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Computational study of effects of jet fans on the ventilation of a highway curved tunnel
Tunnelling and Underground Space Technology 25 (2010) 382–390
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Computational study of effects of jet fans on the ventilation of a highway curved tunnel Feng Wang a,b,*, Mingnian Wang a, S. He b, Jisheng Zhang b, Yuanye Deng a a b
School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China School of Engineering, University of Aberdeen, Aberdeen AB24 3UE, UK
a r t i c l e
i n f o
Article history: Received 21 June 2009 Received in revised form 20 January 2010 Accepted 1 February 2010 Available online 12 March 2010 Keywords: Curved tunnel Jet fans CFD Velocity field Pressure-rise coefficient
a b s t r a c t A computational study was carried out to investigate the aerodynamic behavior of jet fans in a curved road tunnel and its effects on the tunnel ventilation system. It has been found that the variations of the static and dynamic pressure in a curved tunnel are non-monotonic. After the issue of the jets, the pressure initially increases gradually, but this is followed by a sudden drop and then a recovery. This is attributed to the interaction between the jets and the curved walls of the tunnel. A sudden increase in pressure is resulted as the jet reaches the convex wall, whereas that the concave wall is approached causes a pressure reduction. The flow becomes asymmetrical downstream of the jets. The development of the jets depends on the separation of the fans and the distance between the fans and the tunnel walls. Increasing the space between the fans or moving them away from the tunnel ceiling makes the jets spreading more quickly across the cross-section. However, it takes a longer distance for the jets to develop when the fans are close to each other or to the tunnel wall. The distance required for pressure to be fully recovered is approximately 90–120 m in this study. The biggest pressure-rising coefficient is obtained when the fans are arranged according to the distance of 2.4 m between the fans, the fans offset of 0.5 m from the centre line towards the convex wall, and the ratio of the distance between fans and the ceiling to the diameter of fans of 1.77. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The air quality in a road tunnel would easily deteriorate if the exhaust gas emitted from the vehicles is not promptly removed, because the road tunnel is normally enclosed or partially enclosed (Chung and Chung, 2007). As a result, effective ventilation in a road tunnel is extremely important to prevent the harmful substances from affecting tunnel users and to maintain good visibility in tunnels. In long vehicle tunnels, mechanical ventilation systems are often employed to keep the amount of toxic gases below safety limits (Chung and Chung, 2007; Chen et al., 1998; Chow and Chan, 2003; Bari and Naser, 2005). Such systems are classified into longitudinal ventilation, transverse ventilation, semi-transverse ventilation and combinations of them. Among these ventilation systems the longitudinal ventilation system has been most widely adopted (Vega et al., 2008; Van Maele and Merci, 2008; Indrehus and Vassbotn, 2001; Bring et al., 1997). Because of the topographic constraint, some road tunnels have to be made curved in a horizontal plan, even with a small radius in
* Corresponding author. Address: School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China. E-mail address: [email protected] (F. Wang). 0886-7798/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2010.02.001
some cases. For example, there are two tunnels under construction in China which have a minimum curve radius of 600 m. There is clearly a need for analyzing the differences between the ventilation performance of straight tunnels and that of curved tunnels. It is of particular interest to study the performance of the jet fans which are used to provide thrust to drive the air flow inside the tunnel and to push the vehicle exhausts out of the tunnel. Many studies have been conducted on the ventilation of straight tunnel. Chen et al. (1998) used a 1/10 scale model tunnel with jet fans and exhaust pipes installed to study their effects on the distribution of the polluted air. It was shown that a higher air velocity issued by jet fans resulted in a higher exhaust concentration in the lower region of the tunnel which is detrimental to the drivers and walkers despite it brought a higher flow velocity inside the tunnel. Mutama and Hall (1996) investigated the aerodynamics of a jet fan using a wind tunnel and their results showed that the initial pressure drop would increase in a significant length of the tunnel when moving the jet fan toward the wall. Back flow was observed when the jet fan was located very close to the wall, but such a flow diminished as the jet fan was traversed toward the tunnel axis. The flow instability occurred in the region close to the wall of the tunnel when the jet fan was located at the axis. Sambolek (2004) used a 1/25 scale model of the Sv. Rok tunnel to study some important
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parameters for the design of the ventilation system and they concluded that the flow resistance coefficient was strongly influenced by the Reynolds number but only moderately influenced by the vehicle speed. The researches above mainly focus on the experimental study and many numerical studies have also recently been conducted. Chung and Chung (2007) carried out a numerical simulation to study effects of jet fans and moving vehicles on the flow field and the dispersion of gaseous pollutants in a road tunnel. The results showed that the pollutants concentration increased with the increase of downstream distance due to the effect of jet fans. And the cross-sectional concentrations of air pollutants were observed to be nearly stratified. Vega et al. (2008) carried out a computational study to analyze the fire behavior in Memorial tunnel. The results demonstrated that computational fluid dynamics (CFD) modeling is a powerful tool to predict the flow behavior under a longitudinal ventilation system in a road tunnel and the numerical results have a good agreement with previous experimental data. Jang and Chen (2002) adopted an optimization procedure to determine four major aerodynamic coefficients for the design of a road tunnel ventilation system, namely the friction coefficients of the tunnel wall, the averaged drag coefficients of small-sized and large-sized vehicles, and the pressure-rise coefficient of jet fans, based on the measurement data of the dynamic traffic and the traffic-induced wind speed. They found that the pressure-rise coefficient of jet fans was 0.56 which was almost traffic-density independent. Although extensive studies on the ventilation in straight road tunnels have been conducted as seen from the above literature review, the authors are unaware of any detailed study in curved tunnels. The main objectives of this paper are to investigate the aerodynamic behaviors of jet fans in a curved tunnel, including the characteristic of the airflow and the pressure distribution for different locations of jet fans and to establish an optimal arrangement. Recently, CFD has been widely used to solve airflow under the normal traffic condition or the emergency ventilation in road straight tunnels, which could provide detailed supplementary information to those obtained from experimental study and field measurement. In the study presented here, a 3D CFD model of a curved tunnel with embedded jet fans has been developed incorporating a standard k–e turbulent model, which has been adopted in several previous studies of similar problems. The findings from the present study are expected to be useful for designing ventilation system in curved highway tunnels.
