Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 1329187, 13 pages
https://doi.org/10.1155/2018/1329187

Research Article

Numerical Investigation of Particle Concentration Distribution Characteristics in Twin-Tunnel Complementary Ventilation System

Rui Ren,¹ Shuoshuo Xu,¹ Zhaodan Ren,² Shuangzhuo Zhang,² Hao Wang,³ Xiuling Wang,¹ and Siyue He¹

¹School of Highway, Chang’an University, Xi’an 710064, China
²China Railway Siyuan Survey and Design Group Co., Ltd, Wu’han 430063, China
³School of Civil & Construction Engineering, Oregon State University, 101 Kearney Hall, Corvallis, OR 97331, USA

Correspondence should be addressed to Xiuling Wang; wangxiuling@chd.edu.cn

Received 6 January 2018; Revised 2 June 2018; Accepted 20 June 2018; Published 12 July 2018

Academic Editor: Babak Shotorban

Copyright © 2018 Rui Ren et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

Longitudinal ventilation systems are commonly installed in new tunnels. In this paper, based on the similarity law, the scale model with a view to different conditions is carried out to study the effectiveness of twin-tunnel complementary ventilation system. The system can offer enough amount of fresh air to meet requirement of driving safety by using longitudinal ventilation without ventilation shaft. Field measurements were also performed to validate the numerical model. Results reveal that particle concentration distribution is influenced by the distance from air interchange cross-passages to uphill tunnel inlet () and the flow volume of air interchange cross () passage and jet fan thrust () in tunnel. And is the most important factor about influencing the ventilation efficiency.

1. Introduction

To provide sufficient fresh air and dilute toxic gases from vehicles, mechanical ventilation systems with jet fans or shafts are often employed [1, 2]; however ventilation shafts need high energy consumption ventilation equipment such as jet fans. This paper introduced a relatively novel ventilation system, namely, twin-tunnel complementary ventilation system. The system has two-air interchange cross-passages between uphill tunnel and downhill tunnel which can meet the requirement of fresh air in tunnel. Compared with traditional ventilation system, the twin-tunnel complementary ventilation system is a relatively innovative method, which has a number of advantages including low consumption of energy and construction, multiplexing, more reasonable distribution of pollutant concentration, and good visibility.

Ventilation of resident buildings plays an important role in providing better indoor air quality (IAQ) and thermal comfort [3–7]. Many simulations and field tests have been conducted about building ventilation [8, 9]. In recent years, the construction of tunnels has developed rapidly in China [10–20] and a lot of difficult problems have been solved [21–30]. Ventilation of tunnels plays an important role in reducing the emission of toxic gas, maintaining good visibility, and controlling the fire in tunnels [31–33]. The mechanical ventilation can be performed with three approaches: longitudinal, transverse [34, 35], semitransverse [36, 37]. Among these ventilation systems, longitudinal ventilation system equipped with jet fans has been most widely adopted owing to effective utilization of the piston wind [38]. In the last decades, many scholars have done much research on the mechanical ventilation system of long tunnels. Bogdan. S et al. [39] proved that appropriate number of jet fans is the important factor to reach desirable air quality in longitudinal ventilation system. Wang et al. [40, 41] investigated the aerodynamic behavior of jet fans in a curved road tunnel and its effects of deflected angles of jet fans on the tunnel ventilation system. The pollution concentration increases along the tunnel in the airflow direction with longitudinal ventilation system. In order to increase the need for effective ventilation for removing toxic gases emitted by vehicles from the tunnels especially during traffic jams, Bari et al. [42] studied the ventilation effectiveness of the Banana jet fan. Comparing the performance of longitudinal ventilation systems for road tunnel equipped with alternative jet fans and traditional jet fans in case of fire, Musto and Rotondo [43] presented the results that longitudinal ventilation system equipped with alternative jet fan require lower total thrust with respect to traditional jet fans to prevent back-layering. Kazemipour, Afshin, and Farhanieh [44] investigated the influence of longitudinal jet fan location relative to fire and its vertical position. They showed that the jet fan performance degraded because jet fan air flow spread would attack the rising smoke plume and lead to dynamic losses; then its actual thrust increased with lowering the jet fan installation height. Lee, Ryou [45], and Tang et al. [46, 47] performed the influence of smoke movement in a longitudinal ventilated tunnel fires. In short tunnels, the nature ventilation and the piston effect of moving vehicles are usually sufficient to drive fresh air in and discharge polluted air out [48, 49]. However, in long vehicle tunnels, the mechanical ventilation system is required to dilute toxic gases emitted by vehicles [50–53]. And because of the topographic constraint, in some large single-slope double-line tunnels, the particle emissions in uphill tunnel are larger than in downhill tunnel. If the longitudinal ventilation with jet fans is adopted in the single-slope twin-tunnels, the airflow requirements cannot be fulfilled due to high wind speeds in the uphill tunnel and only smaller amounts of air are needed in downhill tunnel to ensure air quality and visibility thresholds. Traditionally, a shaft or inclined shaft is used as the ventilation in tunnels for air exchange [54–57], which bring about increase of ventilation system initial investment and operation energy consumption. To solve the imbalance of ventilation requirement between uphill tunnel and downhill tunnel, Bemer and Day (1991) [58] proposed the concept of “twin-tunnel complementary” ventilation for the first time, which considers the tunnel as a single unit rather than as two separated tunnels. The concept came into practice for the first time in Ping-Lin tunnel in Taiwan, and the investment and operation cost of the tunnel reduced largely [59]. From then on, several studies have been performed in order to better understand the system [60–65].

