Research Article Numerical Study on Different …downloads.hindawi.com/journals/mpe/2014/194125.pdfResearch Article Numerical Study on Different Series Modes of Jet Fan in a Longitudinal

Research ArticleNumerical Study on Different Series Modes of Jet Fan ina Longitudinal Tunnel Ventilation System

Guihong Pei and Jie Pan

School of Civil Engineering and Architecture Southwest Petroleum University Chengdu 610500 China

Correspondence should be addressed to Jie Pan 1120400231qqcom

Received 26 May 2014 Revised 21 August 2014 Accepted 4 September 2014 Published 29 September 2014

Academic Editor Jaromir Horacek

Copyright copy 2014 G Pei and J Pan This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Efficient ventilation systems will contribute to maintaining air quality in the tunnel In order to improve ventilation performancein normal traffic condition the 3D tunnel models were established according to the original design for the tunnel located in centralplains of China Based on the commercial CFD software Fluent 63 and 119896-120576 turbulence model numerical simulations were carriedout to study the patterns of jet flow and the optimization of fan combinations It is found that the axial velocity profile obtainedfrom numerical simulation agrees quite well with turbulent free jet theory although there is a little difference on the magnitudeThe comparison of four combination modes under the condition of operating four fans indicates that the ventilation effectivenessis affected mainly by both the interval of adjacent groups of fans and the combination modes of operational fans According tothe simulation results a novel combination mode which consists of a group double paralleled fans and two groups single fan isdesigned The novel combination mode is regarded as the optimum combination mode with respect to maximizing air velocity inthe tunnel Compared to the traditional combination modes it will increase the air velocity by 57

1 Introduction

The air quality inside tunnel is gradually taken seriouslybecause of the increasing of tunnel length Owing to thespecial structure of tunnels when a fire occurs the smokespreads fast and widely which prohibits the safe evacuationof occupants and the firefighters from extinguishing the firewhile in most tunnels the ventilation system plays a crucialrole in controlling the smoke and maintaining acceptableconditions within the tunnel during evacuation rescue andfirefighting procedures [1] Statistics have shown that smokeis the most fatal factor in fire and about 85 of victimsin building fire were killed by hot and toxic smoke [2]Therefore efficient ventilation in a road tunnel is extremelyimportant to prevent the smoke and the harmful substancesfrom affecting tunnel users The longitudinal ventilationmode with jet fans is highly anticipated due to its flexibilityreliability lower cost and easy control Therefore it not onlygets the favor of engineers to be used inmost of the tunnel butalso causes the attention of scholars to do deeper research

The four main methods of studying tunnel ventilationat home and abroad are theoretical calculations model

tests field measurements and numerical simulations Forexample Ohashi et al used numerical method to study thevertical concentration distribution of pollutants in Kan-Etsuhighway tunnel of Japan which is 10885 km long The resultshad provided the basis for design of ventilation and airpollution control in highway tunnel [3] Rohne carried outan experimental research in which the fans were located neara flat plate to study the resistance and jet thrustThe influenceof different installation separation of fans on the ratio ofresistance and thrust had been investigated at the same timethe influence of various distances from the plate on the ratioof resistance and thrust also had been analyzed [4] Gao ofLanzhou Jiaotong University had analyzed the characteristicsof jet flow and the pressure-rise of jet fan Not only therelationship between the pressure-rise and the induced lengthbut also the relationship between the pressure-rise and theseparation of jet fans had been investigated by him [5] Zhongof South China University of Technology had conductedfield measurements in Dabaoshan tunnel and the test resultsprovided valuable data for the installation location of jetfans in longitudinal ventilation system [6] According to theideas of the composite structure method Wang and Xia of

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 194125 9 pageshttpdxdoiorg1011552014194125

2 Mathematical Problems in Engineering

Changrsquoan University had carried out numerical simulationson longitudinal ventilation and the optimization ventilationmethod was picked out [7] Colella et al [1 8 9] hadconducted a large number of researches in the field oftunnel ventilation and they had obtained plenty of importantresults They applied multiscale modeling approach to studythe ventilation flows and fire in a tunnel domain Themultiscale modeling approach uses different levels of detailswhen describing the fluid flow in different tunnel regionsThe far field region is modeled by using a 1D ldquonetworkrdquomodel and the near field region is modeled by using a 3DCFD model The ldquonetworkrdquo and the CFD models exchangeinformation at the 1Dndash3D interfaces [8] The adoption ofmultiscale modeling approach allows for a more rational useof the computational resources without loss of accuracy [9]The research results obtained by scholars mentioned abovehad laid the foundation for the study of tunnel ventilationsystem All the scholars had put forward some valuableopinions

The longitudinal ventilation systems with jet fans havebeen continuously updated On the one hand as the widthof the tunnel increases 2 or 3 jet fans are paralleled andsuspended in the tunnel vault On the other hand the numberof jet fans in series increases with the increasing of the tunnellength In general only the total number of operational jetfans will be given in design plan while the combinationmode of jet fans in normal traffic condition is not stipulatedThe wind speed is different in various combination modesand so it is the air pressure Therefore there is clear needto analyze the difference of pressure distribution and veloc-ity distribution in various combination modes Numericalsimulations were carried out to study the air flow and theoptimization of fan combinations inside tunnel based onCFDsoftware Fluent 63 According to the simulation results thebest combinationmodewhich is conductive in improving theventilation performance in the tunnel is selected