2. Model description 2.1. Governing equations The flow in a longitudinal ventilated tunnel is assumed to be steady incompressible because the purpose here is focused on the flow behavior without consideration of the fire occasion. The commercial computational fluid dynamics software FLUENT was used to solve the continuity and the momentum equations. Recently Large Eddy Simulation (LES) has been applied to some studies of tunnel fire and the ventilation flow, but the huge computational cost prevents it being used for large scale tunnel simulations although it is capable of better predicting complicated flows (Van Maele and Merci, 2008; Hu et al., 2008). On the other hand, the Reynolds-Averaged Navier–Stokes (RANS) models offer a good compromise between result accuracy and computational cost. The research on the comparison of flow performance in a pipe with three different RANS models, namely k–e, k–x, Reynolds stress models (RSM), is found that the simulation results among the three models in the mean velocity profile and the friction factor match quite well with the experimental results and RSM consumes
more time though it can give some additional information on the shear stress correlations (Vijiapurapu and Cui, 2010). Furthermore, the standard k–e turbulent model has the advantage of being extensively used in simulation of tunnel ventilation and has been validated against the experimental data (Chung and Chung, 2007; Vega et al., 2008; Solazzo et al., 2008; Huang et al., 2008). Accordingly, the standard k–e turbulent model due to Launder and Spalding (Launder and Spalding, 1974) was adopted in this research. Additionally, second order, upwind discretization was used for convective terms and a central difference scheme was used for diffusion terms. The coupling between velocity and pressure was dealt with the SIMPLE algorithm. The governing equations solved in Fluent for the present problem can be written as: Continuity equation:
@ui ¼0 @xi
ð1Þ
Momentum equation:
@ qui uj @p @ ¼ þ @xi @xj @xj
@ðqu0i u0j Þ @u @u l iþ j þ @xj @xi @xj
ð2Þ
k equation:
uj
@k 1 @ ¼ @xj q @xj
lþ
lt @k lt @ui @uj @ui þ þ e rk @xj q @xj @xi @xj
ð3Þ
e equation: uj
@e 1 @ ¼ @xj q @xj
lþ
lt @ e C 1 lt e @ui @uj @ui e2 þ C2 ð4Þ þ re @xj q k @xj @xi @xj k
The turbulent viscosity lt:
lt ¼ C l qk2 =e where u and u0 are the mean velocity and the corresponding fluctuation component, q is the air density, l and lt are the molecular viscosity and the turbulent viscosity, k and e are the turbulent kinetic energy and its dissipation rate, The standard set of constants were adopted for the k–e equations, Cl = 0.09; C1 = 1.44; C2 = 1.92; rk = 1.0; re = 1.3. 2.2. The tunnel The present study is motivated by the need for the understanding of the aerodynamics behavior in Tiezhaizi NO I tunnel which is one of the main highway tunnels linking Chengdu with Kunming in China. It consists of two separated channels, one for each direction in one-way, two-lane traffic. One of the channels is 2778 m long and the other is 2931 m. The tunnel has a curved section of a minimum curve radius of 600 m. The longitudinal ventilation system is adopted in the curved tunnel. A numerical modeling of the tunnel, together with jet fans and exhaust pipe, was developed to investigate the effects of jet fans (Fig. 1). Ohashi et al. (1976) showed that a distance of 60–100 m was sufficient to allow the jet flow to fully develop in a straight tunnel. Accordingly, a model tunnel of 330 m length with a radius of 600 m was built here, and the length of the curved tunnel was considered to be significantly longer to ensure the development of the flow to be complete. The cross-section of the tunnel is approximately 68.55 m2 with a hydraulic diameter of Dt = 8.57 m. The model jet fans have a diameter of 0.9 m and are hung on the ceiling of the tunnel and are installed in groups of two (Fig. 2). The fans themselves were modeled by embedding a tube section in the tunnel. The jet was created by specifying a flow (see next section for detailed).
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Fig. 1. Simulation domain and mesh for jet fans region.
Fig. 2. Cross-section of highway curve tunnel.
2.3. Mesh analysis Several different mesh sizes have been tried to assess the mesh requirements, as described in the Table 1. A 0.4 m mesh in the longitudinal direction was proposed in a similar research made by Betta et al. (2009). A 0.4 m mesh in the region of jet fans inlets and outlets is thereby chosen here (Fig. 1). The horizontal axial velocity profiles and the velocity profile along the tunnel centerline on the cross-section 60 m away from the jet fan outlet in the tunnel are shown in Fig. 3a and b, respectively. The difference of the horizontal axial velocity profiles among the three mesh types is observed to be slight. However, the velocity profile along the tunnel centerline for mesh A has considerable difference from the other two mesh types. Finally mesh B was used for all the simulations because it offers an acceptable compromise between the accuracy of simulation results and computational cost. 2.4. Boundary conditions The boundary conditions are specified as follows. The non-slip stationary wall boundary condition is applied on the solid walls
Fig. 3. Velocity profiles for different mesh sizes: (a) horizontal axial velocity profiles; (b) central vertical velocity profiles.
of the tunnel and the wall of jet fans. A uniformly distributed velocity boundary is prescribed at the tunnel inlet, which produces designed ventilation velocity for the tunnel. The outflow boundary condition is used at the tunnel outlet, namely @ U=@n ¼ 0 (where U = u, k or e). The fans inlet also adopts the outflow boundary condition (Chung and Chung, 2007). The jet fans velocity Uj = 33 m/s is specified for the fan outlet according to the actual design data. In this paper, the cross-sectional locations of jet fans are varied to analyze the effect on the characteristic of the airflow (Fig. 2). The cases simulated are listed in Table 2, where a and L2 are the distance between fans and that between the ceiling and fans, and d is the diameter of the jet fans. b represents the offset of the fans from the centerline of the tunnel. The fans are symmetrically distributed for b = 0, b is positive when the fans are moved to the right (towards the concave wall) and is negative when moved to the left (towards the convex wall). 3. Results and discussion
Table 1 The mesh description.
3.1. The pressure-rise coefficient of jet fans
Mesh type
Mesh size in the longitudinal direction (m)
Mesh size on the jet fans (m)
Mesh size on the cross-section of tunnel (m)
Total cells
A B C
0.4
0.2 0.18 0.15
0.25 0.20 0.18
589,212 857,592 1,116,810
The tunnel ventilation system is designed based on the onedimensional mathematical model as follows:
Dpv þ Dpj þ Dpd Dpf Dpi ¼ qL
dv t dt
ð5Þ
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F. Wang et al. / Tunnelling and Underground Space Technology 25 (2010) 382–390 Table 2 Simulation cases. Case
L2/d
a (m)
b (m)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
1.77 1.77 1.77 1.77 1.77 1.77 1.77 1.77 1.77 1.77 1.77 1.77 1.77 1.5 1.5 1.2 1.2
2.0 2.0 2.0 2.0 2.0 2.4 2.4 2.4 2.4 2.4 2.8 2.8 2.8 2.4 2.4 2.8 2.8
1.0 0.5 0 0.5 1.0 1.0 0.5 0 0.5 1.0 0.5 0 0.5 0 0 0 0
where the different components are J X q Ac cdj ðv c v t Þjðv c v t Þj Nj 2 At j¼1 Aj vt Dpj ¼ N g q v 2j 1 At vj
Dpv ¼
ð6Þ ð7Þ
Dpd ¼ Pin Pout qL Dpf ¼ f v t jv t j 2D Dpi ¼ k
q 2
ð8Þ ð9Þ
v t jv t j
ð10Þ
where Dpv is the traffic force, Dpj is the fan thrust, Dpd is the pressure difference between the inlet and outlet portals, Dpf is the wall friction, Dpi is the local resistant caused by the flow separation at the inlet portal. Nj is the number of vehicles in group j and cdj and Ac are the corresponding effective drag coefficient of vehicles and the frontal area of vehicles, vc is the speed of vehicles, N is the number of jet fans, vj and vt are the discharging velocity of jet fans and the mean air velocity in the tunnel, Aj and At are the discharging area of jet fans and the cross-section area of the tunnel, q is the air density and g is the pressure-rise coefficient of jet fans, f and k are the friction coefficient of tunnel and the coefficient of entrance loss respectively. The relatively high mean air velocity is needed to maintain good air quality in tunnel. The traffic force and the fan thrust are the most important driving forces among them. But attention here is mainly focused on the fan thrust and the pressure-rise coefficient. From Eq. (7), we can conclude that the fan thrust only depends on the pressure-rise coefficient of jet fans g and the number of fans as the designed parameters of a tunnel and fans are got. A higher pressure-rise coefficient of jet fans can significantly decrease the number of fans and therefore reduce the investment and operating expense of the tunnel ventilation system. To validate the computational model used in this study, a simulation using the same computational method and mesh density was first carried out for a straight tunnel – Zhong Liangshan Tunnel in China for which field data are available (Key Road Construction
Fig. 4. Pressure-rise coefficient variation for various fans positions: (a) L2/d = 1.77; (b) b = 0 m.
Office, 1998). The results of the simulation were compared with the field data for pressure-rise coefficient of jet fans in Table 3. It can be seen that the prediction agrees quite well with the measurement with a difference of less than 1%. We therefore conclude that the numerical method and turbulence model used in this study are appropriate for such applications. Fig. 4a shows the variations of the pressure-rise coefficient of the jet flow as a function of the horizontal positioning (b) of the fans for several fan separations. It can be seen that the peak pressure-rise coefficient could be achieved when b = 0.5 m for any a, but the maximum can be achieved when a = 2.4 m. The pressurerise coefficient drops sharply as b moves away from 0.5 m. When b = 0 m, the maximum pressure-rise coefficient could be obtained for a = 2.8 m. Fig. 4b shows the variation of the coefficient with the vertical positions of jet fans when the fans are symmetrically placed in the tunnel. For all values of a, the coefficient increases rapidly as L2/d increases. The coefficient for a = 2.4 m overshoot that for a = 2.8 m at L2/d = 1.5 but this is reversed at L2/d = 1.77. Clearly the choice of L2/d is limited in practice.