In this paper, CFD simulations were conducted under different conditions (AIAA, 1998) [66]. More specifically, experimental measurement was carried out to validate the results of a three-dimensional numerical model. The aim of study is to reveal the distribution of pollution concentration in twin-tunnel complementary ventilation system. The results can help engineers to better understand the effect on the pollution concentration adjustment between uphill tunnel and downhill tunnel, to design an effective ventilation system for double-line tunnel.

2. Complementary Ventilation System

2.1. Engineering Overview

A substantial number of tunnel projects have been constructed in complex geological area as western development strategies have been implemented in China [25, 67–71]. The purpose of the present study is to understand the effect of the twin-tunnel complementary ventilation system on the distribution of pollutants in Dabieshan tunnel which is one of the main highway tunnels linking Wuhan with Macheng. The tunnel consists of two separated tunnels with large single-slope whose direction is one-way. The uphill tunnel is 4910 m with slope of 4% and the downhill tunnel is 4908 m with slope of -4%, show in Figure 1. The tunnel cross-section is 62.8 m² and the maximum width and the height of the tunnel cross-section are 11.2 m and 7.5 m, respectively. When the vehicle speed reaches 50km/h, the requirement for fresh air volume of the uphill tunnel () and downhill tunnel () is 460m³/s and 95m³/s respectively, and the air velocity of and is 7.35m/s and 1.5m/s, respectively. Due to high wind speeds in the uphill tunnel, airflow requirements cannot be fulfilled, so the tunnel needs a shaft or inclined shaft in the uphill tunnel for air exchange. However, the average airflow requirements of uphill tunnel and downhill tunnel is only 277.5m³/s and the average air velocity of the twin-tunnel is only 4.42 m/s, and then the twin-tunnel complementary ventilation system was employed.

Figure 1: Dabieshan Tunnel.

The twin-tunnel complementary ventilation system has two-air interchange cross-passages to connect the two tunnels, which divide the tunnels into 6 sections, and the distance between two-air interchange cross-passages is 100m, far less than the length of tunnel. Section 1, section 2, and section 3 are in uphill tunnel and section 4, section 5, and section 6 are in downhill tunnel, as shown in Figure 2. The high concentrated polluted air in section 1 passes through 1# air interchange cross-passage into section 6, a part of the pollutants in section 1 will be transferred to section 6, and the total amount of transferred pollutants is . Combing with transferred pollutants, the pollutions in section 6 discharges through the downhill tunnel outlet, and the particle concentration of downhill tunnel is . The low concentrate polluted air in section 4 through the 2# air interchange cross-passage into the section 3, a part of the pollutants in section 4 will be transferred to the section 3, and the total amount of transferred pollutants is . Combing with transferred pollutants, the pollutions in section 3 discharges through the uphill tunnel outlet, and the particle concentration of uphill tunnel outlet is . The particle concentration ratio of uphill tunnel and downhill tunnel is index, which is used to evaluate the efficiency of adjusting the particle concentration distribute in uphill tunnel and downhill tunnel by twin-tunnel complementary ventilation. When , the efficiency of adjusting achieves the best result, and when the , the adjusting is excessed.

