* Corresponding author. Fax: #886-2-36-39290.
and Industrial Aerodynamics 86 (2000) 15}36
A novel approach to the transient ventilation
of road tunnels
Hong-Ming Jang , Falin Chen
*
Department of Mechanical Engineering, Chinese Culture University,Taipei, Taiwan 111, Republic of China
Institute of Applied Mechanics, National Taiwan University,Taipei, Taiwan 107, Republic of China Received 25 April 1999; received in revised form 25 August 1999; accepted 25 October 1999
Abstract
We propose in this paper a novel approach to predict the transient behavior of the ventilation of road tunnel based on the tra$c data measured at the outlet portal of tunnel. The approach starts with a so-called tra$c group-partition dilemma, which essentially partitions the tra$c #ow into various groups so that the transient behavior of the induced wind speed can be accurately predicted. As a result, one may employ the present approach to predict the ventilation situation along a road tunnel, which can be a long tunnel in motorway, and needs only to measure the tra$c data at one location in or near the tunnel, for example, the outlet portal. Accordingly, the present approach shall become a rather economic and e$cient scheme to be considered to monitor the ventilation situation in road tunnels as the approach is converted into a computer program, which can be used in the real-time ventilation control of the tunnel 2000 Elsevier Science Ltd. All rights reserved.
Keywords: Ventilation; Tunnel
1. Introduction
A well-designed ventilation system of road tunnel ensures not only good air quality but also safety for the users of tunnel. Engineers are constantly searching for an economic and reliable way of ventilation, which can e$ciently exchange the air between atmosphere and tunnel. For a tunnel with one-bound tra$c, the piston e!ect due to moving vehicles is the major factor driving the motion of the air in tunnel. The
0167-6105/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 7 - 6 1 0 5 ( 9 9 ) 0 0 1 3 5 - X
mechanical devices, such as jet fans, serve only when an emergency state is alarmed. The wind speed induced by the piston e!ect accordingly becomes a major issue to be studied when the design of ventilation proceeds. To simulate the wind induced by tra$c, the one-dimensional mathematical model based on the conservation of mo-mentum within the tunnel is usually considered [1}4]. It is noted that the transient state of ventilation is crucial to the users of tunnel, in terms of both the quality of air and the safety during emergency. We therefore in the present paper propose a novel approach to predict the transient behavior of the ventilation in one-bound tra$c tunnel.
To study the transient behavior of ventilation in road tunnel, one may investigate the unsteady #ow "eld within the tunnel. We nevertheless note that to study the unsteady two- or three-dimensional #ow in road tunnel, especially for which is of several kilometers long, the approach through numerical computation is rather ine$cient and non-practical. Our present approach is developed upon the basis of one-dimensional model. It is noted that the factors in#uencing the #uid motion in tunnel include the motion of vehicles, the pressure rise imposed by the jet fans, the pressure di!erence between inlet and outlet portals, the resistance due to tunnel wall, and so on [4]. Among these factors the dynamic variation of the tra$c #ow and the switch-on and -o! of the jet fan are dominant [5]. In a road tunnel, the tra$c #ow changes rapidly and thus the induced wind speed shall be of signi"cant variation with time. In order to reveal the intimate relation between the transient tra$c and the #uctuating wind speed, we must "rst obtain the real transient tra$c information along the tunnel and then properly introduce it into the theoretical model [5]. To reach this goal, nevertheless, collecting the complete vehicular tra$c information along the tunnel is by no means practical. The practical way is instead to measure the tra$c #ow at a particular location in or near the tunnel, which can be the outlet portal, for example. The tra$c #ow in terms of the tra$c density as well as the speed of vehicles are then analyzed on the basis of the so-called tra$c group-partition dilemma, with which the tra$c #ow is partitioned into vehicle-groups. Consequently, the transient behavior of the ventilation in any location of the whole tunnel, in terms of the time variations of wind speed, pressure, and temperature, can all be predicted by the theoretical approach based on the tra$c data measured at one location. When the present approach is converted into computer code, the real time control of the ventilation of the whole tunnel can be made possible if only one point of tra$c data is provided. The present approach may therefore provide an e$cient and economic way for the ventilation control in road tunnel.
In the following paper, we will "rst in Section 2 describe the Fu}De tunnel in which the experiments were implemented. In Section 3 the typical tra$c #ow and the ventilation situation of Fu}De tunnel are illustrated. The 1-D theoretical model of the ventilation is derived in Section 4. The so-called tra$c group-partition dilemma is described in Section 5, in which the procedure and rules prescribed for the partition process are discussed. In Section 6 an intensive compari-son between the computed results and the corresponding measured data is carried out. Finally, conclusions reached on the basis of present analyses are given in section 7.