Table 3 Comparison between field measuremental and computational results. Cross-section area of tunnel (m2)
Area of jet fans (m2)
Tunnel mean air velocity (m/s)
Jet velocity (m/s)
Field result g
Computational result g
Errors%
51.70
0.64
1.73
28.44
0.848
0.856
0.93
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Fig. 5. Velocity profiles for a = 2.4 m b = 0 m and L2/d = 1.77.
3.2. velocity profile Fig. 5 shows the horizontal axial velocity profiles at various axial location for the condition of a = 2.4 m, b = 0 m and L2/d = 1.77. L represents the axis distance from the issue of the fans in the curved tunnel. At the early stage, the velocity profile exhibits the characteristic of two free jets, and the flow away from the jets drops below initial value. That is because part of the free-stream air is entrained into the high-speed jet flows. With the diffusion and entrainment downstream, the jets spread radially and its core velocity gradually decreases. At L = 5 m, the outer edge of the jets start to interact with each other at the centerline of the tunnel where the flow speed increases rapidly. On the other hand the velocity next to the wall does not increase until much later when the jets diffuse to the tunnel walls. Then, the velocity gradually increases and overshoots the initial value. At L = 20 m, the two jets merge into a single one. The velocity subsequently decreases due to the diffusion of the jets (L = 40 m). But at L = 50 m, the velocity near the right (concave) wall rises and the velocity near the left (convex) wall falls abruptly because of the influence of the curved walls. The velocity profile continues to evolve downstream becoming very asymmetric at L = 60 m. Here, the velocity is significantly smaller than that at L = 20 m. The velocity peaks towards the right concave wall and decreases gradually toward the left. At L = 120 m, the velocity profile is an uniform flow across the core with a thin boundary layer next to the wall. Fig. 6 shows the effect of the separation of the fans on the axial velocity at several axial locations for b = 0 m and L2/d = 1.77. At the early stage, i.e. L = 5 m (Fig. 6a), the flow basically behaves as two free jets although some interactions start to show at the centerline with an increased velocity for a = 2.0 m. The velocity next to the walls remains unchanged since the development of the jets has not arrived there yet. Further downstream at L = 10 m (Fig. 6b), the velocity of the jet cores decreases rapidly but the velocity around the tunnel centerline increases significantly. The spread of the jets is much greater. The jets spread is greatest for a = 2.8 m and the tunnel centerline velocity is biggest for a = 2.0 m. Fig. 6c shows axial velocity profiles at L = 20 m. The two jets have merged completely and the peak velocity moves to the tunnel centerline for a = 2.0 m, whereas two peaks still remain in the velocity profile for a = 2.8 m. For a bigger separation, the jets diffuse more quickly to the surrounding air, which causes a higher background flow but a smaller peak at the tunnel centerline. It can also be seen that the velocity next to the right concave wall is slight higher than that next to the convex left
Fig. 6. Velocity profiles at different axial positions for various a: (a) L = 5 m; (b) L = 10 m; (c) L = 20 m; (d) L = 60 m.
wall. Such an asymmetric feature is much clearly shown in Fig. 6d (L = 60 m). The velocity profiles exhibits a peak velocity near the
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right wall and it falls gradually towards the left. The velocity profile is steep for a = 2.0 m but much gradual for a = 2.8 m. The velocity on the right of the cross-section for a = 2.0 m is higher than that for other a values but the opposite is true on the left of the cross-section. Consequently when fans are located symmetrically in the cross-section, the bigger separation can cause a decrease in the time needed for the jets to reach the wall. Fig. 7 shows the effect of the offset of the fans from the centerline on velocity profile, i.e. b = 1.0 m to b = 1.0 m. The flow exhibits the characteristic of free jets at the initial stage (Fig. 7a) for the various values of b. The shape of velocity profiles is similar and the only difference is the offset. Fig. 7b shows velocity profiles at L = 10 m. For b = 1.0 m, the development of the jets is obviously subjected to the constraint of the left wall, whereas the jets develop quite well on the right hand side of the cross-section. Similarly when b = 1.0 m, the jets are subjected to the constraint of the right wall and is well-developed on the left. Those two profiles are effectively mirror images to each other. Consequently, the curvature of the tunnel has no influence at this stage. Further downstream, however, the influence of the curvature can be clearly seen, see for example Fig. 7c for L = 20 m. It can be seen that the flow velocity next to right wall for b = 0.5 m and b = 1.0 m is significant higher than that next to the left wall for b = 0.5 m and b = 1.0 m. For b = 0 m, the velocity next to right wall is also bigger than that next to the left wall. The reason is clear: as the jet flow reaches the right (concave) wall, it is subjected to a favorable pressure gradient and starts to accelerate. On the other hand, as flow reaches to the left (convex) wall, it is subject to an adverse pressure gradient and the flow starts to decelerate. Hence the mirror image of the two profiles ceases to exist. Further downstream, the flow becomes asymmetric and skewed towards the right wall (Fig. 7d). The velocity is most skewed for b = 1.0 m. With the decrease of b, the velocity profile becomes less skewed although the velocity is clearly higher near the right wall even for b = 1.0 m. In conclusion, the velocity profile as a good indicator for the development of jets and exchange of momentum is significantly influenced by the horizontal positioning of the fans and the effect of the curvature of the tunnel is also clearly shown. The velocity profile along the tunnel centerline is shown in Fig. 8a–c, for L2/d = 1.2, 1.5, 1.77, respectively, with a = 2.4 m and b = 0 m. At L = 3 m, the velocity has been little affected by the jets and the velocity profile is typical of a turbulent channel flow although it is slightly skewed towards the top. At L = 5 m, the flow velocity starts to rise sharply at the height of the fans and reaches the maximum at L = 20 m. Further downstream the jet flow slows down gradually due to the wall friction and exchange of momentum between the jets and the background flow. Even towards L = 120 m, the velocity in the top half of the tunnel is still higher than that in the bottom half. Fig. 8a and b shows a higher velocity gradient resulted near the ceiling because the fans are closer to the ceiling. Consequently a stronger shear has been resulted between the flow and the wall, which causes an increase in the wall friction. Fig. 8c shows a better velocity profile with the jets spreading further to the bottom half of the tunnel. It can be concluded that a bigger value of L2/d enables more momentum of the jet to be transmitted to the background flow and less to be dissipated due to wall friction. 3.3. Pressure field The pressure variation is very important information needed for understanding the characteristic of the flow and for calculating the pressure-rise coefficient. Detailed axial variations of the static pressure are shown in Fig. 9. Here, cross-sectional averaged static pressure is normalized using the velocity head. It can be seen that the pressure field is affected significantly by the positioning of the
Fig. 7. Velocity profiles at different axial positions for various b: (a) L = 5 m; (b) L = 10 m; (c) L = 20 m; (d) L = 60 m.
jet fans. Fig. 9a shows the axial variation of the static pressure for various values of a with b = 0 m and L2/d = 1.77. The pressure is
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Fig. 8. Central vertical velocity profiles for various L2/d: (a) L2/d = 1.2 m; (b) L2/ d = 1.5 m; (c) L2/d = 1.77 m.
minimum for all a at the location where the fan inlet is, which has clearly been resulted from the suction effect of the fans. The pressure increases rapidly at the initial stage of jets development up to L = 10 m, followed by a less rapid change which continues to around L = 40 m. Then, there is a sudden drop followed by a recovery. The drop occurs slight earlier for a = 2.8 m than others and is also the smallest. The drop occurs the latest for a = 2.0 m. This is a very interesting phenomenon which was not observed in straight tunnels (Mutama and Hall, 1996). The pressure continues to in-
Fig. 9. Axial static pressure variation: (a) various a; (b) various b; (c) various L2/d.