Figure 2: Twin-tunnel complementary ventilation system.

Where and are the fresh air requirement volume in the uphill tunnel and the downhill tunnel, respectively, and are the amount of particle emission from the cars in the uphill tunnel and the downhill tunnel, respectively, is the distance from the air interchange cross-passages to uphill tunnel inlet, is the flow volume of air interchange cross-passage, is jet fan thrust in tunnel, and is the length of tunnel.

2.2. Methodology

Field measurement was carried out to reveal the characteristics of air flow and particle concentration distribution in the twin-tunnels with twin-tunnel complementary ventilation system. There are a total of eight cross-sections to be tested as shown in Figure 3. A hot wire anemometer which has a resolution of 0.01 m/s was employed to test the air velocity, and Light transmittance instrument which has resolution of 0.0001/m was used to measure the particle concentration by testing the extinction coefficient in 100 m range. Testing preparation and testing process is shown in Figure 4. The cross-section of the base tunnel (cross-sections I-I, II-II, III-III, IV-IV, V-V, and VI-VI) is divided into fourteen parts and the cross-section of the cross-passage (cross-sections VII-VII and VIII-VIII) is divided into nine parts, as shown in Figure 3. The air velocity and particle concentration at the centroid of each part were recorded for 10min at 1min intervals. All the air velocity and particle concentration records of each part were averaged to and separately. Hence, the average air velocity and particle concentration of the cross-section can be calculated as (1)~(2):

where (1) for base tunnel and (2) for cross-passage and is the area of part in the cross-section.

Figure 3: Field measurement scheme: (a) the location of monitored cross-sections, (b) detail of the cross-sections VII-VII and VIII-VIII, and (c) detail of the cross-sections I-I, II-II, III-III, IV-IV, V-V, and VI-VI.

(a)

(b)

Figure 4: Field measurement: (a) testing preparation in 2# air interchange cross-passage and (b) testing progress in tunnel.

3. Numerical Methodology

3.1. Governing Equations

The computational fluid dynamics (CFD) software ANSYS Fluent (15.0) was used to simulate the flow field and pollution transport of the twin-tunnel complementary ventilation system. Fluent software has been applied to solve 3-D continuity, momentum, turbulence kinetic energy, turbulence energy dissipation rate, and pollutant transport equations in steady and incompressible condition. A standard - turbulence model and simple algorithm are used for the model. The governing equations are

Here is Reynolds averaged velocity vector, is the density, is the kinetic viscosity, is the eddy viscosity, is gravity acceleration, is pressure, is turbulence kinetic energy, and are the turbulent kinetic energy dissipation rate, is the concentration of the pollutant in the domain, is the pollutant source term, and is the scalar diffusion coefficient. The constants in the model are ,  ,  ,  , and  . To simplify the model, the amount of particle emitted from vehicle in tunnel was considered as the pollutant source whose distribution is continuous and uniform in tunnel longitudinal direction, which was based on assuming that the rate of particulate matter emitted from vehicle per second is stable and the vehicle passes through the tunnel at constant speed.

3.2. CFD Simulation Model of the Twin-Tunnel Complementary Ventilation System

The tunnel investigated is a twin-tunnel tunnel, the uphill tunnel length is 4910m, and the downhill tunnel length is 4908m. To reduce the element number of model and reduce the computation cost and achieve an accurate solution, the reduced scale numerical simulation model was obtained from the full scale one by means of Euler scaling method, which preserves geometrical, kinematic and dynamic similitude, and similarities of the initial and boundary condition.

In the reduced scale numerical simulation model, the shape was similarity to the full scale model, the cross-sectional scaling ratio of 1/1 (8), and thus the length-scaling ratio of section 2 and section 5 is also 1/1 (9), but the length-scaling ratio of section 1, section 3, section 4, and section 6 is 1/6 (10) to reduce the length of the numerical simulation model and reduce the element number, because the airflow velocity field is uniform distributed in the longitudinal direction in these sections.

where L is the length, D is the equivalent diameter, and the subscripts and indicate the full scale tunnel and reduced scale numerical simulation model of tunnel, respectively.

Euler scaling method is based on the Euler number preservation and the Euler number is defined as

where is the pressure losses due to boundary layer resistance of the sections in the tunnel.