2. Description of tested tunnel and experimental facilities
The tunnel tested is the Fu}De tunnel of the Northern Second Motorway (NSM) of Taiwan, locating in the suburban of Taipei city, the capital of Taiwan having a population about 2.6 million. It is one of the several long tunnels of the NSM, consisting of two one-bound-tra$c tubes, one south bound (1762m) and one north bound (1726m), each of which has three lanes, see Fig. 1(a) in which the outlet portal is shown. All the testing facilities were setup in the southbound tube. From Fig. 1(a) one can see that the tra$c was heavy while was still smooth. Up to the present days, most of the vehicles using Fu}De tunnel have been the small-size passenger cars. The tra$c density of large-sized truck or trailer is rather low. On the upper-right corner of Fig. 1(a) shows a CCD camera which is used by the Motorway Engineering Bureau to monitor the tra$c of tunnel, not the one used by us to measure the tra$c data. The weather was rainy and foggy, not unusual in the summer of Taipei.
We set up the following testing facilities along the Fu}De tunnel. On the right-hand- side of the outlet portal, two sets of data acquisition system were equipped, see Fig. 1(b). The upper-larger box contained the data logger to collect the data of wind speed, pressure, temperature, humidity, and the concentration of carbon monoxide (CO). The lower smaller box contained the data logger with which the tra$c data detected by the computerized optical camera (called Autoscope) were recorded. All the data were temporarily recorded in the memory unit of the loggers and would be copied to the hard disk of a note book computer after a certain period. The data were then brought back to the laboratory to be analyzed. The time interval to record one set of data can be adjusted to be as small as 10 s. The memory of the loggers was big enough that, based on this smallest time interval, a test period of more than 24 h could be proceeded.
The Autoscope was set up on the top of the tunnel outlet, facing down the outgoing tra$c, see Fig. 1(c). In the same picture one can see the anemometer measuring wind velocity (including magnitude and direction) and the sensors measuring the temper-ature, pressure, and humidity of the atmosphere. The Autoscope system, including camera and data logger, was manufactured by the Image Sensing Systems Inc. and of model number 2004. Through the Autoscope the number of vehicles, speed of vehicles, and types of vehicles in both day and nighttime can be measured. We calibrated its accuracy regarding the number of vehicles by using a mechanical counter. After several times of calibration, each time a 30-min test was implemented, the error resulted from the Autoscope was found to be as low as 5% or less.
The anemometer was a propeller-type sensor (Fig. 1(d)) to measure the wind velocity, manufactured by R. M. Young Co. of model 5103. The measurable range of wind speed was from 0 to 60 m/s with an accuracy of 0.3 m/s. We noted that the induced wind in tunnel was essentially unidirectional and the wind speed varied in a range from 0 to 10 m/s, so that this type of anemometer was good for the test. The measurement was also made for the variations of pressure, temperature, CO concen-tration, and humidity although these measurements were primarily not to be used for the present analyses. They nevertheless can be good references for the engineers who are in charge of the supervision of both the tra$c and the ventilation of the tunnel.
Fig. 1. The Fu}De tunnel and the testing facilities. (a) The outlet portal of the Fu}De tunnel. The tunnel has three lanes. The small-sized cars dominate the tra$c #ow. The CCD camera on the upper-right of tunnel is used by the Motorway Engineering Bureau to monitor the tra$c of the tunnel. (b) The two data loggers for collecting the data of wind velocity, pressure, temperature, and so on (upper box) and for recording the data from the Autoscope camera (lower box). The two fellow students were transferring the data from both loggers to the hard disc of a notebook PC. (c) The Autoscope camera and the testing facility of the atmosphere data, including the wind speed and direction, temperature, pressure, humidity, and so on. (d) The anemometer in tunnel. The box shown on the upper-right corner of the picture contains the sensors for temperature, pressure, CO concentration, and humidity.
Along the southbound tube we measured three points, locating, respectively, at 50, 500, and 1000 m from the outlet portal. On each point all the sensors mentioned above were set up. The sensors were "xed on the cable-truss, which was about 1 m below the ceiling of the tunnel. As we have found from the test results, the wind speed
Fig. 2. The tra$c #ow accounted for by the number of vehicles passing through the outlet portal per 5min on 17/02/97. Four sets of data represent, respectively, the number of vehicles in the outer lane, the inner lane, the middle lane, and the total number of the three lanes. It is seen that there were two peaks of the tra$c #ow, at, respectively, around 8 : 00 am and 6 : 00 pm.
measured at these three locations were virtually the same, suggesting that the incom-pressible assumption is appropriate for the ventilation of road tunnel. The data regarding the wind speed will be used to test the accuracy of the present theoretical approach.