2 The Mathematical Model

The jet flow of fans in the tunnel can be described as followsthe velocity of gas has increased to 20sim30ms when flowingthrough the jet fans Then the jet flow sprays into the tunnelwhere the velocity of surrounding gas is about 3ms Becauseof the entrainment between jet flow gas and surrounding gasthe vortex is formedwhich leads to the lateral pulseThen thejet flow has momentum exchange and energy exchange withsurrounding gas [10 11]

The jet flow of fans in the tunnel had been regardedas turbulent free jet in many articles The basic equationsof turbulent free jet are the continuity equation and themomentum equation They can be represented as follows

120597119906119894

120597119909119894

=120597119906119894

120597119909119894

+1205971199061015840

119894

120597119909119894

= 0

120597119906119894

120597119905+ 119906119895

120597119906119894

120597119909119895

= 119891119894minus1

120588

120597119901

120597119909119894

+1

120588

120597

120597119909119895

(120583120597119906119894

120597119909119895

minus 12058811990610158401198941199061015840119895)

(1)

where 119906119894is turbulent velocity 119906

119894is time-averaged velocity 1199061015840

119894

is velocity fluctuation and 119891119894is mass force (119894 119895 = 1 2 3)

Turbulent free jet is a common form of jet flow and theimportant features are shown as follows [12]

(1) Velocity distributions in each section of the turbulentfree jet are similar the maximum velocity is axisvelocity and with the distance from the axis is fartherthe velocity becomes lower

(2) The thickness of mixing layer of turbulent free jet haslinear increase with the distance

(3) Momentum flux conservation is satisfied for theturbulent free jets and the surrounding fluid

(4) In the zone of established flow the boundary layeris fully developed so the velocity obeys the Gaussdistribution

As momentum flux conservation is satisfied for eachsection of the turbulent free jets when it is round jet themomentum flux can be represented as follows

119869 = int

infin

0

1205881199062sdot 2120587119903 119889119903 = 120588119906

2

01205871199032

0 (2)

where 1199060is the velocity of nozzle exit section and 119903

0is the

radius of the nozzleThe axis velocity of any section and the flow rate of any

section can be respectively represented as follows

119906119898= 62119863

119909sdot 1199060 (3)

119876 = 032119909

119863sdot 1198760 (4)

where 119906119898is the axis velocity119863 is the diameter of the nozzle

119909 is the distance from the nozzle and 1198760is the flow rate

3 The Calculation Model

In this paper 3D models were established on the basis ofthe tunnel which is located in the central plains of ChinaThe one-way tunnel consists of two separated channels andeach one is three-lane traffic One of the channels is 1891mlong and the other is 1908m The width of a channel is1426m and the height is 76m The cross-section of tunnelis about 88m2 Considering that the simulation calculationwill be relatively complicated if the actual situation was takeninto account the geometric model of the tunnel is simplifiedby ignoring the drainage channel cable trench and othersecondary factorsThe simple dimensions of the tunnel cross-section are shown in Figure 1 In the ventilation system thereare 18 individual reversible jet fans with the diameter of900mm suspended on the ceiling of the tunnel (not installedin niches) These jet fans are divided into six groups and ineach group there are three jet fansThe arrangement of jet fansis shown in Figure 2 (1891m) The width height and lengthof the channel are along 119909-coordinate 119910-coordinate and 119911-coordinate respectively

Mathematical Problems in Engineering 3

Table 1 Combination modes of operational jet fans

Operating condition Combination modes1 Turn on 4 jet fans of group 1 and group 3 (turn off the middle one of each group)2 Turn on the middle jet fan of each group from group 1 to group 4

3 Turn on 4 jet fans of group 1 group 2 and group 3 (turn on jet fans on left and rightsides of group 1 and turn on the middle jet fans of other two groups)


2275m 2275m

R1 = 76m R1 = 76m

R2 = 6m R2 = 6m

103

m

103

m

1426m

121m09m

639m

Figure 1 Simple dimensions of the tunnel cross-section

1 2 3 4 5 6

200 150 150 150 150 1819101891

Figure 2 Layout of the jet fans in the tunnel used as case studyshowing the relative positions of the jet fans and portals (m)

Generally the number of operational fans is calculatedby designers according to the norm The design instructionspoint out that only four operational jet fans will ensure theair quality inside the tunnel when the speed of the vehiclesis between 40 kms and 60 kms In the study present herethe numerical simulations were carried out according tothe normal traffic condition with 4 jet fans operating Asthe series mode is often designed on the basis of designersrsquoexperience in this paper four different combination modeshave been designed The four combination modes are shownin Table 1

The tunnel length is so long that the computationalcost will be large if the models were built according to theprototype of the tunnel In order to reduce the computationalcost the symmetry of the solution across the longitudinalplane was considered So the models were built based on theright half part of the tunnel (the cross-section of tunnel issymmetrical) As the cross-section of the tunnel is irregularunstructured meshes have been used in the computationaldomain The calculated domain has been divided into aplurality of subregions In the region near the jet fans themeshes are intensive while in the region far away from the

jet fans the meshes are coarseThemeshes of different tunnelcross-sections are shown in Figure 3 The total number ofmeshes throughout the computational domain is more thanfive hundred thousand The calculations in the four modelswere cold-flow steady stateThe standard 119896-120576 turbulentmodelwas applied to the 3D models and the second order upwinddiscretization was used for other terms except for pressureterm which was dealt with the standard discretization TheSIMPLEC algorithm was used for the coupling betweenvelocity and pressure In addition the boundary conditionswere specified as follows The nonslip stationary wall bound-ary condition was applied on the walls of tunnel and jet fansThe pressure inlet boundary and pressure outlet boundarywere prescribed at tunnel inlet and tunnel outlet respectivelyand the relative pressure was set as 0 PaThe fan inlet and fanoutlet were specified as velocity inlet boundary and velocityoutlet boundary respectively and the velocity was set as307mswhich is the issue velocity of jet fanwith the diameterof 900mm