During the process of researching fluid motion, fluid flow of both the reduced scale numerical simulation model and full scale model must be kinematical similarity and dynamic similarity; thus, the velocity of each section in the reduced scale numerical simulation model should be as same as them in the full scale model and the velocity is scaled as

According to Euler scaling method, in which the Euler number of each section in full scale model and the Euler number of the corresponding section in reduced scale numerical simulation model are equal, the scaling factor for the pressure losses can be calculated as

from which the pressure loss scaling factor is

where is the pressure losses of each section in full scale model and is the pressure losses of the corresponding section in reduced scale numerical simulation model, which can be obtained by the following expression:

where is friction loss factors of sections in full scale model and the is equivalent friction loss factions of sections in reduced scale numerical simulation model.

Introducing (10), (15), and (16) into (14), then the final function relation among the equivalent friction loss factors of reduced scale numerical simulation model () and friction loss factors of full scale model () in section 1, section 3, section 4, and section 6 is as follows:

Introducing (9), (15), and (16) into (14), then the final function relation among the equivalent friction loss factors of reduced scale numerical simulation model () and friction loss factors of full scale model () in section 2, section 5 is as follows:

According to “Guidelines for Design of Ventilation of Highway Tunnels” (2014) [72], the friction loss faction of tunnel , so the equivalent friction loss factions of section 1, section3, section 4, and section 6 in the reduced scale numerical simulation model are 6 times the friction loss factions in full scales model, respectively, and the equivalent friction loss factions of section 2 and section5 in the reduced scale numerical simulation model are as same as the friction loss factions in the full scales model, respectively, which is shown as follows:

In the reduced scale numerical simulation model investigated, the equivalent friction loss factions    should satisfy (19), in order to preserve the flow in which each section was similar to the flow in corresponding section in the full scale tunnel, respectively. Based on this method, the different scaling ratios did not affect the simulation results.

The reduced scale of twin-tunnel complementary ventilation system to be modeled consists of twin parallel tunnels with the length 900m including 100m section 2 and 100 m section 5, width 12m and height 8m, and the connecting transverse ducts with the width 5 m and height 6.35 m. For grid generation process, a multizone grid approach was applied. Structured mesh was used over the entire computational domain except for air interchange cross-passage zones. Unstructured mesh was applied for air interchange cross-passage zones. Independence mesh tests were carried out with four different mesh sizes to achieve optimal grid for the computational domain. The mesh sizes analyzed were shown in Table 1. The mesh analysis carried out the velocity profile along the tunnel center line on the cross-section 50m away from each air interchange passage outlet in the tunnel shown in Figure 5. The velocity profile along the tunnel center line for mesh A has considerable difference from the other two mesh types. Finally mesh C was used for all the simulations in order to achieve acceptable computational time and numerical accuracy. Figure 6 shows the meshing details of the numerical model which has 583586 elements.

Table 1: Mesh types and sizes.

Mesh
Mesh size in the longitudinal direction(m)
Mesh size on the cross-section of tunnel(m)
Total cells

A
2
1
121937

B
1.5
0.8
296037

C
1
0.5
583586

D
0.5
0.5
813981

Figure 5: Mesh analysis.

Figure 6: Geometry and meshing of the numerical model.

3.3. Boundary Condition

The no-slip stationary wall boundary condition was used for solid walls of the tunnel and the connecting ducts, the inlet, and outlet gage pressure boundary condition (, ) were set for all surrounding open surfaces of inlet block and outlet block. The total amount of particle emission from the vehicles in uphill tunnel is 1.843m³/s, and the total amount of particle emission from the vehicles in downhill tunnel is 0.442m³/s. To simulate the airflow in fan located in the tow interchange air cross-passages, a constant velocity was specified on a specific zone located in the air interchange cross-passages. In other words, there is a volume at the middle of air interchange cross-passages whose velocity is fixed so the air is sucked from the fan inlet and exited from the outlet. In this paper, the volume flow rate of the air interchange cross-passage and distance from tow interchange air cross-passage to uphill tunnel inlet and the jet fan thrust in twin-tunnel are varied to analyze the effect on the characteristic of pollution concentration distribution. In the simulation of different conditions, there are 6 levels of adopted, 2400m, 2880m, 3120m, 3360m, 3600m, and 3840m. There are 6 levels of and 5 levels of . The levels of factors in number simulation are listed in Table 2.

Table 2: The levels of factors in number simulation.