3. Typical tra7c 6ow and ventilation situation
Figs. 2 and 3 illustrate the tra$c #ow on 17/02/97 (the 17th of February 1997), revealing the typical vehicular tra$c on weekdays. In Fig. 2 the number of vehicle was recorded every 5 min (or called the tra$c volume, de"ned as number of vehicles per unit time) and the data are shown on the basis of both each lane and of the three lanes as a whole. It is shown that the middle lane was always the "rst choice for a larger part of the drivers; the outer lane was the next and the inner lane was the last. The tra$c was low from mid-night to about 6 : 00 am, the number of vehicles in average was less than 20 vehicles per 5 min. After 6 : 00 am the number of vehicles increased dramati-cally and reached the maximum at about 7 : 30 am, and then remained in a heavy-tra$c situation to about 9 : 00 am and decreased afterwards. The heaviest heavy-tra$c #ow could be as high as 240 vehicles per 5 min, being equivalent to a tra$c density of 32 veh/km, or about 55 vehicles in the southbound of Fu}De tunnel at the same time. Starting from 10 : 00 am to 5 : 00 pm, the averaged tra$c volume was about 100 vehicles 5 min. Another tra$c peak occurred at about 6 : 00 pm, the tra$c volume
Fig. 3. The tra$c #ow accounted for by the number of vehicles passing through the outlet portal per 5 min on 17/02/97. Two sets of data represent, respectively, the tra$c #ow of the small-sized vehicles and the large- and medium-sized vehicles. It is seen that the small-sized car accounted for a great portion of the tra$c.
was about 200 vehicles 5 min, a little less than the peak at 8 : 00 am. The tra$c became more relax after 6 : 00 pm, the tra$c volume decreased gradually with time and reached to the minimum at around 4 : 00 am.
Fig. 3 shows the tra$c data of the same day, while the data were partitioned into two groups: the small-sized vehicles and large- and medium-sized vehicles. It is seen that more than 90% of the vehicles passing through Fu}De tunnel were of small-sized vehicles. The large- and medium-sized vehicles showed up mostly in the daytime. We also show in Fig. 4(a) the speed of vehicle, which in average was about 90 km/h, just on the speed limit of motorway in Taiwan, suggesting that the tra$c was smooth and normal and followed the criteria of design quite well. The variation of vehicle speed was quite dramatic during the night, which was because the tra$c density was low and the averaged speed was evaluated on the basis of fewer vehicles. Fig. 4(b) illustrates the variation of the tra$c density in the same day, showing that on the tra$c peak the tra$c density could be as high as 50 veh/km and the averaged value in the daytime was about 20 veh/km.
It is interesting to see the variation of the wind speed, which is primarily induced by the motion of vehicles and accordingly is closely related to the tra$c #ow in tunnel. We show in Fig. 4(c) the variation of the wind speed measured at the point 50 m from the outlet portal. It is seen that the wind speed could be as high as 6 m/s at the tra$c peak, and was about 4 m/s in the daytime and about 2 m/s between 3 : 00 and 5 : 00 am. Obviously the wind speed increased with larger tra$c #ow, while it was not linearly proportional to the number of vehicles. Fig. 4(d) also shows the variation of the CO concentration, which again appeared similarly with the tra$c #ow density,
Fig. 4. Typical tra$c #ow and ventilation situation in Fu}De tunnel on 05/03/97. (a) Averaged vehicle speed (km/h). (b) Tra$c density (veh/km). (c) Induced wind speed (m/s). (d) CO concentration (ppm).
suggesting that the variation of the CO concentration be also closely related to the tra$c #ow.
4. The one-dimensional theoretical model
The induced wind speed in tunnel is mainly driven by both the piston force due to moving vehicles and the pressure rise imposed by jet fans. Besides, the friction of tunnel wall, the pressure di!erence between two portals, and the friction loss at the inlet of the tunnel also in#uence the wind speed although to a smaller extent. Based on the force balance among these factors, the one-dimensional force equation can be formulated in a control volume which is chosen to be con"ned by the tunnel wall, the cross section surfaces at the inlet and the outlet. The external forces imposing upon the control volume are the piston force due to vehicle motion F, the thrust force imposed by jet fans F, the force due to the static pressure di!erence between two portals F, the frictional resistance of tunnel wall F, and the frictional loss due to the #ow separation at inlet portal F
. The e!ect of the compressibility of air in the control volume is neglected. The relation between the resultant force and the induced wind speed <can be written as
GFG"oA¸
d<
where FG, i"1,5 are F" , H o 2CdH(;H!<)";H!<"AvH, (2) F"n$oA$"<$"(<$!<)KH, (3) F"(P !P)A, (4) F"!fo2 ¸ DA<"<", (5) F"!Ko2A<"<", (6) In above equations,o is the density of air, A is the mean cross section area of tunnel, ¸
is the length of tunnel, CdH, ;H, and AvH are respectively the drag coe$cient, the speed and the frontal area of vehicle j, N is the total number of vehicles in tunnel, f is the friction factor of tunnel wall, n$, A$, <$, KH are, respectively, the number, the discharging area, the discharging speed and the pressure-rise coe$cient of jet fans, and
K is the friction loss coe$cient of inlet portal. We also note that P , P and P are,
respectively, the static pressures at inlet portal, outlet portal and atmosphere, which are related by
P "P!12o<!o
2(p!h)A d<dt, (7)
whereh is the elevation angle of foothill slope around the inlet portal and P"P is considered. Eq. (7) is derived from the unsteady Bernoullis equation, in which the second term of the right-hand side accounts for the dynamic pressure and the third term accounts for the unsteady #ow contribution on the pressure di!erence between two portals.