crease until L = 90, after which it gradually decreases. At this stage, the frictional loss offsets the momentum transfer causing a pressure decrease. The results show that the maximum pressure-rise is achieved when a = 2.8 m, i.e. the jets having the largest separation. Fig. 9b shows the pressure variation for the different values of b with a = 2.4 m and L2/d = 1.77. At the fans entrance and the early stages of the jet development, the pressure variations are very similar for the various values of b, but later (10 m < L < 35 m), a smaller b causes a faster pressure-rise. Again the abrupt changes in pressure can be observed between
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L = 35 m and L = 60 m. The pattern of change is somehow different for different values of b. The pressure rises sharply and subsequently drops and recovers for b = 1.0, 0.5 and 0 m, whereas for b = 0.5 m and b = 1.0 m there is initially a big drop in pressure followed by a significant increase, then a smaller drop and another recover. The highest pressure-rise is achieved for b = 0.5 m. The effect of L2/d on the pressure variation for a = 2.4 m and b = 0 m can be seen in Fig. 9c. There is an initial rather big drop followed by a sharp rise in pressure for L2/d = 1.77. For L2/d = 1.2, the level of the pressure ‘‘oscillation” is much smaller but the pressure drops and rises twice. In addition the overall pressure-rise towards downstream is significantly lower than in other cases. Consequently, the inflexion of pressure depends on the cross-sectional positioning of the fans. Fig. 10 shows the axial variation of the cross-sectional averaged dynamic pressure head, normalized by the jet dynamic head.
R n¼
1 2
qu2 dA At
=qU 2j
ð11Þ
where u is the velocity amplitude at a computational cell, A is its area. Fig. 10a shows the axial variation of the dynamical pressure for various values of a with b = 0 m and L2/d = 1.77. As expected, the maximum dynamic pressure occurs at the cross-section where the jets are issued. The dynamic pressure subsequently drops gradually due to the exchange of momentum of the jets with surrounding air. At around L = 40 m, the dynamical pressure reaches a minimum, then rises rapidly, and subsequently falls again. The increase occurs earliest for a = 2.8 m which corresponds to the drop of the averaged cross-sectional static pressure. Further downstream, the dynamical pressure continues to decrease with the development of jets. The same could be observed in Fig. 10b and c which shows the axial dynamical pressure variation for various values of b with a = 2.4 m and L2/d = 1.77 and for various values of L2/d with a = 2.4 m and b = 0 m, respectively. When b = 0.5 and 1.0 m, the dynamic pressure oscillates twice between L = 35 m and L = 60 m which corresponds to the change of the static pressure. Similar phenomenon exists for L2/d = 1.2 shown in Fig. 10c. In fact fans are located very near the ceiling of the tunnel, the space between fans and concave wall decrease due to the reduced width of the tunnel near top ceiling (see Fig. 2). At the downstream of the jets, the various curves converge to a single line despite the significant differences during the development stage. From the variation of the axial static pressure and the axial dynamic pressure, it can be concluded that the distance required for the pressure-rise to complete is approximately 90–120 m. Let us re-visit the perturbation of the axial development of the pressure. The basic principle of the development of a free jet can be viewed as a progressive transfer of energy from dynamic pressure to static pressure. A more complete exchange of momentum between the high-speed jet and the surrounding lower speed air will result a greater static pressure increase. In a straight tunnel, the energy transfer between the dynamic and static pressure is one-way and rather straightford. Now, with a curved highway tunnel, the energy transfer is more complicated and is non-monotonical as shown earlier. Various inflexions occur during the development of the static pressure and dynamical pressure in the curved tunnel. Fig. 11 shows a schematic drawing to explain the likely cause of the above phenomenon. As the jets expand to reach the wall, they will encounter the curved walls. When it encounters the left (convex) wall, it will form a boundary layer flow subject to an adverse pressure gradient. Near this wall, velocity decreases and pressure increases—causing the sudden static pressure increase observed earlier. On the other hand, as the jet soon approaches the right (concave) wall, the process is reversed and a local increase of velocity is induced next to the wall—hence a reduced static pressure. The detailed perturbation of
Fig. 10. Axial dynamical pressure variation: (a) various a; (b) various b; (c) various L2/d.
Fig. 11. A schematic drawing of the development of jets.
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Fig. 12. Representative cross-sectional velocity magnitude at various longitudinal locations with: a = 2.4 m, b = 0 m and L2/d = 1.77. Unit is m/s.
the axial pressure variation is dependent on when the jets reach the convex, concave walls, which is dependent on the positioning of the jets. Fig. 12 shows the velocity contours at the locations where the pressure/dynamic heads perturbate. The reduction and increase of the velocity at the top right corner of the tunnel are clearly shown. 4. Conclusions A computational study was carried out to investigate the characteristics of flows in a curved tunnel produced by jet fans located at various cross-sectional positions. Initially, before the jets reaching the wall, the development of the jets is effectively one of a free jet. The velocity of the surrounding air is gradually increased as a result of the influence of the jets. At the downstream of a curved tunnel, the jet flow is asymmetric. The asymmetry is stronger with decreasing a or increasing b. The development of the jets depends on the separation between the fans, as well as the distance between the fans and the tunnel walls. The velocity field shows that the jets spread more quickly across the cross-section when a or L2/ d is increased. It was also shown that it took longer distance for the jets to develop when the fans are closer to each other or to the tunnel wall. The variation of the static pressure and dynamical pressure is non-monotonical between the longitudinal distance L = 30 and 60 m which is unique to the curved tunnel. Because of the interaction between the jets and the convex/concave walls, a peak/weak static pressure occurs. The distance required for the pressure-rise to be completed is approximately 90–120 m and the pressure-rise coefficient is the maximum for a = 2.4 m, b = 0.5 m and L2/d = 1.77. The above understanding should prove to be useful for the design of jet fan ventilation for curved tunnels. Acknowledgement The constructive comments and suggestions made by the anonymous reviewers have significantly improved the quality of the paper. References Bari, S., Naser, J., 2005. Simulation of smoke from a burning vehicle and pollution levels caused by traffic jam in a road tunnel. Tunnelling and Underground Space Technology 20, 281–290.