4 The Numerical Simulation Resultsand Analysis

41 The Analysis of the Jet Mode in the Tunnel The jet flowinside tunnel is quite complex due to the restriction of variousfactors In order to validate the jet mode inside tunnel in thispaper the space within 200m away from the fan outlet isselected as the research region The variation of axis velocityalong the tunnel length direction is shown in Figure 4 (119909 =0 119910 = 639 velocity profile along 119911-coordinate direction)The results of numerical simulation are compared with thetheoretical value which is calculated based on formula (3)

The blue line in Figure 4 is the theoretical curve and thered line is the curve obtained from the simulation resultsComparing the two curves it can be seen that the velocitydecay trend of numerical simulation curve is consistent withthat of theoretical curve although there is certain differencein magnitude Within 50m away from the fan outlet thevelocity drops sharply with the increasing of distance then inthe following 50m the velocity drops slowly as the distanceincreasesWhen the distance from the fan outlet is more than100m the difference of velocity is slight in other words itessentially remains the same

The theoretical length of the zone of flow establishment isexpressed as

1198710= 62 sdot 119863 (5)


(a) (b)

Figure 3 Different meshes used for half of the tunnel cross-sections (the left cross-section shows the domain containing jet fan pairs andthe right cross-section shows the domain containing single jet fan)

where 1198710is the length of the zone of flow establishment

and 119863 is the diameter of jet nozzle So there is a horizontalline about 6m on the theoretical curve which represents thelength of zone of flow establishment For the reason that inthe enclosed tunnel the limit of space and the wall frictionwould lead to the insufficient development of turbulent freejet Hence on the numerical simulation curve there is nohorizontal line and the velocity drops from the exit of jetfan Within 15m away from the fan outlet the theoreticalvelocity is higher than that of numerical simulation whilewhen the distance from the fan outlet is more than 15m it isreversed and the velocity of numerical simulation overshootthe theoretical velocity The reasons for the generation of thisphenomenon can be described as follows after the airflowspraying out of jet fan the entrainment will occur betweenthe jet flow and surrounding gas As the jet flow spreadsforward more and more free-stream air is entrained into thehigh-speed jet flow With the entrainment downstream thevelocity gradually decreases and finally is evenly distributedat the cross-sectionThe exchange of momentum between jetflow and surrounding gas leads to the rise of pressure andthen the movement of air flow is driven by pressure gradientAccordingly from Figure 4 we can conclude that the jet flowinside tunnel has a little difference with the turbulent free jetbut it can still be regarded as the turbulent free jet

42 The Analysis of Twin-Jet In the 3D simulation modelsthere exists twin-jet in the tunnel According to the flowcharacteristics the twin-jet region can be divided into con-verging region and combined region In converging regionthe entrainment between twin-jet and free-stream air leads tothe spread of outer edgeThen the outer edges of the two jetsbegin to interact with each other at the centerline Eventuallythe two jets merge into a single one in combined region

0

5

10

15

20

25

30

35

0 50 100 150 200 250

Velo

city

(ms

)

Position (m)

Theory analysisNumerical simulation

Figure 4The comparison of the theoretical velocity and calculatedvelocity of jet changing with the distance from jet fan (at the heightof the axis of jet fan)

The change process of twin-jet from converging region tocombined region is illustrated in Figure 5

Figure 5 shows the horizontal velocity profiles at differentaxial location for the condition of 119911 = 639m The differentaxial location in other words is the different axis distancefrom the fan outlet and 119911 represents the height from groundAt the early stage the velocity profile exhibits the typicalcharacteristic of twin-jet As the jets spread downstream thecore velocity gradually decreases Within 10m away fromfan outlet the peak velocity drops sharply from 307ms to17ms The velocity of the region around centerline has nochange still below 4ms whereas it can be seen that the outeredge of each jet has expanded When the distance from fanoutlet is more than 10m the outer edges of two jets graduallymerge with each other At the same time the velocity ofcenterline gradually increases In the following 40m the peakvelocity gradually drops and eventually becomes unobvious


0

5

10

15

20

25

30

35

minus6 minus4 minus2 0 2 4 6

Velo

city

(ms

)

Position (m)

05m10m20m

30m40m50m

Figure 5 Horizontal velocity profiles for various distances from jetfan pair at the height of fan axis

minus5

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7 8

Tota

l pre

ssur

e (Pa

)

Height (m)

05m10m20m

30m40m50m

Figure 6 Pressure profiles along the vertical direction for variousdistances from the jet fan pair (in the central axis of the tunnel cross-section)

At the position of 20m away from fan outlet the peakvelocity is 12ms while at the position of 50m away from fanoutlet there is no obvious peak velocity because the velocityis substantially evenly distributed In the region more than20m away from fan outlet the velocity of the region aroundcenterline remains 7sim8ms