5. Tra7c group-partition dilemma
Eq. (1) illustrates that there are "ve major external forces in#uencing the induced wind speed, and the piston e!ect of vehicle motion plays a major role in determining the transient behavior of induced wind. In fact, we have found that the tra$c #ow in Fu}De tunnel varied constantly, suggesting that the unsteady transient behavior of the induced wind could predominate over the steady state to in#uence on the ventilation in tunnel. In order to more precisely re#ect the transient phenomena of the induced wind, the variation of tra$c #ow must be described in details for the F of Eq. (2). To account for the tra$c #ow variation, we propose accordingly a tra$c group-partition dilemma, with which the unsteady features of the tra$c #ow can be captured on the basis of the groups of vehicles in tunnel. The unsteady induced wind speed can accordingly be calculated through Eq. (1) with an F (see Eq. (21)) which can really re#ect e!ects due to tra$c #ow through the group-partition dilamma to be described in the next two sections.
5.1. Background and rules of partition
Not like previous studies [1}4] which considered that all the N vehicles inside the tunnel were of the same drag coe$cient C, same frontal area A, and same averaged speed ;M (t), we consider in this study di!erent values of above three physical para-meters based on a group of vehicles. The vehicles are separated into three di!erent types according to the length of vehicle l detected by the optical Autoscope. The large-sized vehicles were de"ned to be of a length l'11 m, the small-sized vehicles were of a length l(7.6 m, and the medium-sized vehicles were of a length in between. The Autoscope also detected both the speed of each vehicle passing the outlet portal and the number of vehicles passed in each of the consecutive time intervals. Based on these data the averaged speed for each type of vehicle in each time interval were calcualted. Namely, the vehicles were partitioned according to types and time inter-vals. Both the number of vehicles and the averaged speed of each partitioned group were then recorded in the data logger. For the present data logger, the time interval is adjustable between 10 s to 60 min.
For convenience for following discussion, we itemize the rules with which the tra$c #ow is partitioned:
1. Vehicles are partitioned into three types according to their lengths.
2. Vehicles of the same type, which pass the outlet portal in the same time interval, are considered to be in the same group.
3. The vehicles in the same group are assumed to travel through tunnel with a constant speed, which is equal to their averaged speed measured at the outlet portal. Please note that since each group moves in its own speed, the overtaking between di!erent groups is preserved in the present approach.
5.2. Procedure of group partition
Consider the tra$c #ow to be analyzed is in a period of ¹ h and the time interval to record the tra$c #ow is*t s. This period of ¹ h is uniformly divided into M intervals, so that M"¹;3600/*t. In each *t, vehicles are further separated into three groups according to their individual lengths. The vehicles passed the outlet portal in this time period are therefore totally partitioned into 3M groups, whereas some of the groups may include zero vehicle. The group of type i (i"1 for small-sized vehicles, two for medium-sized vehicles, and three for large-sized vehicles) passing the outlet portal at the kth time interval (k"1, 2, 3,2, M) is denoted by the subscript ik. The number and the averaged speed of the ikth group are denoted by nGI and ;MGI(m/s), respectively, which were measured by the Autoscope. The extent (or the length) covering the ikth group is equal to the distance traveled by this group in the corresponding time interval, being denoted by l I and can be written as
lGI(m)";MGI(m/s);*t(s). (8)
The leading position of this group x I(t) can be written as
where ¸(m) is the length of tunnel and the origin of the x!coordinate is set to be at the inlet portal. Because the vehicles in the same group are assumed to travel with the same speed, the lGI must therefore be constant. The vehicles in the same group are assumed to be uniformly distributed so that the tra$c density of this group is de"ned as DGI"nGI/lGI, which accounts for the tra$c density of vehicles of type i in the region between x"xGI(t)!lGI and x"xGI(t) at the moment t.