Betta, Vittorio, Cascetta, Furio, Musto, Marilena, Rotondo, Giuseppe, 2009. Numerical study of the optimization of the pitch angle of an alternative jet fan in a longitudinal tunnel ventilation system. Tunnelling and Underground Space Technology 24, 164–172. Bring, Axel, Malmstrom, Tor-Goran, Boman, Carl Axel, 1997. Simulation and measurement of road tunnel ventilation. Tunnelling and Underground Space Technology 12, 417–424. Chen, T.Y., Lee, Y.T., Hsu, C.C., 1998. Investigation of piston-effect and jet fan-effect in model vehicle tunnels. Journal of Wind Engineering and Industrial Aerodynamics 73, 99–110. Chow, W.K., Chan, M.Y., 2003. Field measurement on transient carbon monoxide levels in vehicular tunnels. Building and Environment 38, 227–236. Chung, Chung-Yi, Chung, Pei-Ling, 2007. A numerical and experimental study of pollutant dispersion in a traffic tunnel. Environmental Monitoring and Assessment 130, 289–299. Hu, Cheng-Hu, Ohba, Masaaki, Yoshie, Ryuichiro, 2008. CFD modeling of unsteady cross ventilation flows using LES. Journal of Wind Engineering and Industrial Aerodynamics 96, 1692–1706. Huang, Hong, Ooka, Ryozo, Chen, Hong, et al., 2008. CFD analysis on traffic-induced air pollutant dispersion under non-isothermal condition in a complex urban area in winter. Journal of Wind Engineering and Industrial Aerodynamics 96, 1774–1788. Indrehus, Oddny, Vassbotn, Per, 2001. CO and NO2 pollution in a long two-way traffic road tunnel: investigation of NO2/NOx ratio and modeling of NO2 concentration. Journal of Environmental Monitoring 3, 220–225. Jang, Hong-Ming, Chen, Falin, 2002. On the determination of the aerodynamic coefficients of highway tunnels. Journal of Wind Engineering and Industrial Aerodynamics 90, 869–896. Chongqing Key Road Construction Office, Southwest Jiaotong University. 1998. Report of Research on Longitudinal Ventilation in a Long Road Tunnel (in Chinese). Launder, B.E., Spalding, D.B., 1974. The numerical computation of turbulent flows. Computer Methods in Applied Mechanics and Engineering 3, 269–289. Mutama, K.R., Hall, A.E., 1996. The experimental investigation of jet fan aerodynamics using wind tunnel modeling. Journal of Fluid Engineering 118, 322–328. Ohashi, H., Kawamura, T., Baba, T., 1976. A study on a longitudinal ventilation system using the enlarged jet fans. In: Proceedings of the 2nd International Symposium on the Aerodynamics and Ventilation of Vehicle Tunnels. Sambolek, Miroslav, 2004. Model testing of road tunnel ventilation in normal traffic conditions. Engineering Structures 26, 1705–1711. Solazzo, Efisio, Cai, Xiaoming, Vardoulakis, Sotiris, 2008. Modelling wind flow and vehicle-induced turbulence in urban streets. Atmospheric Environment 42, 4918–4931. Van Maele, Karim, Merci, Bart, 2008. Application of RANS and LES field simulations to predict the critical ventilation velocity in longitudinally ventilated horizontal tunnels. Fire Safety Journal 43, 598–609. Vega, Monica Galdo, Diaz, Katia Maria Arguelles, et al., 2008. Numerical 3D simulation of a longitudinal ventilation system: memorial tunnel case. Tunnelling and Underground Space Technology 23, 539–551. Vijiapurapu, Sowjanya, Cui, Jie, 2010. Performance of turbulence models for flows through rough pipes. Applied Mathematical Modelling 34, 1458–1466.
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Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Computational study of effects of jet fans on the ventilation of a highway curved tunnel Feng Wang a,b,*, Mingnian Wang a, S. He b, Jisheng Zhang b, Yuanye Deng a a b
School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China School of Engineering, University of Aberdeen, Aberdeen AB24 3UE, UK
a r t i c l e
i n f o
Article history: Received 21 June 2009 Received in revised form 20 January 2010 Accepted 1 February 2010 Available online 12 March 2010 Keywords: Curved tunnel Jet fans CFD Velocity field Pressure-rise coefficient
a b s t r a c t A computational study was carried out to investigate the aerodynamic behavior of jet fans in a curved road tunnel and its effects on the tunnel ventilation system. It has been found that the variations of the static and dynamic pressure in a curved tunnel are non-monotonic. After the issue of the jets, the pressure initially increases gradually, but this is followed by a sudden drop and then a recovery. This is attributed to the interaction between the jets and the curved walls of the tunnel. A sudden increase in pressure is resulted as the jet reaches the convex wall, whereas that the concave wall is approached causes a pressure reduction. The flow becomes asymmetrical downstream of the jets. The development of the jets depends on the separation of the fans and the distance between the fans and the tunnel walls. Increasing the space between the fans or moving them away from the tunnel ceiling makes the jets spreading more quickly across the cross-section. However, it takes a longer distance for the jets to develop when the fans are close to each other or to the tunnel wall. The distance required for pressure to be fully recovered is approximately 90–120 m in this study. The biggest pressure-rising coefficient is obtained when the fans are arranged according to the distance of 2.4 m between the fans, the fans offset of 0.5 m from the centre line towards the convex wall, and the ratio of the distance between fans and the ceiling to the diameter of fans of 1.77. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The air quality in a road tunnel would easily deteriorate if the exhaust gas emitted from the vehicles is not promptly removed, because the road tunnel is normally enclosed or partially enclosed (Chung and Chung, 2007). As a result, effective ventilation in a road tunnel is extremely important to prevent the harmful substances from affecting tunnel users and to maintain good visibility in tunnels. In long vehicle tunnels, mechanical ventilation systems are often employed to keep the amount of toxic gases below safety limits (Chung and Chung, 2007; Chen et al., 1998; Chow and Chan, 2003; Bari and Naser, 2005). Such systems are classified into longitudinal ventilation, transverse ventilation, semi-transverse ventilation and combinations of them. Among these ventilation systems the longitudinal ventilation system has been most widely adopted (Vega et al., 2008; Van Maele and Merci, 2008; Indrehus and Vassbotn, 2001; Bring et al., 1997). Because of the topographic constraint, some road tunnels have to be made curved in a horizontal plan, even with a small radius in
* Corresponding author. Address: School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China. E-mail address: [email protected] (F. Wang). 0886-7798/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2010.02.001
some cases. For example, there are two tunnels under construction in China which have a minimum curve radius of 600 m. There is clearly a need for analyzing the differences between the ventilation performance of straight tunnels and that of curved tunnels. It is of particular interest to study the performance of the jet fans which are used to provide thrust to drive the air flow inside the tunnel and to push the vehicle exhausts out of the tunnel. Many studies have been conducted on the ventilation of straight tunnel. Chen et al. (1998) used a 1/10 scale model tunnel with jet fans and exhaust pipes installed to study their effects on the distribution of the polluted air. It was shown that a higher air velocity issued by jet fans resulted in a higher exhaust concentration in the lower region of the tunnel which is detrimental to the drivers and walkers despite it brought a higher flow velocity inside the tunnel. Mutama and Hall (1996) investigated the aerodynamics of a jet fan using a wind tunnel and their results showed that the initial pressure drop would increase in a significant length of the tunnel when moving the jet fan toward the wall. Back flow was observed when the jet fan was located very close to the wall, but such a flow diminished as the jet fan was traversed toward the tunnel axis. The flow instability occurred in the region close to the wall of the tunnel when the jet fan was located at the axis. Sambolek (2004) used a 1/25 scale model of the Sv. Rok tunnel to study some important
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parameters for the design of the ventilation system and they concluded that the flow resistance coefficient was strongly influenced by the Reynolds number but only moderately influenced by the vehicle speed. The researches above mainly focus on the experimental study and many numerical studies have also recently been conducted. Chung and Chung (2007) carried out a numerical simulation to study effects of jet fans and moving vehicles on the flow field and the dispersion of gaseous pollutants in a road tunnel. The results showed that the pollutants concentration increased with the increase of downstream distance due to the effect of jet fans. And the cross-sectional concentrations of air pollutants were observed to be nearly stratified. Vega et al. (2008) carried out a computational study to analyze the fire behavior in Memorial tunnel. The results demonstrated that computational fluid dynamics (CFD) modeling is a powerful tool to predict the flow behavior under a longitudinal ventilation system in a road tunnel and the numerical results have a good agreement with previous experimental data. Jang and Chen (2002) adopted an optimization procedure to determine four major aerodynamic coefficients for the design of a road tunnel ventilation system, namely the friction coefficients of the tunnel wall, the averaged drag coefficients of small-sized and large-sized vehicles, and the pressure-rise coefficient of jet fans, based on the measurement data of the dynamic traffic and the traffic-induced wind speed. They found that the pressure-rise coefficient of jet fans was 0.56 which was almost traffic-density independent. Although extensive studies on the ventilation in straight road tunnels have been conducted as seen from the above literature review, the authors are unaware of any detailed study in curved tunnels. The main objectives of this paper are to investigate the aerodynamic behaviors of jet fans in a curved tunnel, including the characteristic of the airflow and the pressure distribution for different locations of jet fans and to establish an optimal arrangement. Recently, CFD has been widely used to solve airflow under the normal traffic condition or the emergency ventilation in road straight tunnels, which could provide detailed supplementary information to those obtained from experimental study and field measurement. In the study presented here, a 3D CFD model of a curved tunnel with embedded jet fans has been developed incorporating a standard k–e turbulent model, which has been adopted in several previous studies of similar problems. The findings from the present study are expected to be useful for designing ventilation system in curved highway tunnels.