The pressure variation is very important for understand-ing the characteristic of the jet flow Figure 6 shows thepressure profiles in the central axis of different cross-sectionswith various distances from fan outlet Here the abscissastands for the height from ground From this figure it can beseen that there exists negative pressure region Within 10maway from fan outlet from ground to the roof of tunnel theair pressure is lower than 0 Pa because of the entrainment andmutual interference of twin-jet As the jet boundary graduallyexpands to the lower space of tunnel the negative pressureregion becomesmore andmore small At the position of 20m30m and 40m away from fan outlet the upper bounds of

negative pressure region are 4m 3m and 2m respectivelyWhen the distance from fan outlet is more than 50m thereis no negative pressure region

In order to verify the reasonableness of numerical cal-culation it is necessary to compare the calculated data withthe experimental data In the literature [9] Colella et al hadmeasured the longitudinal air velocities of various points inthe condition with only 5th jet fan pair operating in theWest tunnel of the Dartford tunnels in UK These points aredistributed in six different cross-sections at 20m intervalsstarting 20m downstream from the jet fan discharge surfaceAs the tunnel size and fan model in literature [9] are differentfrom that we used in numerical simulation we just comparedthe air velocity change trend along the longitudinal directionof two cases From the various measured points in theliterature [9] we picked out two points in central line ofevery cross-section with the heights of 275m and 45m fromground (the location of the two points also can be regard asabout 235m and 06m below the height of fan axis) Andfrom the calculated data we picked out the points at thesame location (in the central line of cross-section and about235m and 06m below the height of fan axis) in differentcross-sections with 20m 40m 60m 80m 100m and 120mdownstream from the jet fan discharge surface respectivelyThe comparison of change trend of velocities between themeasured data and calculated data are shown in Figure 7(a)and Figure 7(b)

From Figure 7(a) and Figure 7(b) we can conclude thatthe velocity change trend of numerical simulation is con-sistent with that of experimental measurements It can beseen from Figure 7(a) that at the location of 06m belowthe height of fan axis both the experimental velocity andcalculated velocity decrease as the distance from the jet fandischarge surface increases while from Figure 7(b) it canbe concluded that as the distance from the jet fan dischargesurface increases for both the experimental velocity andcalculated velocity there exists velocity fluctuation in a smallrange Therefore the results of numerical calculation will beable to reflect the real change trend of air velocity in thetunnel

43 The Comparison between Twin-Jet and Single Jet Themovement of air inside tunnel under the conditions of twin-jet is different from that of single jet Accordingly the velocitydistribution and pressure distribution in the two conditionswill be different

Figure 8 shows the velocity distributions in the centralaxis of tunnel cross-section of the two cases with the distancefrom the fan outlet are 50m 100m and 150m It can beconcluded that in both cases the velocity difference betweenthe upper space (above 3m) and lower space (below 3m)is smaller as distance increases At the position of 50maway from fan outlet the velocity difference between theupper space and lower space of tunnel is 5sim6ms In thefollowing 100m the velocity difference drops to lower than1ms When the distance from fan outlet is more than 100mthe velocity variation is slight and the velocities are evenlydistributed along tunnel height direction At the position of50m away from fan outlet in upper space the velocity in the


0

2

4

6

8

10

12

0 20 40 60 80 100 120 140

Velo

city

(ms

)

Position (m)

(a)

Experimental dataCalculated data

0

1

2

3

4

5

0 20 40 60 80 100 120 140

Position (m)

Velo

city

(ms

)

(b)

Figure 7The comparison of the change trend of velocities between numerical simulation and experimental measurements (all the points in(a) are at the location of 06m below the height of fan axis all the points in (b) are at the location of 235m below the height of fan axis)

0

1

2

3

4

5

6

7

8

9

0 2 4 6 8

Velo

city

(ms

)

Height (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)

Figure 8 The comparison of vertical velocity profiles for variousdistances from single jet fan and jet fan pair (in the central axis ofthe tunnel cross-section)

condition with two operational fans is higher than that withone operational fan while in lower space it is reversed At thepositions of 100m and 150m away from fan outlet whetherin the upper space or in the lower space the velocity in thecondition with two operational fans is a little higher thanthat with one operational fan Figure 9 shows the velocitydistributions of the two cases at the fan axis height with thedistance from the fan outlet are 50m 100m and 150m It isknown that at the position of 100m away from fan outletthe twin-jet has completely merged into one and the peakvelocity has moved to the centerline No matter how far itis from the fan outlet (50m 100m or 150m) the velocity inthe condition with two operational fans is higher than thatwith one operational fan It can be concluded from Figure 8and Figure 9 that compared to single jet twin-jet is moreconducive to increasing the wind speed inside tunnel

From Figure 10 we can know that no matter how farit is from the fan outlet the pressure of single jet is a littlehigher than that of twin-jet while from Figure 11 it can beseen that at the position of 50m away from fan outlet thepressure of single jet is higher than that of twin-jet only in the

0

1

2

3

4

5

6

7

8


Velo

city

(ms

)

Position (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)

Figure 9The comparison of horizontal velocity profiles for variousdistances from single jet fan and jet fan pair (at the height of fanaxis)

0

5

10

15

20

25

30

35

40

45

0 2 4 6 8

Tota

l pre

ssur

e (Pa

)

Height (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)

Figure 10 The comparison of vertical pressure profiles for variousdistances from single jet fan and jet fan pair (in the central axis ofthe tunnel cross-section)


0

5

10

15

20

25

30

35

40


Tota

l pre

ssur

e (Pa

)

Position (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)

Figure 11The comparison of horizontal pressure profiles for variousdistances from single jet fan and jet fan pair (at the height of fan axis)

center space however apart from center space the pressureof twin-jet is higher than that of single jet That is because atjet axis the motion of fluids is more intense From Figure 10and Figure 11 it can be seen that in both cases the pressuregradually decreases as the distance from fan outlet increases