Consider "rst the case lGI(¸, all vehicles of the ikth group are assumed to be in tunnel at the beginning of the kth time interval and the last vehicle of this group is assumed leaving tunnel at the end of this time interval. So that at any moment t in this time interval, the number of vehicles of this group remaining in tunnel can be calculated by the following equation:
n GI(t)"nGI!nGIt!(k!1)*t
*t (k!1)*t)t)k*t, (10)
where the superscript &&in'' means in tunnel. When lGI'¸ is considered, there are only
nGI¸/lGI vehicles of the ikth group travelling inside the tunnel at the beginning of the kth time interval, and the rest are still not yet entering the inlet portal. In the next
(lGI!¸)/;MGI s, the number of vehicles leaving the tunnel is equal to that entering it so that the number of vehicles of this group travelling in tunnel remains to be
n GI(t)"nGI¸
lGI (k!1)*t)t)(k!1)*t#lGI!¸;M GI . (11) After that, the number of vehicles in tunnel of this ik group reduces constantly with time, i.e.,
n GI(t)"nGIk*t!t
*t (k!1)*t#lGI!¸;M GI )t)k*t. (12) Besides the three groups denoted by the subscript ik for i"1, 2, 3, there probably also exist simultaneously in tunnel other groups which shall be passing the outlet portal in the next time intervals (i.e., (k#1)th, (k#2)th, etc.). To gain a complete tra$c information along the tunnel for the kth time interval, all of these groups must be taken into account. The number of vehicles and the averaged speed of the i(k#1)th group are denoted, respectively, by nGI> and ;MGI>. The extent and the tra$c density of the i(k#1)th group are, respectively, denoted by lGI> and DGI>, which can be calculated, respectively, by the following equations:
lGI>(m)";MGI>(m/s);*t(s), (13)
DGI>"nGI>/lGI>. (14) The leading position of this group is at xGI>, calculated by
The tra$c density and the averaged vehicle speed in the region between
x"xGI>(t)!lGI> and x"xGI> (t) of the i(k#1)th group at moment t are
respectively, DGI> and ;MGI>.
When lGI>(¸/2 is considered, all of the vehicles of the i(k#1)th group are already inside the tunnel at the beginning of the kth time interval and its "rst vehicle shall reach the outlet portal at the end of this time interval. Let n GI>(t) denote the number of vehicles belonging to the i(k#1)th group, we can write it as
n GI>(t)"nGI> (k!1)*t)t)k*t. (16) When ¸/2(lGI>(¸ is considered, there are only ((¸!lGI>)/lGI>)nGI> vehicles of the i(k#1)th group travelling inside the tunnel at the beginning of the
kth time interval. In the next (2lGI>!¸)/;MGI> s, more vehicles of this group shall
be travelling into tunnel until "nally all nGI> vehicles of this group are in tunnel. The value of n GI> is calculated by
n GI>(t)"
¸!lGI> lGI> nGI># t!(k!1)*t *t nGI>, (k!1)*t)t)(k!1)*t#2lGI>!¸ ;M GI> , (17) n GI>(t)"nGI> (k!1)*t#2lGI>!¸ ;M GI> )t)k*t. (18) When lGI>'¸, there is no vehicle of the i(k#1)th group travelling in tunnel at the beginning of the kth time interval. The "rst vehicle of this group will not enter the inlet portal until t"(k!1)*t#(lGI>!¸)/;MGI> and then other vehicles of this group shall continuously enter the tunnel afterwards. At the end of this time interval the "rst vehicle of the group will reach the outlet portal while some vehicles of this group remain outside from the inlet portal. Then the number of vehicles of the i(k#1)th group in tunnel during the kth time interval can be written asn GI>(t)"0 (k!1)*t)t)(k!1)*t#lGI>!¸ ;M GI> , (19) n GI>(t)"t![(k!1)*t#(lGI>!¸)/;MGI>] *t nGI>, (k!1)*t#lGI>!¸ ;M GI> )t)k*t. (20) In the similar manner we can also deduce those information, respectively, for the
i(k#2)th group, i(k#3)th group, i(k#4)th group, i(k#5)th group, etc., until the last
group of the kth time interval is identi"ed. According to the leading position and the extent of each group calculated in the manner described above, the number of the groups in tunnel of i -type vehicle at any moment t can therefore be computed and is denoted as IG(t).
The partitioned tra$c-#ow data regarding a group of vehicle include the vehicular type, the number of vehicles, the averaged speed, the leading position, and the extent of each vehicular group. Besides, the number of group of each type of vehicle in tunnel at any interested moment can also be determined. With these deduced quantities, the resultant force exert on the tunnel air by all the vehicles in tunnel can be written as
F(t)" G I>'GR HI n GHo 2CdG(;MGH!<)";MGH!<"AvG (k!1)*t)t)k*t. (21) Based on the above quantities, one can calculate the tra$c density distribution and the corresponding averaged speed of i-type vehicle along the tunnel at the moment
t with the following equations: DG(t, x)"I>' GR HI DGH+u[x!(xGH!lGH)]!u[x!xGH], (k!1)*t)t)k*t (22) and ;M G(t,x)"I>' GR HI ;M GH+u[x!(xGH!lGH)]!u[x!xGH], (k!1)*t)t)k*t, (23) where u[x!a]"
0, x(a, 1, x'a,is a unit step function. Note that besides the tra$c #ow e!ect, the switch-on and -o! of the jet fans are other factors in#uencing the wind speed in tunnel. This e!ect can be introduced into the theoretical model through n$(t) in F, where n$(t) is the number of fans under operation during the period (t(t(t), while is 0 otherwise.