2. Model description 2.1. Governing equations The flow in a longitudinal ventilated tunnel is assumed to be steady incompressible because the purpose here is focused on the flow behavior without consideration of the fire occasion. The commercial computational fluid dynamics software FLUENT was used to solve the continuity and the momentum equations. Recently Large Eddy Simulation (LES) has been applied to some studies of tunnel fire and the ventilation flow, but the huge computational cost prevents it being used for large scale tunnel simulations although it is capable of better predicting complicated flows (Van Maele and Merci, 2008; Hu et al., 2008). On the other hand, the Reynolds-Averaged Navier–Stokes (RANS) models offer a good compromise between result accuracy and computational cost. The research on the comparison of flow performance in a pipe with three different RANS models, namely k–e, k–x, Reynolds stress models (RSM), is found that the simulation results among the three models in the mean velocity profile and the friction factor match quite well with the experimental results and RSM consumes
more time though it can give some additional information on the shear stress correlations (Vijiapurapu and Cui, 2010). Furthermore, the standard k–e turbulent model has the advantage of being extensively used in simulation of tunnel ventilation and has been validated against the experimental data (Chung and Chung, 2007; Vega et al., 2008; Solazzo et al., 2008; Huang et al., 2008). Accordingly, the standard k–e turbulent model due to Launder and Spalding (Launder and Spalding, 1974) was adopted in this research. Additionally, second order, upwind discretization was used for convective terms and a central difference scheme was used for diffusion terms. The coupling between velocity and pressure was dealt with the SIMPLE algorithm. The governing equations solved in Fluent for the present problem can be written as: Continuity equation:
@ui ¼0 @xi
ð1Þ
Momentum equation:
@ qui uj @p @ ¼ þ @xi @xj @xj
@ðqu0i u0j Þ @u @u l iþ j þ @xj @xi @xj
ð2Þ
k equation:
uj
@k 1 @ ¼ @xj q @xj
lþ
lt @k lt @ui @uj @ui þ þ e rk @xj q @xj @xi @xj
ð3Þ
e equation: uj
@e 1 @ ¼ @xj q @xj
lþ
lt @ e C 1 lt e @ui @uj @ui e2 þ C2 ð4Þ þ re @xj q k @xj @xi @xj k
The turbulent viscosity lt:
lt ¼ C l qk2 =e where u and u0 are the mean velocity and the corresponding fluctuation component, q is the air density, l and lt are the molecular viscosity and the turbulent viscosity, k and e are the turbulent kinetic energy and its dissipation rate, The standard set of constants were adopted for the k–e equations, Cl = 0.09; C1 = 1.44; C2 = 1.92; rk = 1.0; re = 1.3. 2.2. The tunnel The present study is motivated by the need for the understanding of the aerodynamics behavior in Tiezhaizi NO I tunnel which is one of the main highway tunnels linking Chengdu with Kunming in China. It consists of two separated channels, one for each direction in one-way, two-lane traffic. One of the channels is 2778 m long and the other is 2931 m. The tunnel has a curved section of a minimum curve radius of 600 m. The longitudinal ventilation system is adopted in the curved tunnel. A numerical modeling of the tunnel, together with jet fans and exhaust pipe, was developed to investigate the effects of jet fans (Fig. 1). Ohashi et al. (1976) showed that a distance of 60–100 m was sufficient to allow the jet flow to fully develop in a straight tunnel. Accordingly, a model tunnel of 330 m length with a radius of 600 m was built here, and the length of the curved tunnel was considered to be significantly longer to ensure the development of the flow to be complete. The cross-section of the tunnel is approximately 68.55 m2 with a hydraulic diameter of Dt = 8.57 m. The model jet fans have a diameter of 0.9 m and are hung on the ceiling of the tunnel and are installed in groups of two (Fig. 2). The fans themselves were modeled by embedding a tube section in the tunnel. The jet was created by specifying a flow (see next section for detailed).
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Fig. 1. Simulation domain and mesh for jet fans region.
Fig. 2. Cross-section of highway curve tunnel.
2.3. Mesh analysis Several different mesh sizes have been tried to assess the mesh requirements, as described in the Table 1. A 0.4 m mesh in the longitudinal direction was proposed in a similar research made by Betta et al. (2009). A 0.4 m mesh in the region of jet fans inlets and outlets is thereby chosen here (Fig. 1). The horizontal axial velocity profiles and the velocity profile along the tunnel centerline on the cross-section 60 m away from the jet fan outlet in the tunnel are shown in Fig. 3a and b, respectively. The difference of the horizontal axial velocity profiles among the three mesh types is observed to be slight. However, the velocity profile along the tunnel centerline for mesh A has considerable difference from the other two mesh types. Finally mesh B was used for all the simulations because it offers an acceptable compromise between the accuracy of simulation results and computational cost. 2.4. Boundary conditions The boundary conditions are specified as follows. The non-slip stationary wall boundary condition is applied on the solid walls
Fig. 3. Velocity profiles for different mesh sizes: (a) horizontal axial velocity profiles; (b) central vertical velocity profiles.
of the tunnel and the wall of jet fans. A uniformly distributed velocity boundary is prescribed at the tunnel inlet, which produces designed ventilation velocity for the tunnel. The outflow boundary condition is used at the tunnel outlet, namely @ U=@n ¼ 0 (where U = u, k or e). The fans inlet also adopts the outflow boundary condition (Chung and Chung, 2007). The jet fans velocity Uj = 33 m/s is specified for the fan outlet according to the actual design data. In this paper, the cross-sectional locations of jet fans are varied to analyze the effect on the characteristic of the airflow (Fig. 2). The cases simulated are listed in Table 2, where a and L2 are the distance between fans and that between the ceiling and fans, and d is the diameter of the jet fans. b represents the offset of the fans from the centerline of the tunnel. The fans are symmetrically distributed for b = 0, b is positive when the fans are moved to the right (towards the concave wall) and is negative when moved to the left (towards the convex wall). 3. Results and discussion
Table 1 The mesh description.
3.1. The pressure-rise coefficient of jet fans
Mesh type
Mesh size in the longitudinal direction (m)
Mesh size on the jet fans (m)
Mesh size on the cross-section of tunnel (m)
Total cells
A B C
0.4
0.2 0.18 0.15
0.25 0.20 0.18
589,212 857,592 1,116,810
The tunnel ventilation system is designed based on the onedimensional mathematical model as follows:
Dpv þ Dpj þ Dpd Dpf Dpi ¼ qL
dv t dt
ð5Þ
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F. Wang et al. / Tunnelling and Underground Space Technology 25 (2010) 382–390 Table 2 Simulation cases. Case
L2/d
a (m)
b (m)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
1.77 1.77 1.77 1.77 1.77 1.77 1.77 1.77 1.77 1.77 1.77 1.77 1.77 1.5 1.5 1.2 1.2
2.0 2.0 2.0 2.0 2.0 2.4 2.4 2.4 2.4 2.4 2.8 2.8 2.8 2.4 2.4 2.8 2.8
1.0 0.5 0 0.5 1.0 1.0 0.5 0 0.5 1.0 0.5 0 0.5 0 0 0 0
where the different components are J X q Ac cdj ðv c v t Þjðv c v t Þj Nj 2 At j¼1 Aj vt Dpj ¼ N g q v 2j 1 At vj
Dpv ¼
ð6Þ ð7Þ
Dpd ¼ Pin Pout qL Dpf ¼ f v t jv t j 2D Dpi ¼ k
q 2
ð8Þ ð9Þ
v t jv t j
ð10Þ
where Dpv is the traffic force, Dpj is the fan thrust, Dpd is the pressure difference between the inlet and outlet portals, Dpf is the wall friction, Dpi is the local resistant caused by the flow separation at the inlet portal. Nj is the number of vehicles in group j and cdj and Ac are the corresponding effective drag coefficient of vehicles and the frontal area of vehicles, vc is the speed of vehicles, N is the number of jet fans, vj and vt are the discharging velocity of jet fans and the mean air velocity in the tunnel, Aj and At are the discharging area of jet fans and the cross-section area of the tunnel, q is the air density and g is the pressure-rise coefficient of jet fans, f and k are the friction coefficient of tunnel and the coefficient of entrance loss respectively. The relatively high mean air velocity is needed to maintain good air quality in tunnel. The traffic force and the fan thrust are the most important driving forces among them. But attention here is mainly focused on the fan thrust and the pressure-rise coefficient. From Eq. (7), we can conclude that the fan thrust only depends on the pressure-rise coefficient of jet fans g and the number of fans as the designed parameters of a tunnel and fans are got. A higher pressure-rise coefficient of jet fans can significantly decrease the number of fans and therefore reduce the investment and operating expense of the tunnel ventilation system. To validate the computational model used in this study, a simulation using the same computational method and mesh density was first carried out for a straight tunnel – Zhong Liangshan Tunnel in China for which field data are available (Key Road Construction
Fig. 4. Pressure-rise coefficient variation for various fans positions: (a) L2/d = 1.77; (b) b = 0 m.