Factor
Levers of factor

1
2
3
4
5
6

(m)
2400
2880
3120
3360
3600
3840

(m³/s)
125
150
175
200
225
250

(Pa)
75
100
125
150
175
—

3.4. Validation

For validation of the computational model, the experimental measurement data of Dabieshan tunnel ventilation system in section 2.1 is used. In the tunnel ventilation, according to (1), the average air velocity by field measurement in 1# air interchange cross-passages and 2# air interchange cross-passages is 2.55 m/s, and the volume flow rate of air interchange cross-passage () is 87.5m³/s, where is the section area of air interchange passage of 34.5m². In the natural ventilation, the natural wind velocity is tested by field measurement and found be 1.9m/s in the uphill tunnel and 2.1m/s in downhill tunnel, and the natural wind pressure is calculated as 25Pa and 35Pa in the uphill tunnel and downhill tunnel, respectively. The particle emitted from the smoke generating compositions has average value of 0.8651m²/s and 0.7820m²/s in uphill tunnel and downhill tunnel, respectively. The value is calculated by multiplying the amount of fresh air introduced to the tunnel and the average particle concentration in the cross-section nearing the tunnel exit, in the natural ventilation. Figure 7 shows the correlation of the average air velocity of each part in a cross-section between the CFD model and the field measurement. It can be seen that, in testing sections I-I, III-III, IV-IV, and VI-VI, the air velocities obtained by the CFD model fit the field measurement well and the R² coefficients are 0.9556, 0.9743, 0.948, and 0.9616, respectively. In testing sections II-II and V-V, the air flow is affected greatly by the dividing, the air velocity of each part has a wide range of variation, and the coefficients are 0.9297 and 0.9323. In VII-VII and VIII-VIII, the air flow is affected greatly by the confluence and the turbulence, the air velocities obtained by the CFD model fit the field measurement well and the coefficients are 0.9231 and 0.9289. Figure 8 shows the correlation of of the cross-section between the CFD model and the field measurement. There is a good correlation of between the CFD model and field measurement, and the coefficient is 0.9087.

Figure 7: Correlation of average air velocities between CFD value and field measurement.

Figure 8: Correlation of average particle concentration between CFD value and field measurement.

4. The Numerical Simulation Results and Analysis

4.1. Comparison between the Twin-Tunnel Complementary Ventilation and Longitudinal Ventilation

The performance of the twin-tunnel complementary ventilation and longitudinal ventilation in same traffic condition was investigated. The fresh air introduced to the twin-tunnel by each type of ventilation system is equal, the simulation case is listed in Table 3. Figure 9 shows the result of comparing the particle concentration at horizontal plane (y = 1.5m) for the cases of twin-tunnel complementary ventilation and longitudinal ventilation. For the passengers sitting in their personal cars, the head level is at the height of about 1.5 m above the road. As Figure 9 shows, in the twin-tunnel with longitudinal ventilation, and are 0.00591 and 0.00144, respectively, but exceeded the safety limits for particle concentration. In the twin-tunnel with twin-tunnel complementary ventilation, the high concentration pollution air in uphill tunnel passes through 1# air interchange cross-passage into the downhill tunnel, where parts of the pollutants in uphill tunnel were transferred to the downhill tunnel and exhaust through the downhill tunnel outlet and increased to 0.00407 m⁻¹. The low concentration pollution air in downhill tunnel passes through 2# air interchange cross-passage into the uphill tunnel, where parts of the fresh air in downhill tunnel were transferred to the uphill tunnel and dilute pollutant concentration in uphill tunnel and exhaust pass through the uphill tunnel outlet, the reduced to 0.00368 m⁻¹. Thus the twin-tunnel complementary ventilation achieves the effect of adjusting the particle concentration distribution in uphill tunnel and downhill tunnel.

Table 3: Simulation case.

Ventilation system
Fresh air volume(m³/s)

(m³/s)

(Pa)

(m)

Uphill tunnel
Downhill tunnel

Twin-tunnel complementary ventilation
300
300
200
125
3360

Longitudinal ventilation
300
300
0
169
NO

Figure 9: Particle concentration contours (m⁻¹) at horizontal planes y = 1.5m for tunnel with twin-tunnel complementary ventilation, (a) there is flow in air interchange cross-passages, and (b) there is no flow in air interchange cross-passages.