44 The Analysis of Different Operating Conditions Thepressure inside tunnel has increased when the jet is fullydeveloped In the region that the distance from the fan outletis less than 100m the pressure has reached the top and themovement of air is driven by pressure gradient In generalthe larger the pressure gradient is the greater the windspeed is And in a certain range it is more conductive indischarging waste gas when the wind speed is relatively highSince the tunnel ventilation system is composed of seriesof fans the distance between adjacent two groups and thenumber of operational fans will affect the air pressure andwind speed inside tunnelTherefore we analyzed the velocitydistribution and pressure distribution of four combinationmodes and chose the best combination mode Thus thesection 15m high from ground is selected for research Thecomparison between first operating condition and secondoperating condition is shown in Figure 12

Figure 12(a) shows the velocity distribution along thetunnel on the center line of the plane 15m high fromground Figure 12(b) shows the pressure distribution at thesame position It can be seen that the gas pressure andwind speed of second operating condition are lower thanthose of first operating condition Although there are onlytwo groups of fans in series in first operating condition theeffect of pressure-rise and velocity-rise is better than thatof second operating condition In Figure 12(a) within 100maway from fan outlet of each group the wind speed suddenlydrops to below 25ms and then recovers to above 3msThe difference between maximum velocity and minimumvelocity is 18ms in first operational condition while thevelocity difference is 12ms in second operational conditionThe velocity difference in the mode of twin-jet is larger than

that of single jet Except for the region mentioned abovethe wind speed is essentially unchanged in the other regionof the tunnel Near the entrance of tunnel the velocity offirst operating condition is 03ms higher than that of secondoperating condition and so it is in the middle of tunnelwhile near the exit of tunnel the velocity difference of twooperating conditions is 04ms In Figure 12(b) it can beknown from the curve that the pressure-rise in the modewith double paralleled fans is higher than that with twojet fans in series In addition in the second condition thedistance between last two groups of fans is so far that theeffect of pressure-rise is not continuous As a consequencethe effect of pressure-rise in the mode with two groups ofdouble paralleled fans in series is better than that with fourgroups of single fan in series In the middle of tunnel thepressure of first operating condition is 10 Pa higher thanthat of second operating condition whereas near the exitof tunnel the pressure difference of two conditions is only2 Pa In conclusion it can be confirmed that the ventilationperformance depends on both the series mode and thenumber of fans in series

Figure 13(a) shows the velocity distribution along thetunnel on the center line of the plane 15m high from theground Figure 13(b) shows the pressure distribution at thesameposition FromFigure 13(a) we can conclude that in thenovel series modes the velocity and pressure inside tunnelwill change with the separation of adjacent groups of fansIn third operating condition the distance between adjacentgroups of fans is short the velocity difference of maximumvelocity and minimum velocity in first ldquovelocity oscillationrdquois 19ms in second and third ldquovelocity oscillationrdquo thevelocity difference is 08ms In fourth operating conditionthe distance between adjacent groups of fans is long andthe velocity difference in first second and third ldquovelocityoscillationrdquo is 18ms 11ms and 11ms respectively Onthe other hand near the entrance of tunnel the velocity ofthird operating condition is only 01ms higher than thatof fourth operating condition and so it is in the middle oftunnel Near the exit of tunnel the velocity of third operatingcondition is 02ms higher than that of fourth operatingcondition It can be seen from Figure 13(b) that the pressureinside tunnel of third operating condition is higher than thatof fourth operating condition In the middle of tunnel thepressure of third operating condition is 8 Pa higher than thatof fourth operating condition and near the exit of tunnel thepressure difference of two operating conditions is 1 Pa Thatis because in third operating condition the pressure insidetunnel has been continuously enhanced for three times in ashort distance while at the same distance the pressure onlyhas been continuously enhanced twice in fourth operatingcondition Although the pressure is enhanced at the positionof 1500m in fourth operating condition the pressure offourth operating condition is still lower than that of thirdoperating condition Consequently it can be concluded thatit is more conductive in enhancing the velocity and pressureinside tunnel when the distance between adjacent groups offans is short

Reviewing Figure 13(a) and Figure 13(b) it is not difficultto find that it is more conductive in enhancing the velocity


15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

Position (m)

1

2

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

(b)

Figure 12 The comparison of velocity profiles and pressure profiles along the longitudinal direction of first operating condition and secondoperating condition (the velocity profiles and pressure profiles obtained from the section 15m high from the ground)

15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

Position (m)

3

4

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

(b)

Figure 13 The comparison of velocity profiles and pressure profiles along the longitudinal direction of third operating condition and fourthoperating condition (the velocity profiles and pressure profiles obtained from the section 15m high from the ground)

and pressure inside tunnel when most operational fans arelocated near the tunnel entrance Since the operational fansof first operating condition and third operating conditionare all located near the tunnel entrance we should make acomparison between the traditional series mode and novelseries mode to choose the better one

The Figure 14(a) and Figure 14(b) present that in firstoperating condition either the pressure or the velocity islower than that in third operating condition In Figure 14(a)near the entrance of tunnel the velocity of third operatingcondition is 02ms higher than that of first operatingcondition and when the distance from the entrance of tunnelis more than 500m the velocity of third operating conditionis 015ms higher than that of first operating condition Socompared to the traditional series mode the velocity canbe increased about 57 with the novel series mode FromFigure 14(b) it can be seen that the pressure of third operatingcondition is continuously enhanced for three times within500m while in first operating condition it is continuouslyenhanced twice at the same distance When the distancefrom the entrance of tunnel is more than 500m the pressureof third operating condition is a little higher than that of

first operating condition In conclusion the third operatingcondition is more beneficial in exhausting waste gas in thelight of calculation data