Office, 1998). The results of the simulation were compared with the field data for pressure-rise coefficient of jet fans in Table 3. It can be seen that the prediction agrees quite well with the measurement with a difference of less than 1%. We therefore conclude that the numerical method and turbulence model used in this study are appropriate for such applications. Fig. 4a shows the variations of the pressure-rise coefficient of the jet flow as a function of the horizontal positioning (b) of the fans for several fan separations. It can be seen that the peak pressure-rise coefficient could be achieved when b = 0.5 m for any a, but the maximum can be achieved when a = 2.4 m. The pressurerise coefficient drops sharply as b moves away from 0.5 m. When b = 0 m, the maximum pressure-rise coefficient could be obtained for a = 2.8 m. Fig. 4b shows the variation of the coefficient with the vertical positions of jet fans when the fans are symmetrically placed in the tunnel. For all values of a, the coefficient increases rapidly as L2/d increases. The coefficient for a = 2.4 m overshoot that for a = 2.8 m at L2/d = 1.5 but this is reversed at L2/d = 1.77. Clearly the choice of L2/d is limited in practice.
Table 3 Comparison between field measuremental and computational results. Cross-section area of tunnel (m2)
Area of jet fans (m2)
Tunnel mean air velocity (m/s)
Jet velocity (m/s)
Field result g
Computational result g
Errors%
51.70
0.64
1.73
28.44
0.848
0.856
0.93
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Fig. 5. Velocity profiles for a = 2.4 m b = 0 m and L2/d = 1.77.
3.2. velocity profile Fig. 5 shows the horizontal axial velocity profiles at various axial location for the condition of a = 2.4 m, b = 0 m and L2/d = 1.77. L represents the axis distance from the issue of the fans in the curved tunnel. At the early stage, the velocity profile exhibits the characteristic of two free jets, and the flow away from the jets drops below initial value. That is because part of the free-stream air is entrained into the high-speed jet flows. With the diffusion and entrainment downstream, the jets spread radially and its core velocity gradually decreases. At L = 5 m, the outer edge of the jets start to interact with each other at the centerline of the tunnel where the flow speed increases rapidly. On the other hand the velocity next to the wall does not increase until much later when the jets diffuse to the tunnel walls. Then, the velocity gradually increases and overshoots the initial value. At L = 20 m, the two jets merge into a single one. The velocity subsequently decreases due to the diffusion of the jets (L = 40 m). But at L = 50 m, the velocity near the right (concave) wall rises and the velocity near the left (convex) wall falls abruptly because of the influence of the curved walls. The velocity profile continues to evolve downstream becoming very asymmetric at L = 60 m. Here, the velocity is significantly smaller than that at L = 20 m. The velocity peaks towards the right concave wall and decreases gradually toward the left. At L = 120 m, the velocity profile is an uniform flow across the core with a thin boundary layer next to the wall. Fig. 6 shows the effect of the separation of the fans on the axial velocity at several axial locations for b = 0 m and L2/d = 1.77. At the early stage, i.e. L = 5 m (Fig. 6a), the flow basically behaves as two free jets although some interactions start to show at the centerline with an increased velocity for a = 2.0 m. The velocity next to the walls remains unchanged since the development of the jets has not arrived there yet. Further downstream at L = 10 m (Fig. 6b), the velocity of the jet cores decreases rapidly but the velocity around the tunnel centerline increases significantly. The spread of the jets is much greater. The jets spread is greatest for a = 2.8 m and the tunnel centerline velocity is biggest for a = 2.0 m. Fig. 6c shows axial velocity profiles at L = 20 m. The two jets have merged completely and the peak velocity moves to the tunnel centerline for a = 2.0 m, whereas two peaks still remain in the velocity profile for a = 2.8 m. For a bigger separation, the jets diffuse more quickly to the surrounding air, which causes a higher background flow but a smaller peak at the tunnel centerline. It can also be seen that the velocity next to the right concave wall is slight higher than that next to the convex left
Fig. 6. Velocity profiles at different axial positions for various a: (a) L = 5 m; (b) L = 10 m; (c) L = 20 m; (d) L = 60 m.
wall. Such an asymmetric feature is much clearly shown in Fig. 6d (L = 60 m). The velocity profiles exhibits a peak velocity near the
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right wall and it falls gradually towards the left. The velocity profile is steep for a = 2.0 m but much gradual for a = 2.8 m. The velocity on the right of the cross-section for a = 2.0 m is higher than that for other a values but the opposite is true on the left of the cross-section. Consequently when fans are located symmetrically in the cross-section, the bigger separation can cause a decrease in the time needed for the jets to reach the wall. Fig. 7 shows the effect of the offset of the fans from the centerline on velocity profile, i.e. b = 1.0 m to b = 1.0 m. The flow exhibits the characteristic of free jets at the initial stage (Fig. 7a) for the various values of b. The shape of velocity profiles is similar and the only difference is the offset. Fig. 7b shows velocity profiles at L = 10 m. For b = 1.0 m, the development of the jets is obviously subjected to the constraint of the left wall, whereas the jets develop quite well on the right hand side of the cross-section. Similarly when b = 1.0 m, the jets are subjected to the constraint of the right wall and is well-developed on the left. Those two profiles are effectively mirror images to each other. Consequently, the curvature of the tunnel has no influence at this stage. Further downstream, however, the influence of the curvature can be clearly seen, see for example Fig. 7c for L = 20 m. It can be seen that the flow velocity next to right wall for b = 0.5 m and b = 1.0 m is significant higher than that next to the left wall for b = 0.5 m and b = 1.0 m. For b = 0 m, the velocity next to right wall is also bigger than that next to the left wall. The reason is clear: as the jet flow reaches the right (concave) wall, it is subjected to a favorable pressure gradient and starts to accelerate. On the other hand, as flow reaches to the left (convex) wall, it is subject to an adverse pressure gradient and the flow starts to decelerate. Hence the mirror image of the two profiles ceases to exist. Further downstream, the flow becomes asymmetric and skewed towards the right wall (Fig. 7d). The velocity is most skewed for b = 1.0 m. With the decrease of b, the velocity profile becomes less skewed although the velocity is clearly higher near the right wall even for b = 1.0 m. In conclusion, the velocity profile as a good indicator for the development of jets and exchange of momentum is significantly influenced by the horizontal positioning of the fans and the effect of the curvature of the tunnel is also clearly shown. The velocity profile along the tunnel centerline is shown in Fig. 8a–c, for L2/d = 1.2, 1.5, 1.77, respectively, with a = 2.4 m and b = 0 m. At L = 3 m, the velocity has been little affected by the jets and the velocity profile is typical of a turbulent channel flow although it is slightly skewed towards the top. At L = 5 m, the flow velocity starts to rise sharply at the height of the fans and reaches the maximum at L = 20 m. Further downstream the jet flow slows down gradually due to the wall friction and exchange of momentum between the jets and the background flow. Even towards L = 120 m, the velocity in the top half of the tunnel is still higher than that in the bottom half. Fig. 8a and b shows a higher velocity gradient resulted near the ceiling because the fans are closer to the ceiling. Consequently a stronger shear has been resulted between the flow and the wall, which causes an increase in the wall friction. Fig. 8c shows a better velocity profile with the jets spreading further to the bottom half of the tunnel. It can be concluded that a bigger value of L2/d enables more momentum of the jet to be transmitted to the background flow and less to be dissipated due to wall friction. 3.3. Pressure field The pressure variation is very important information needed for understanding the characteristic of the flow and for calculating the pressure-rise coefficient. Detailed axial variations of the static pressure are shown in Fig. 9. Here, cross-sectional averaged static pressure is normalized using the velocity head. It can be seen that the pressure field is affected significantly by the positioning of the
Fig. 7. Velocity profiles at different axial positions for various b: (a) L = 5 m; (b) L = 10 m; (c) L = 20 m; (d) L = 60 m.