Eqs. (1)}(7) are to form the governing equation for the induced wind speed in road tunnel, which can be rewritten as
d<
dt"a(t)<#b(t)<#c(t). (24) The coe$cients a, b and c are functions of the parameters regarding tunnel geometry, the tunnel #ow, the mechanical ventilation system, the tra$c, and so on. They can be expressed explicitly in terms of partition-group parameters as follows:
a(t)"
G I>'GR HI n GHo 2CdGAvGIGH!f o 2 ¸ DAIO!K o 2AI/(oA¸), (25) b(t)"! G I>'GR HI n GHoCdG;MGHAvGIGH!n$oA$<$KHI$/(oA¸), (26) c(t)" G I>'GR HI n GHo 2CdG;MGHAvGIGH#n$oA$<$KHI$#(P !P)A/(oAR¸). (27)where IGH"
!11 ;;M GH'<M GH(<, I$" 1 <$'< !1 <$(<, I" 1 <'0 !1 <(0 Eq. (24) is a nonlinear "rst-order ordinary di!erential equation with variable coe$-cients, which together with the deduced tra$c information can be numerically integrated from the initial wind speed <(0) step by step to obtain the induced wind speed hereafter. An implicit central-di!erence scheme is employed to solve Eq. (24).5.3. An example of group-partition
To show an example of the partitioned tra$c #ow in tunnel, we select the tra$c data measured in the morning of 23/07/97. This set of data includes the number of vehicles/10 s and averaged speed for each type of vehicles passing through the outlet portal, as shown respectively in Figs. 5 and 6. Every point in both "gures accounts for the averaged tra$c-#ow data in every 10 s, which is the smallest time interval can be set by the present data logger. Those points showing zero vehicular #ow rate and zero-averaged speed represent that there was no vehicle passing through the outlet portal during the 10-s interval. From both "gures we can see again that during these morning hours the tra$c was dominated by the small-sized vehicles, the same as what is shown in Fig. 3. The data of Fig. 5 scatter widely than those of Fig. 3, which is because the former was evaluated in a much shorter time interval (every 10 s) than the latter (every 5 min). Fig. 6 shows that in most of the time the averaged speeds of three types of vehicles were all around 90 km/h, while at the rush-hour around 7 : 45 am the speeds all decreases to about 60 km/h, which is obviously due to the heavy tra$c including a large number of large-sized vehicles. Note that although the large-sized vehicles were of a smaller amount, they afterall caused signi"cant distur-bances in the tra$c #ow.
A typical example resulted from the group-partition procedure is obtained by analyzing the tra$c-#ow data of Figs. 5 and 6 between 7 : 00 : 00 (h : min : s) and 7 : 01 : 40, and the result regarding the small-sized vehicle is shown in Fig. 7. In Fig. 7(a), it is seen that between 7 : 00 : 00 and 7 : 00 : 10 there were approximately eight groups of small-sized vehicle in the tunnel. The vehicles of these eight groups were of virtually uniform speed throughout the tunnel so that the group pattern of these groups did not change with time signi"cantly. As one can see, the last group left tunnel at 7 : 01 : 15, taking about 1 min and 10 s to pass through the Fu}De tunnel (1762 m long). This implies that the averaged speed of each group is approximately 90.6 km/h, being consistent with the data shown in Fig. 6. It is nevertheless possible to see from Fig. 7(b) that, although very little, the speed of each group was di!erent from others. Due to these speed di!erences, overlaps between some groups occurred. In overlaps, the tra$c densities are higher and appear as peaks in Fig. 7(a). Similar analysis applied for the tra$c #ow of the medium-sized and the large-sized vehicles. Because the tra$c density of these two types was small as well as scattered, the partition of tra$c was clearer and the overlaps between groups hardly appeared.
Fig. 5. The volume of tra$c accounted for by the number of vehicles per 10 s for (a) small-sized vehicle (b) medium-sized vehicle and (c) large-sized vehicle. Each point represents the number of vehicles of the group passing the outlet portal in the 10-s interval. It is seen that the small-sized vehicle accounts for a major portion of the tra$c and the tra$c volume at the rush hour (between 7 : 20 to 8 : 00 am) is more than twice than the other time. On the other hand, the medium- and the large-sized vehicles were of relatively small amount, except there happened to be a motorcade of large-sized vehicles passing the outlet portal between 7 : 40 and 7 : 50 (see enlarged "gure on the upper-right corner), which reduced the averaged vehicular speed to about 60 km/hr (see Fig. 6).