5 Conclusion

Numerical simulations were conducted to research the char-acteristics of air flow in a tunnel The jet flow inside tunnelis a little different from the turbulent free jet because of thewall friction and the constraint of space But the changetrend of axial velocity obtained from simulation results agreesquite well with turbulent free jet theory In this paper fourcalculationmodels were carried out to investigate the velocitydistribution and pressure distribution inside tunnel withdifferent combination modes of jet fans From the simulationresults it can be concluded that the ventilation performancemainly depends on the series mode and the separation ofadjacent groups of fans The novel combination mode whichconsists of double paralleled fans and single fan is regardedas the optimum combination mode When most operationalfans are located near the tunnel entrance it is more con-ductive in increasing the velocity and pressure inside tunnel


15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

1

3

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

Position (m)

(b)

Figure 14 The comparison of velocity profiles and pressure profiles along the longitudinal direction of first operating condition and thirdoperating condition (the velocity profiles and pressure profiles obtained from the section 15m high from the ground)

In conclusion it is needed to consider various factors whenchoosing the appropriate series mode in ventilation system

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This paper is financially supported by Natural Science Foun-dation of China (Grant no 51174170) and National Scienceand Technology Major Project of China under Grant no2011ZX05013004 The authors are grateful to Professor Jian-jun Liu for his constructive comments on this paper

References

[1] F Colella G Rein R Borchiellini and J L Torero ldquoA novelmultiscale methodology for simulating tunnel ventilation flowsduring firesrdquo Fire Technology vol 47 no 1 pp 221ndash253 2011

[2] J Ji Z H Gao C G Fan and J H Sun ldquoLarge Eddy Simulationof stack effect on natural smoke exhausting effect in urban roadtunnel firesrdquo International Journal of Heat and Mass Transfervol 66 pp 531ndash542 2013

[3] H Ohashi A Mizuno I Nakabori and M Ueki ldquoA newventilationmethod for theKan-etsu road tunnelrdquo inProceedingsof the 4th International Symposium on the Aerodynamics ampVentilation of Vehicle Tunnels Held at York England BHRAFluid Engineering vol 4 p 31 1982

[4] E Rohne ldquoThe friction losses on walls caused by a row of fourparallel jet flowsrdquo in Proceedings of the 6th ISAVVT BHRA FluidEngineering pp 151ndash164 Durham UK 1988

[5] M L Gao and J M Wu ldquoRegulating action and analysis of jetfans in the longitudinal ventilation of vehicle tunnelrdquo Journal ofLanzhou Railway Institute vol 17 no 1 pp 88ndash94 1998

[6] H S Zhong W M Li and J M Xu ldquoA study on the ventilationcontrol modes in one-way traffic tunnelsrdquo Modern TunnelingTechnology vol 42 no 2 pp 76ndash80 2005

[7] Y DWang andY X Xia ldquoNumerical simulation of longitudinalventilation of highway tunnelrdquo China Journal of Highway andTransport vol 15 no 1 pp 82ndash85 2002

[8] F Colella G Rein R Carvel P Reszka and J L Torero ldquoAnal-ysis of the ventilation systems in the Dartford tunnels using amulti-scale modelling approachrdquo Tunnelling and UndergroundSpace Technology vol 25 no 4 pp 423ndash432 2010

[9] F Colella G Rein V Verda and R Borchiellini ldquoMultiscalemodeling of transient flows from fire and ventilation in longtunnelsrdquo Computers and Fluids vol 51 no 1 pp 16ndash29 2011

[10] J L Zheng ldquoThe simulation of tunnel ventilation system andthe conclusionrdquo Underground Engineering and Tunnels no 1pp 41ndash45 1997

[11] D F Chen ldquoAn overview of ventilation design of long tunnelsrdquoUnderground Engineering and Tunnels no 3 pp 34ndash37 1995

[12] Z Y Dong Jet Mechanics Science Press New South WalesAustralia 2005

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Changrsquoan University had carried out numerical simulationson longitudinal ventilation and the optimization ventilationmethod was picked out [7] Colella et al [1 8 9] hadconducted a large number of researches in the field oftunnel ventilation and they had obtained plenty of importantresults They applied multiscale modeling approach to studythe ventilation flows and fire in a tunnel domain Themultiscale modeling approach uses different levels of detailswhen describing the fluid flow in different tunnel regionsThe far field region is modeled by using a 1D ldquonetworkrdquomodel and the near field region is modeled by using a 3DCFD model The ldquonetworkrdquo and the CFD models exchangeinformation at the 1Dndash3D interfaces [8] The adoption ofmultiscale modeling approach allows for a more rational useof the computational resources without loss of accuracy [9]The research results obtained by scholars mentioned abovehad laid the foundation for the study of tunnel ventilationsystem All the scholars had put forward some valuableopinions

The longitudinal ventilation systems with jet fans havebeen continuously updated On the one hand as the widthof the tunnel increases 2 or 3 jet fans are paralleled andsuspended in the tunnel vault On the other hand the numberof jet fans in series increases with the increasing of the tunnellength In general only the total number of operational jetfans will be given in design plan while the combinationmode of jet fans in normal traffic condition is not stipulatedThe wind speed is different in various combination modesand so it is the air pressure Therefore there is clear needto analyze the difference of pressure distribution and veloc-ity distribution in various combination modes Numericalsimulations were carried out to study the air flow and theoptimization of fan combinations inside tunnel based onCFDsoftware Fluent 63 According to the simulation results thebest combinationmodewhich is conductive in improving theventilation performance in the tunnel is selected