jet fans. Fig. 9a shows the axial variation of the static pressure for various values of a with b = 0 m and L2/d = 1.77. The pressure is
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Fig. 8. Central vertical velocity profiles for various L2/d: (a) L2/d = 1.2 m; (b) L2/ d = 1.5 m; (c) L2/d = 1.77 m.
minimum for all a at the location where the fan inlet is, which has clearly been resulted from the suction effect of the fans. The pressure increases rapidly at the initial stage of jets development up to L = 10 m, followed by a less rapid change which continues to around L = 40 m. Then, there is a sudden drop followed by a recovery. The drop occurs slight earlier for a = 2.8 m than others and is also the smallest. The drop occurs the latest for a = 2.0 m. This is a very interesting phenomenon which was not observed in straight tunnels (Mutama and Hall, 1996). The pressure continues to in-
Fig. 9. Axial static pressure variation: (a) various a; (b) various b; (c) various L2/d.
crease until L = 90, after which it gradually decreases. At this stage, the frictional loss offsets the momentum transfer causing a pressure decrease. The results show that the maximum pressure-rise is achieved when a = 2.8 m, i.e. the jets having the largest separation. Fig. 9b shows the pressure variation for the different values of b with a = 2.4 m and L2/d = 1.77. At the fans entrance and the early stages of the jet development, the pressure variations are very similar for the various values of b, but later (10 m < L < 35 m), a smaller b causes a faster pressure-rise. Again the abrupt changes in pressure can be observed between
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L = 35 m and L = 60 m. The pattern of change is somehow different for different values of b. The pressure rises sharply and subsequently drops and recovers for b = 1.0, 0.5 and 0 m, whereas for b = 0.5 m and b = 1.0 m there is initially a big drop in pressure followed by a significant increase, then a smaller drop and another recover. The highest pressure-rise is achieved for b = 0.5 m. The effect of L2/d on the pressure variation for a = 2.4 m and b = 0 m can be seen in Fig. 9c. There is an initial rather big drop followed by a sharp rise in pressure for L2/d = 1.77. For L2/d = 1.2, the level of the pressure ‘‘oscillation” is much smaller but the pressure drops and rises twice. In addition the overall pressure-rise towards downstream is significantly lower than in other cases. Consequently, the inflexion of pressure depends on the cross-sectional positioning of the fans. Fig. 10 shows the axial variation of the cross-sectional averaged dynamic pressure head, normalized by the jet dynamic head.
R n¼
1 2
qu2 dA At
=qU 2j
ð11Þ
where u is the velocity amplitude at a computational cell, A is its area. Fig. 10a shows the axial variation of the dynamical pressure for various values of a with b = 0 m and L2/d = 1.77. As expected, the maximum dynamic pressure occurs at the cross-section where the jets are issued. The dynamic pressure subsequently drops gradually due to the exchange of momentum of the jets with surrounding air. At around L = 40 m, the dynamical pressure reaches a minimum, then rises rapidly, and subsequently falls again. The increase occurs earliest for a = 2.8 m which corresponds to the drop of the averaged cross-sectional static pressure. Further downstream, the dynamical pressure continues to decrease with the development of jets. The same could be observed in Fig. 10b and c which shows the axial dynamical pressure variation for various values of b with a = 2.4 m and L2/d = 1.77 and for various values of L2/d with a = 2.4 m and b = 0 m, respectively. When b = 0.5 and 1.0 m, the dynamic pressure oscillates twice between L = 35 m and L = 60 m which corresponds to the change of the static pressure. Similar phenomenon exists for L2/d = 1.2 shown in Fig. 10c. In fact fans are located very near the ceiling of the tunnel, the space between fans and concave wall decrease due to the reduced width of the tunnel near top ceiling (see Fig. 2). At the downstream of the jets, the various curves converge to a single line despite the significant differences during the development stage. From the variation of the axial static pressure and the axial dynamic pressure, it can be concluded that the distance required for the pressure-rise to complete is approximately 90–120 m. Let us re-visit the perturbation of the axial development of the pressure. The basic principle of the development of a free jet can be viewed as a progressive transfer of energy from dynamic pressure to static pressure. A more complete exchange of momentum between the high-speed jet and the surrounding lower speed air will result a greater static pressure increase. In a straight tunnel, the energy transfer between the dynamic and static pressure is one-way and rather straightford. Now, with a curved highway tunnel, the energy transfer is more complicated and is non-monotonical as shown earlier. Various inflexions occur during the development of the static pressure and dynamical pressure in the curved tunnel. Fig. 11 shows a schematic drawing to explain the likely cause of the above phenomenon. As the jets expand to reach the wall, they will encounter the curved walls. When it encounters the left (convex) wall, it will form a boundary layer flow subject to an adverse pressure gradient. Near this wall, velocity decreases and pressure increases—causing the sudden static pressure increase observed earlier. On the other hand, as the jet soon approaches the right (concave) wall, the process is reversed and a local increase of velocity is induced next to the wall—hence a reduced static pressure. The detailed perturbation of
Fig. 10. Axial dynamical pressure variation: (a) various a; (b) various b; (c) various L2/d.
Fig. 11. A schematic drawing of the development of jets.
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Fig. 12. Representative cross-sectional velocity magnitude at various longitudinal locations with: a = 2.4 m, b = 0 m and L2/d = 1.77. Unit is m/s.
the axial pressure variation is dependent on when the jets reach the convex, concave walls, which is dependent on the positioning of the jets. Fig. 12 shows the velocity contours at the locations where the pressure/dynamic heads perturbate. The reduction and increase of the velocity at the top right corner of the tunnel are clearly shown. 4. Conclusions A computational study was carried out to investigate the characteristics of flows in a curved tunnel produced by jet fans located at various cross-sectional positions. Initially, before the jets reaching the wall, the development of the jets is effectively one of a free jet. The velocity of the surrounding air is gradually increased as a result of the influence of the jets. At the downstream of a curved tunnel, the jet flow is asymmetric. The asymmetry is stronger with decreasing a or increasing b. The development of the jets depends on the separation between the fans, as well as the distance between the fans and the tunnel walls. The velocity field shows that the jets spread more quickly across the cross-section when a or L2/ d is increased. It was also shown that it took longer distance for the jets to develop when the fans are closer to each other or to the tunnel wall. The variation of the static pressure and dynamical pressure is non-monotonical between the longitudinal distance L = 30 and 60 m which is unique to the curved tunnel. Because of the interaction between the jets and the convex/concave walls, a peak/weak static pressure occurs. The distance required for the pressure-rise to be completed is approximately 90–120 m and the pressure-rise coefficient is the maximum for a = 2.4 m, b = 0.5 m and L2/d = 1.77. The above understanding should prove to be useful for the design of jet fan ventilation for curved tunnels. Acknowledgement The constructive comments and suggestions made by the anonymous reviewers have significantly improved the quality of the paper. References Bari, S., Naser, J., 2005. Simulation of smoke from a burning vehicle and pollution levels caused by traffic jam in a road tunnel. Tunnelling and Underground Space Technology 20, 281–290.
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