4.2. The Relationship of the Air Interchange Cross-Passages Position and Particle Concentration Profiles

Figure 10 shows that when the interchange air volume is constant, the particle concentration of uphill tunnel outlet is decreased with the increasing of , which is the distance from uphill tunnel inlet to air interchange cross-passage, and the particle concentration of downhill tunnel outlet is increased with the increasing of , and particle concentration ratio of uphill tunnel outlet and downhill tunnel outlet is decreased following the increasing of ; when , the efficiency achieves the best result, and when , the adjusting is excessed. Using of 200m³/s and of 125 Pa as examples, when is 2400m, is 0.00472, is 0.00306, and is 1.54. When is increased to 3840m, is decreased by 33.26%, is increased by 49.34%, and is decreased by 55.2%. The amount of particles transferred from uphill tunnel to downhill tunnel through 1# air interchange cross-passage increased with the increasing of , which leads to the increase of the amount of particles in downhill tunnel outlet. Meanwhile, the amount of relatively fresh air transferred from downhill tunnel to uphill tunnel through 2# air interchange air cross-passage increased with the increasing of , which leads to decrease of the amount of particles in uphill tunnel outlet; so is decreased.

(a)

(b)

(c)

Figure 10: Particle concentration profiles variation for various air interchange cross-passages positions: (a) the particle concentration in uphill tunnel outlet, (b) the particle concentration in uphill tunnel outlet, and (c) the particle concentration ratio of uphill tunnel outlet and downhill tunnel outlet.

To further analyze the relation between and , when and are same () (shown as Figure 10(c)), the interchange air volume is decreased following the increasing of distance . This indicates that the increase of can reduce in twin-tunnel complementary ventilation design.

4.3. The Relationship of the Interchanged Air Volume and Particle Concentration Profiles

Figure 11 shows that and the are decreased following the increasing of or . When is constant, is decreased following the increasing of ; however, when is constant, is increased following the increasing of . Section 4.2 discusses the relation between and . Using of 3360 m and of 175 Pa as example, when the interchange air volume increases from 150 m³/s to 275 m³/s, decreases by 26.19%, decreases by 4.34%, and decreases by 30.5%. Using of 3360m and the fan thrust of 125 Pa as example, when the interchange air volume increases from 150 m³/s to 275 m³/s, decreases by 40.6%, decreases by 12%, and decreased by 32.5%. It can be seen that the influence of on is greater than that of and the influence degree of is decreased with the increasing of . On the other hand, using of 175 m³/s as example, when the jet fan thrust increases from 25 Pa to 175 Pa, decreases by 9.46%, decreases by 47.85%, and increases by 73.6%. It can be seen that the influence of on the is less than that of . To further analyze the relation between and , when and are the same () (shown as Figure 11(c)), the jet fan thrust is increased following the increasing of interchanged air volume .

(a)

(b)

(c)

Figure 11: Particle concentration profiles variation for various interchanged air volume: (a) the particle concentration in uphill tunnel outlet, (b) the particle concentration in uphill tunnel outlet, and (c) the particle concentration ratio of uphill tunnel outlet and downhill tunnel outlet.

4.4. Orthogonal Analysis of the Ventilation Parameters

As discussed above, the parameters, including the distance between uphill tunnel inlet to air interchange cross-passage and the volume flow rate of the air interchange cross-passage and jet fan thrust , have influence on the efficiency of adjusting the particle concentration distribution in uphill tunnel and downhill tunnel by twin-tunnel complementary ventilation. The orthogonal method experimental design is used to explore the influence degree of every factor, and the result is used to optimize the twin-tunnel complementary ventilation system design. Based on consideration of the prototype, four levels for each factor are determined in this study. The factors and levels are shown in Table 4. Considering accuracy of the test and total number of test, an orthogonal table of (4⁵) is determined for the problem with three factors and four levels for each factor, as shown in Table 5. A, B, and C indicate the factors of , , and . The vacant columns without factors and interaction are used for error analysis. Observed variables of the test results are simulation results of the efficiency of adjusting the particle concentration distributed in twin-tunnel of levels of three factors, as shown in Table 5.

Table 4: Factors and levels of orthogonal experiment.

Factor
Levers of factor

1
2
3
4
5

A
(m³/s)
150
175
200
225
250

B
(m)
2880
3120
3360
3600
3840

C
(Pa)
75
100
125
150
175

Table 5: Orthogonal table and test results.

