steady
and slow increase but experiences a sharp increase at an
intermediate height H = 0.12 m for mixed ventilation
system. Then the temperature increases progressively
along the height of tunnel. In reality, thermal stratifica-
tion still exists although it is very small, its effect is not
negligible during all phases or a front separating the hot
section and cold section exists in the tunnel, as it is al-
ready presented in Figur e 7. In reality such a front is
unstable. The advance of the front is followed by spot-
ting sudden rises in temperature as it passes.
It is very difficult to define the interface smoke-fresh
air from continuous temperature profile especially for
large velocity of ventilation. We note that the profile has
an inflection point in its upper part. This inflection point
corresponds to the maximum temperature gradient, can
therefore be regarded as representing the boundary be-
tween two layers of flow. The thermal stratification and
the consequent flow patterns correlated well with the
Froude number, for the case where we have used open-
ing and for other case.
Buoyancy and the inertia force are the two dominant
factors that affect the fire-induced thermal stratification.
The fire-induced buoyancy trends to maintain the stabil-
ity of stratification, while the forced ventilation-induced
inertia force trends to mix the flows. Thus, the
fire-induced stratification depends upon the magnitudes
of these two competing mechanisms. Froude number was
usually used to characterize the fire-induced hot layer
which represents the ratio of inertia force to buoyancy
force [9]:
is the difference between the temperature
near the ceiling and the temperature near the floor,
is the average temperature in a section,
is the av-
erage flow velocity; g is the acceleration due to gravity;
is the height of the channel.
avgin in
avg in
V uu
= ≈
Figu re 8 plots the Froude number of hot layer versus the
ventilation velocity, The Froude number who is used as
indicating of stratification.
At Region
, the buoyant flow stratification is
stable, where a distinct interface exists between the upper
smoke layer and the lower air layer. The effect of
buoyancy is more significant than the momentum forces
in this case. Note also that for the temperature profiles
we can see the point of inflection in the shape of the
curve. The flow is more stably stratified because com-
bined effect of momentum of heat input corresponds to
very low Froude number.
At Region
, the buoyant flow stratification is
insignificant but with interfacial instability. By increas-
ing the ventilation velocity, the buoyant flow stratifica-
tion becomes unstable, with a strong mixing between the
buoyant flow and the air flow. Froude number as shown
in Figure 8, for the same heat release rate converted
equal to 10.5 kW, the Froude number is more important
for the longitudinal ventilation system in all longitudinal
Between the right opening and exit of the tunnel, in
sections 10.3 m and 14.92 m, the flow is unstable for the
velocity of ventilation roughly equal to 0.85m/s and it is
completely destratified for velocities of ventilation supe-
rior to last for the two ventilation systems.
In approaching of the tunnel exit, the difference be-
tween the Froude number of longitudinal ventilation
system and the Froude number of mixed ventilation sys-
tem increases.
In Section 7.3 m, between the source and the right
opening, and with a velocity of ventilation equal to 0.85
m/s, the Froude number between 0.8 and 0.9 for the
mixed ventilation system (1) and equal to 1.35 for the
longitudinal ventilation system (2).
At the velocity of ventilation equal to 0.62 m/s, re-
garded as the critical velocity of ventilation in the longi-
tudinal ventilation system, the flow is well laminated in
the downstream side o f the tunnel.
Study of the Temperature Distribution in a Road Tunnel under the Effe ct of Two Ventilation Systems
Copyright © 2011 SciRes. JEP
Figure 7. The vertical temperature profiles at downstream
of the tunnel, at (a) 7.3 m; (b) 10.3 m; (c) 14.92 m for 10.5
kW and U in = 0.85 m/s. (1) mixed ventilation system ;(2)
longitudinal ventilation system.
Figure 8. Froude number versus the velocity of ventilation
in tunnel fires at different s ections.
Fr = 0.3 in section 7.3 m and Fr 0.9 in sections 10.3
m and 14.92 m, for the mixed ventilation system. For the
longitudinal ventilation system, the flow is laminated just
at the section 7.3 m, between the source and the right
opening. Fr = 1 at the section 10.3 m i.e the flow is un-
stable and Fr = 1.15 at the exit of the tunnel here the de-
stratified flow.
This last interpretation on the stratification with U =
0.62 m/s shows the favors to use of the openings to the
ceiling and their influence on the stratification of flow.
The flow is much more stratified with mixed ventilation
system especially using the critical velocity o f ventilation
of the longitudinal ventilation system.
The longitudinal velocity aff ects the thermal stratific a-
tion especially:
Firstly, longitudinal velocity generally results in the
decrease in the hot layer temperature and increase the
longitudinal velocity of upper buoyant flow, by enhanc-
ing the heat and mass exchange between the hot stratified
layer and the lower cool layer.
Secondly, longitudinal velocity air flow increases the
mixture between the upper hot layer and lower cool
The characteristics of buoyant flow stratification de-
pend upon the magnitudes of buoyancy of the smoke
flow itself and the inertia force induced by longitudinal
air flow.
Instability of stratification resulted in a strong mixing
between the buoyant flow and the air flow, and thus a
thickened buoyant smoke layer. It also resulted in the
smoke flow being pulled down to the lower spaces of the
channel. Under such a condition, the human evacuation
could be threatened by the smoke. These factors are
recommended to be taken into account in the design of
ventilation strategy for a fire emergency in a channel-like
For some types of tunnels, sharp tunnels, and while
relying on an important criterion which is manifested by
the temperature distribution and stratification, we can
conclude that it is more efficient to use the ventilation
system mixed longitudinal natural than the longitudinal
ventilation system.
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A tunnel cross-sectional area, m² Subscript
P tunnel perimeter, m Avg average
Cp specific heat, KJKg–1K–1 cf difference between ceiling and floor
Fr Froude n umber, dimensionl e ss c critical
g acceleration of gravity, m·s–2 in tunnel inlet
H tunnel height, m 0 ambient
hydraulic tunnel height, m ref reference
k thermal conductivity, Wm–1·K–1 x,y,z cartesian coordinates, m
P pressure, Pa 1 mixed v entilatio n sys tem
Pr Prandtl number 2 longitudinal ventilation system
Sc Schmidt number
Cd proportionality constant
Cf empirical constant
Ck empirical constant
Cs Smagorinsky constant (LES)
Q heat release rate of the fire, KW
dimensionless heat release rate defined for
correlation of critical velocity by Wu and
T temperature, ˚C
density, Kg·m–1
U ventilation velocity, m·s–1
dimensionless ventilation velocity
V velocity, m·s–1
W tunnel width, m
L tunnel length, m
d opening length, m
the dimensions of the smallest grid ce ll, m