The group-partition procedure is applied to the whole period of interest (6 : 00 : 00}12 : 00 : 00) and the deduced tra$c information along the tunnel is pro-vided for the theoretical ventilation model through Eq. (21) to calculate the induced
Fig. 6. The averaged speed of (a) small-sized vehicle, (b) medium-sized vehicle and (c) large-sized vehicle on 23/07/97 from 6 : 00 to 12 : 00 am. Except at about 7 : 45 am when the motorway was su!ering from a minor tra$c jam caused by a motorcade of large-sized vehicles, the averaged speed was about 90 km/h, which is the speed limit of the motorway, re#ecting a fact that the tra$c in Fu}De tunnel was generally as smooth as designed. The enlarged "gure shows that there were a motorcade of large-sized vehicle between 7 : 40 to 7 : 50 am.
wind speed and the pressure distribution in tunnel. The reason that the vehicle groups are partitioned according to di!erent size of vehicle is due to the fact that the drag coe$cient of vehicle is size-dependent. The drag coe$cient, as will be shown later, is of signi"cant in#uence on the induced wind speed, especially the transient behavior of the induced wind to which we pay much attention in this study. In addition to the
Fig. 7. Results obtained by the group-partition procedure for small-sized vehicles from 7 : 00 : 00 to 7 : 01 : 40 on 23/07/1997. (a) The tra$c density in terms of number of vehicles per meter. The vehicles in tunnel are partitioned into several groups, all move with constant speeds. The peak between two neighboring groups indicates that there is overlap between them and the valley represents that there is no vehicle of the same kind in between. (b) The vehicle speed of each group. Each group is assumed to move constantly with its own speed. The speed di!erences between groups is small.
Table 1
Values of parameters used in the present study [5]
o 1.16 kg/m ¸ 1762 m D 10.38 m A 93.88 m f 0.025 C (small-sized vehicles) 0.2
C (medium- and large-sized vehicles) 0.56
Av (small-sized vehicles) 2.5 m
Av (medium- and large-sized vehicles) 7.11 m
KH 0.4
A$ 2.01 m
<$ 30 m/s
K 0.6
The drag coe$cients are lower than the values deter-mined by single-vehicle experiments, which used to be in average about 0.3 for small-sized and 0.8 for medium- and large-sized vehicles. Because on the road the vehicles were covered by the wakes induced by other vehicles, in which irregular vortices prevail. The drags of the air imposing on the vehicles are therefore greatly reduced, say 30% [5]. The vaule of KH was determined from another analysis [5], in which we applied the unsteady one-dimensional model and employed relevant experimental data to seek the proper value of KH in Fu}De tunnel.
drag coe$cient of vehicle, there are other parameters being also in#uential on the induced wind speed, such as the friction factor of tunnel wall and the pressure-rise coe$cient of jet fans. These parameters need to be determined before the analysis of the induced wind can be implemented. The latter two parameters a!ect only the averaged behavior of wind and the drag coe$cient a!ects both the averaged and the transient behavior of the wind. The detail procedure for determining these parameters can be found in Ref. [5]. The values of the parameters used in the present analysis are listed in Table 1.
6. Comparison between theoretical and experimental results
Besides the tra$c data, the in situ measurement system also provides the data of wind speed, pressure, and temperature of the air in tunnel at three locations, respec-tively, at 50, 500, and 1000 m from the outlet portal. In this paper, the measured and theoretical wind speeds are used to compare each other and the computed pressure distributions along the tunnel are discussed .
We apply the theoretical model as well as the group-partition procedure on the tra$c data measured in the morning of 23/07/97, which have been shown in
Fig. 8. A comparison between the wind speeds obtained by both theoretical and experimental approaches. The data were measured in the morning of 23/07/1997. Note that the comparison is generally very nice except at about 7 : 45 am when the tra$c was heavy and the large-sized vehicles account for a signi"cant portion of the tra$c, suggesting that the drag forces of all the vehicles behind those large-sized trucks may be a little overestimated. Otherwise, the theoretical model based on the partitioned tra$c groups might be able to more accurately predict the transient behavior of the induced wind speed.
Figs. 5 and 6. The computed-induced wind speed varying with time is shown in Fig. 8, in which the measured wind speed is also shown for the purpose of comparison. It is found that the comparison is very nice, especially that the transient behavior of the induced wind speed in terms of both the phase and the amplitude of variation are all in good agreement. We note nevertheless that at about 7 : 50 am when the number of truck increases dramatically, the computed results are larger than the measured data, suggesting that the drag coe$cient of the vehicles behind those large trucks can be overestimated in this tra$c situation. Namely, the drag coe$cient of the vehicles shaded by the wake of trucks shall be smaller than that shown in Table 1. Otherwise, as small-sized vehicle dominates the tra$c, the prediction from present theoretical approach can perfectly re#ect the reality.
More evidence supporting the present theoretical approach can be obtained from other cases of di!erent occasions. To con"rm further the superiority of the present theoretical approach, we had examined a set of data measured in the evening of 27/07/97, which due to some unknown reasons were piecewise discontinuously recorded. Whereas the tra$c data measured by the Autoscope were complete, so that we were able to apply the present theoretical approach to predict the induced wind speed in the whole period. Results (not shown in the present paper) showed that the theoretical results could essentially "ll up the gaps between the discontinuous data, resulting in a complete picture of the variation of the induced wind in the tunnel.