Factor

NO.
A
D
B
E
C

1
175
1
312
1
100
1.045

2
175
2
336
2
125
0.992

3
175
3
360
3
150
0.945

4
175
4
384
4
175
0.902

5
200
1
336
3
175
1.019

6
200
2
312
4
150
1.093

7
200
3
384
1
125
0.690

8
200
4
360
2
100
0.730

9
225
1
360
4
125
0.727

10
225
2
384
3
100
0.579

11
225
3
312
2
175
1.065

12
225
4
336
1
150
0.888

13
250
1
384
2
150
0.622

14
250
2
360
1
175
0.761

15
250
3
336
4
100
0.744

16
250
4
312
3
125
0.913

K₁
3.884
3.413
4.116
3.384
3.098
T = 13.715

K₂
3.532
3.425
3.643
3.409
3.322
Q = 12.164

K₃
3.260
3.444
3.162
3.456
3.548
P = 11.757

K₄
3.040
3.433
2.794
3.466
3.747

R
0.844
0.031
1.322
0.083
0.649

0.099
0.000
0.248
0.001
0.059

The sum of squared deviations caused by each factor is defined as (20). The total square sum of deviations corresponding to all the vacant columns is defined as (21) and Q, P, and T are defined as (22)~(24)

where n is the number of tests, is number of levels, is value of test results, and means the sum of text results at one column when the number of the levers is .

The degree of freedom corresponding to sum of squared deviations of one column is defined as (25) and the degree of freedom of error is defined as (26). The mean square of a factor is calculated by (27) and is calculated by (28) (Table 6). value of factors can be calculated by (29) and the results are shown in Table 7. The greater the difference value and the corresponding critical value are, the more significant the influence of the factor on the test results is. When the significance level is selected as 0.05, the critical value is shown in Table 7. The greater the difference and the corresponding critical value are, the more significant the influence of the factor on the test results is. It can be seen that the important order of three factors having an effect on the is sequence of the importance is , , and . Therefore, in the design of the system, the position of air interchange cross-passage is to be considered first; then controlling the interchanged air volume and meeting the fresh air volume required are to be considered. R also indicates influence degree of a factor on the test results. A column with maximum value of shows that the levels of the factor have the biggest influence on the test results; it is the most important factor. There is a relation of R, which is that , as shown in Table 4, and the sequence of factors according to their importance is the same as the result of .

Table 6: Values of mean square.

0.033
0.000
0.083
0.000
0.020
0.000

Table 7: Contrast table of significance.

Source of difference

F0.05
Significance
(relative)

A
0.0994
3
0.0331
155.878
6.39
II

B
0.2480
3
0.0827
389.032
6.39
I

C
0.0590
3
0.0197
92.557
6.39
III

0.0013
6
0.0017

Total
0.4076
15

5. Conclusions

When is increased, is decreased and increases. Using of 200m³/s and of 125 Pa as examples, following being increased from 2400 to 3840m, is decreased by 33.26%, and is increased by 49.34%, while the influence of on is greater than . When and are same (), the efficiency of ventilation system achieves the best result, and the is decreased following the increasing of .

When or is increased, and are decreased. Using of 3360m and of 175 Pa as example, when increases from 150 m³/s to 275 m³/s, decreases by 26.19% and decreases by 4.34%, so the influence of on is greater than . However, using of 175 m³/s as example, when increases from 25 Pa to 175 Pa, decreasse by 9.46% and CD decreases by 47.85%, so the influence of on is less than . When and are the same (), is increased following the increasing of .

reflects the efficiency of twin-tunnel complementary ventilation system, and the efficiency increases with decreasing. According to the orthogonal experiment result, the important order of three factors having an effect on is sequence of the importance, which is , , . This means that increasing has most important influence on decreasing , is considered firstly in ventilation designing, and increasing also can decrease , which is considered in the ventilation operation secondly, and is mainly to supply part of the fresh air and guide the air flow in the direction of the tunnel; decreasing has the least important influence on decreasing .

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

The authors would like to acknowledge the financial support for this work provided by the China Railway Siyuan Survey and Design Group R&D Program (2017k81-1), the Special Fund for Basic Scientific Research of Central Colleges of Chang’an University (nos. 310821172004, 310821153312, 310821165011, 310821151018, and 310821173312), the Special Fund for Scientific Research Project of Shaanxi Provincial Education Department (2013JK0958), and the Project on Social Development of Shaanxi Provincial Science and Technology Department (nos. 2018SF-382, 2018SF-378).

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