2 The Mathematical Model

The jet flow of fans in the tunnel can be described as followsthe velocity of gas has increased to 20sim30ms when flowingthrough the jet fans Then the jet flow sprays into the tunnelwhere the velocity of surrounding gas is about 3ms Becauseof the entrainment between jet flow gas and surrounding gasthe vortex is formedwhich leads to the lateral pulseThen thejet flow has momentum exchange and energy exchange withsurrounding gas [10 11]

The jet flow of fans in the tunnel had been regardedas turbulent free jet in many articles The basic equationsof turbulent free jet are the continuity equation and themomentum equation They can be represented as follows

120597119906119894

120597119909119894

=120597119906119894

120597119909119894

+1205971199061015840

119894

120597119909119894

= 0

120597119906119894

120597119905+ 119906119895

120597119906119894

120597119909119895

= 119891119894minus1

120588

120597119901

120597119909119894

+1

120588

120597

120597119909119895

(120583120597119906119894

120597119909119895

minus 12058811990610158401198941199061015840119895)

(1)

where 119906119894is turbulent velocity 119906

119894is time-averaged velocity 1199061015840

119894

is velocity fluctuation and 119891119894is mass force (119894 119895 = 1 2 3)

Turbulent free jet is a common form of jet flow and theimportant features are shown as follows [12]

(1) Velocity distributions in each section of the turbulentfree jet are similar the maximum velocity is axisvelocity and with the distance from the axis is fartherthe velocity becomes lower

(2) The thickness of mixing layer of turbulent free jet haslinear increase with the distance

(3) Momentum flux conservation is satisfied for theturbulent free jets and the surrounding fluid

(4) In the zone of established flow the boundary layeris fully developed so the velocity obeys the Gaussdistribution

As momentum flux conservation is satisfied for eachsection of the turbulent free jets when it is round jet themomentum flux can be represented as follows

119869 = int

infin

0

1205881199062sdot 2120587119903 119889119903 = 120588119906

2

01205871199032

0 (2)

where 1199060is the velocity of nozzle exit section and 119903

0is the

radius of the nozzleThe axis velocity of any section and the flow rate of any

section can be respectively represented as follows

119906119898= 62119863

119909sdot 1199060 (3)

119876 = 032119909

119863sdot 1198760 (4)

where 119906119898is the axis velocity119863 is the diameter of the nozzle

119909 is the distance from the nozzle and 1198760is the flow rate

3 The Calculation Model

In this paper 3D models were established on the basis ofthe tunnel which is located in the central plains of ChinaThe one-way tunnel consists of two separated channels andeach one is three-lane traffic One of the channels is 1891mlong and the other is 1908m The width of a channel is1426m and the height is 76m The cross-section of tunnelis about 88m2 Considering that the simulation calculationwill be relatively complicated if the actual situation was takeninto account the geometric model of the tunnel is simplifiedby ignoring the drainage channel cable trench and othersecondary factorsThe simple dimensions of the tunnel cross-section are shown in Figure 1 In the ventilation system thereare 18 individual reversible jet fans with the diameter of900mm suspended on the ceiling of the tunnel (not installedin niches) These jet fans are divided into six groups and ineach group there are three jet fansThe arrangement of jet fansis shown in Figure 2 (1891m) The width height and lengthof the channel are along 119909-coordinate 119910-coordinate and 119911-coordinate respectively






2275m 2275m

R1 = 76m R1 = 76m

R2 = 6m R2 = 6m

103

m

103

m

1426m

121m09m

639m


1 2 3 4 5 6

200 150 150 150 150 1819101891









1198710= 62 sdot 119863 (5)


(a) (b)





0

5

10

15

20

25

30

35

0 50 100 150 200 250

Velo

city

(ms

)

Position (m)






0

5

10

15

20

25

30

35


Velo

city

(ms

)

Position (m)

05m10m20m

30m40m50m


minus5

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7 8

Tota

l pre

ssur

e (Pa

)

Height (m)

05m10m20m

30m40m50m










0

2

4

6

8

10

12

0 20 40 60 80 100 120 140

Velo

city

(ms

)

Position (m)

(a)


0

1

2

3

4

5

0 20 40 60 80 100 120 140

Position (m)

Velo

city

(ms

)

(b)


0

1

2

3

4

5

6

7

8

9

0 2 4 6 8

Velo

city

(ms

)

Height (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)




0

1

2

3

4

5

6

7

8


Velo

city

(ms

)

Position (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)


0

5

10

15

20

25

30

35

40

45

0 2 4 6 8

Tota

l pre

ssur

e (Pa

)

Height (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)



0

5

10

15

20

25

30

35

40


Tota

l pre

ssur

e (Pa

)

Position (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)









15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

Position (m)

1

2

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

(b)


15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

Position (m)

3

4

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

(b)





5 Conclusion



15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

1

3

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

Position (m)

(b)





Acknowledgments


References




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra














2275m 2275m

R1 = 76m R1 = 76m

R2 = 6m R2 = 6m

103

m

103

m

1426m

121m09m

639m


1 2 3 4 5 6

200 150 150 150 150 1819101891









1198710= 62 sdot 119863 (5)