Fig. 9. The predicted pressure distribution along the tunnel. (a) The pressure distributions represented in time and space. (b) The pressure distributions at four di!erent times. Note that there were three sudden jumps of pressure after 8 : 08 : 55 in tunnel, which is due to the fact that the three jet-fans in tunnel were turned on at that time.
Because the pressure sensors we posed in tunnel were not of enough precision to detect the small #uctuation of pressure, the transient behavior of the pressure along the tunnel could not be detected by the measurement but can be predicted by the present theoretical approach. Based on the wind speed and the partitioned tra$c #ow along the tunnel, the pressure distribution along the tunnel can be obtained by numerically integrating the momentum equation from the inlet portal towards the outlet portal. The computed pressure distribution along the tunnel from 8 : 08 : 00 to 8 : 09 : 40 are shown in Fig. 9(a), and with a more precise scale the pressure distribu-tions at four di!erent times are shown in Fig. 9(b).
The reason to show the pressure distribution in this selected time period is simply because the three jet fans located, respectively, at 400, 600 and 1000 m from the inlet
Fig. 10. Time evolutions of the pressure at "ve di!erent locations in tunnel. (a) at the inlet portal. (b) at 1000 m from the outlet portal. (c) at 500 m from the outlet portal. (d) at 50 m from the outlet portal. (e) at the outlet portal. Fluctuation of pressure is more intense at the place farther from both the inlet and outlet portals, implying that the pressure #uctuation caused by the piston e!ect of vehicles is more intense within the tunnel while is more relax when close to the portals.
portal were turned on at 8 : 09 in the morning. So that the computed pressure shown in Fig. 9 can illustrate the e!ects imposed from both the jet fans as well as the tra$c. Both Fig. 9(a) and (b) illustrate that before the jet fans were set into operation, the pressure was the lowest near the inlet portal, increased gradually along the tunnel due to the piston e!ect of vehicle motion, and eventually reached the atmosphere pressure at outlet portal. The pressure in most part of tunnel was below the atmosphere pressure, which was about 101330 Pa. While as the three jet fans were set into operation, the lowest pressure occurred at the suction side of the "rst jet fan and the highest pressure appeared at the discharging side of the last jet fan. Each jet fan
could increase the pressure by about 8 Pa. We also show in Fig. 10 the computed pressures at "ve di!erent locations in tunnel. Results show that the inlet portal pressure was always below the atmosphere pressure and the pressure at outlet portal was virtually equal to the atmosphere pressure. Fig. 10(b}d) reveal the important phenomena that the pressure is #uctuating more violently at deeper locations of tunnel.
7. Conclusions
We have proposed a novel approach with which the transient behavior of the induced wind speed in a motorway tunnel can be accurately predicted when the tra$c data measured at the outlet portal are provided. This novel theoretical approach is set up on the basis of the so-called group-partition dilemma, which essentially partitions the vehicles into di!erent groups, according to both the size of vehicle and the measured time intervals. The size of vehicle is categorized into three types, i.e., the large-size, the medium-size, and the small-size, and the time interval can be adjust-able according to the speci"cation of the data logger. To the present logger used to record the tra$c data, a time interval can be as small as 10 s. By substituting the partitioned tra$c data into the one-dimensional force equation, the unsteady induced wind speed in tunnel can be accurately computed. The theoretical results have been shown to be in nice comparison with the measured data. Emphasis has been placed on the prediction of the transient state of the induced wind and the superiority of the present approach has been con"rmed by the nice agreement in terms of the phase and amplitude of the #uctuation of induced wind speed between the theoretical and experimental results. The computed wind speed can then be employed to compute both the temporal variations of temperature and pressure along the tunnel, in which the computed temperature distribution along the tunnel agrees also nicely with the measured data. The present approach is believed to be also valid to predict the unsteady behavior of the variation of pollutant along the tunnel.
As far as the engineering application is concerned, the present theoretical approach may provide a scheme with which the monitoring of ventilation in tunnel can be greatly simpli"ed. The present one-dimensional theoretical model can predict reason-ably the induced wind speed as long as the tra$c data at one point near tunnel, for example the outlet portal, are provided. Through this approach, the transient state of the ventilation in the tunnel can be well predicted when the tra$c is smooth.
Acknowledgements
This work has been supported by the Taiwan Area National Expressway Engineer-ing Bureau, Ministry of Transportation and Communications through grant 860-NO73 and the National Science Council through grants NSC 87-2212-E-034-004, NSC-88-2212-E-034-002 and NSC-88-2212-E-002-030.
References
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[3] P.F. Hartman, N.P. Costeris, L. Swart, Calculation method for longitudinal ventilation system, in: A. Glerum et al. (Ed.), Ventilation of Road Tunnels, Royal Institute of Engineers (KIVI), Division of Civil Engineering, 1991, pp. 55}76.
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ReportC096-1, Taiwan Area National Expressway Engineering Bureau, Ministry of Transportation and Communications, Dec., 1997.