(a) (b)





0

5

10

15

20

25

30

35

0 50 100 150 200 250

Velo

city

(ms

)

Position (m)






0

5

10

15

20

25

30

35


Velo

city

(ms

)

Position (m)

05m10m20m

30m40m50m


minus5

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7 8

Tota

l pre

ssur

e (Pa

)

Height (m)

05m10m20m

30m40m50m










0

2

4

6

8

10

12

0 20 40 60 80 100 120 140

Velo

city

(ms

)

Position (m)

(a)


0

1

2

3

4

5

0 20 40 60 80 100 120 140

Position (m)

Velo

city

(ms

)

(b)


0

1

2

3

4

5

6

7

8

9

0 2 4 6 8

Velo

city

(ms

)

Height (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)




0

1

2

3

4

5

6

7

8


Velo

city

(ms

)

Position (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)


0

5

10

15

20

25

30

35

40

45

0 2 4 6 8

Tota

l pre

ssur

e (Pa

)

Height (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)



0

5

10

15

20

25

30

35

40


Tota

l pre

ssur

e (Pa

)

Position (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)









15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

Position (m)

1

2

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

(b)


15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

Position (m)

3

4

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

(b)





5 Conclusion



15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

1

3

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

Position (m)

(b)





Acknowledgments


References




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










(a) (b)





0

5

10

15

20

25

30

35

0 50 100 150 200 250

Velo

city

(ms

)

Position (m)






0

5

10

15

20

25

30

35


Velo

city

(ms

)

Position (m)

05m10m20m

30m40m50m


minus5

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7 8

Tota

l pre

ssur

e (Pa

)

Height (m)

05m10m20m

30m40m50m










0

2

4

6

8

10

12

0 20 40 60 80 100 120 140

Velo

city

(ms

)

Position (m)

(a)


0

1

2

3

4

5

0 20 40 60 80 100 120 140

Position (m)

Velo

city

(ms

)

(b)


0

1

2

3

4

5

6

7

8

9

0 2 4 6 8

Velo

city

(ms

)

Height (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)




0

1

2

3

4

5

6

7

8


Velo

city

(ms

)

Position (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)


0

5

10

15

20

25

30

35

40

45

0 2 4 6 8

Tota

l pre

ssur

e (Pa

)

Height (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)



0

5

10

15

20

25

30

35

40


Tota

l pre

ssur

e (Pa

)

Position (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)









15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

Position (m)

1

2

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

(b)


15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

Position (m)

3

4

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

(b)





5 Conclusion



15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

1

3

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

Position (m)

(b)





Acknowledgments


References




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

5

10

15

20

25

30

35


Velo

city

(ms

)

Position (m)

05m10m20m

30m40m50m


minus5

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7 8

Tota

l pre

ssur

e (Pa

)

Height (m)

05m10m20m

30m40m50m










0

2

4

6

8

10

12

0 20 40 60 80 100 120 140

Velo

city

(ms

)

Position (m)

(a)


0

1

2

3

4

5

0 20 40 60 80 100 120 140

Position (m)

Velo

city

(ms

)

(b)


0

1

2

3

4

5

6

7

8

9

0 2 4 6 8

Velo

city

(ms

)

Height (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)




0

1

2

3

4

5

6

7

8


Velo

city

(ms

)

Position (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)


0

5

10

15

20

25

30

35

40

45

0 2 4 6 8

Tota

l pre

ssur

e (Pa

)

Height (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)



0

5

10

15

20

25

30

35

40


Tota

l pre

ssur

e (Pa

)

Position (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)









15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

Position (m)

1

2

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

(b)


15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

Position (m)

3

4

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

(b)





5 Conclusion



15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

1

3

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

Position (m)

(b)





Acknowledgments


References




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

2

4

6

8

10

12

0 20 40 60 80 100 120 140

Velo

city

(ms

)

Position (m)

(a)


0

1

2

3

4

5

0 20 40 60 80 100 120 140

Position (m)

Velo

city

(ms

)

(b)


0

1

2

3

4

5

6

7

8

9

0 2 4 6 8

Velo

city

(ms

)

Height (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)




0

1

2

3

4

5

6

7

8


Velo

city

(ms

)

Position (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)


0

5

10

15

20

25

30

35

40

45

0 2 4 6 8

Tota

l pre

ssur

e (Pa

)

Height (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)



0

5

10

15

20

25

30

35

40


Tota

l pre

ssur

e (Pa

)

Position (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)









15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

Position (m)

1

2

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

(b)


15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

Position (m)

3

4

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

(b)





5 Conclusion



15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

1

3

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

Position (m)

(b)





Acknowledgments


References




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

5

10

15

20

25

30

35

40


Tota

l pre

ssur

e (Pa

)

Position (m)

50m (1)50m (2)100m (1)

100m (2)150m (1)150m (2)









15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

Position (m)

1

2

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

(b)


15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

Position (m)

3

4

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

(b)





5 Conclusion



15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

1

3

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

Position (m)

(b)





Acknowledgments


References




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

Position (m)

1

2

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

(b)


15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

Position (m)

3

4

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

(b)





5 Conclusion



15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

1

3

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

Position (m)

(b)





Acknowledgments


References




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










15

2

25

3

35

4

45

0 500 1000 1500 2000

Velo

city

(ms

)

Position (m)

(a)

0 500 1000 1500 2000

1

3

minus5

0

5

10

15

20

25

Tota

l pre

ssur

e (Pa

)

Position (m)

(b)





Acknowledgments


References




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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