Pressure Surges Following Sudden Air Pocket Entrapmentin Storm-Water Tunnels

Jose G. Vasconcelos, A.M.ASCE1; and Gabriel M. Leite2

Abstract: Deep storm-water storage tunnels may undergo pressurization during intense rain events. In the process, air pockets may becomeentrapped and pressurized, causing significant flow changes. Currently, the role of nearby surge relief structures is uncertain with respect toair-water interactions. This paper presents results from experimental and numerical investigations on air pocket entrapment and compressionfollowing reflection of inflow fronts on system boundaries. Steady flows were established in the pipe apparatus, with the upstream portionflowing in the pressurized regime while the downstream flowed in free surface conditions. Sudden flow obstruction caused by valve maneu-vering at the downstream end generated unsteady conditions that were monitored by transducers and a MicroADV probe. Partial valvemaneuver runs were performed, aiming to represent cases in which surge relief is provided during air pocket compression/expansion cycles.Whereas experiments performed without surge relief (complete valve obstruction) yielded an oscillatory pressure pattern upon air pocketentrapment, when relief was available, a single pressure pulse pattern was observed instead, and no subatmospheric pressures were recorded.A simple two-phase model that includes essential features of the problem was developed, and its pressure predictions compared well with theexperimental data. DOI: 10.1061/(ASCE)HY.1943-7900.0000616. © 2012 American Society of Civil Engineers.

CE Database subject headings: Tunnels; Storm sewers; Storm surges; Laboratory tests; Numerical models; Water pressure.

Author keywords: Storm-water tunnels; Air pockets; Pressure surges; Laboratory experiments; Numerical modeling.

Introduction

Storm-water systems may undergo rapid filling during intense rainevents, during which air pockets can become entrapped withinclosed conduits, such as deep storage tunnels and trunk sewers.The motivation for studying such extreme conditions is relatedto pressure surges that may occur in those conduits following com-pression of entrapped air pockets. Reports indicate operational is-sues in storm-water systems linked with pressure surges, resultingin structural damage to manholes (Zhou et al. 2002a), surging withreturn of conveyed water to grade (Guo and Song 1991), geyseringevents triggered by the release of large air pockets (Wright et al.2011), and loss of tunnel storage volume, among others. Suchoperational issues have implications for public safety and health,in addition to significant material costs. Numerical models havebeen used to simulate extreme flows in storm-water tunnels, andare exemplified in works by Cardle and Song (1988), Vasconceloset al. (2006), and Politano et al. (2007). However, all of these stud-ies resulted in single phase models that do not explicitly accountfor the presence of the initial air phase within the tunnels, whichmay have limiting effects on the description of overall systemdynamics.

Previous investigations on mechanisms leading to air pocket en-trapment during rapid filling of closed conduits include the researchof Hamam and McCorquodale (1982) and Li and McCorquodale(1999), who investigated pockets formed by shear flow instabilitiesattributable to the relative motion of the air and water phases. Zhouet al. (2002b) investigated air pockets entrapped during rapid fillingin conduits attributable to limited ventilation. Vasconcelos andWright (2005) presented a new air pocket formation mechanismbased on the interaction of an advancing bore and the depressionwave in the water flow caused by air pressurization. A qualitativeexperimental study presented by Vasconcelos and Wright (2006)considered the filling of a near-horizontal pipeline with varyingventilation configurations, and identified additional pocket entrap-ment mechanisms. Of particular interest was the entrapment causedby the reflection of an open-channel bore against a system boun-dary, which is further described in a subsequent paragraph.

Investigations have also been conducted on pressure surgesfollowing the compression of air pockets in water pipelines.One of the first contributions on this topic is the work by Martin(1976), which considered the compression of an air pocket againstthe downstream end of an upslope pipeline following the openingof a valve at the upstream, separating the pipeline from a reservoirwith a higher piezometric head. The peak pressure head was muchlarger than the reservoir head at the upstream end, and such surgepeaks increased for smaller air pockets. Similar studies on the fill-ing of sloped pipelines performed by Izquierdo et al. (1999) andFuertes et al. (2000) confirmed this behavior when air pockets weretrapped between adjacent water masses. Zhou et al. (2002a)measured pressure surges caused by the rapid filling of an emptyhorizontal pipe that resulted in the compression of air pockets,which were ventilated through different orifice sizes. The studynoted large pressure surges during air pocket compression andexpansion cycles when smaller ventilation orifices were used,and even stronger water hammer pulses when the pocket wascompletely expelled from the system through larger diameter

1Assistant Professor, Dept. of Civil Engineering, Auburn Univ.,238 Harbert Engineering Center, Auburn, AL 36849 (correspondingauthor). E-mail: jvasconcelos@auburn.edu

2Graduate Student, Dept. of Civil Engineering, Auburn Univ.,238 Harbert Engineering Center, Auburn, AL 36849. E-mail: gml0002@auburn.edu

Note. This manuscript was submitted on July 27, 2011; approved onApril 24, 2012; published online on April 26, 2012. Discussion period openuntil May 1, 2013; separate discussions must be submitted for individualpapers. This paper is part of the Journal of Hydraulic Engineering,Vol. 138, No. 12, December 1, 2012. © ASCE, ISSN 0733-9429/2012/12-1081-1089/$25.00.

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / DECEMBER 2012 / 1081

J. Hydraul. Eng. 2012.138:1081-1089.

Dow

nloa

ded

from

asc

elib

rary

.org

by

RM

IT U

NIV

ER

SIT

Y L

IBR

AR

Y o

n 09

/03/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

ventilation orifices. The research was successful in predicting peakpressure surges/pulses during the filling events by applying a modelbased on the lumped-inertia approach (Wylie and Streeter 1993).

More recent models dealing with air-water flows in closed con-duits include the research presented by Leite and Vasconcelos(2011) in the context of water main filling. The model assumesthe applicability of the kinematic wave equations Sturm (2010)used to simulate the open-channel flow in sloped pipelines; pres-surized flow regions were simulated by applying the lumped-inertiaapproach, whereas the air phase was simulated with the ideal gaslaw, as presented in Zhou et al. (2002a). However, the researchcompared results against neither experimental nor field results.Another related numerical investigation involving rapid filling ofpipelines with limited ventilation was presented by Vasconcelosand Wright (2009). The Saint-Venant equation modified by thetwo-component pressure approach (TPA) model (Vasconcelos etal. 2006) was used in an application for which water inflow wouldresult in compression and pressurization of an air layer locatedahead of the inflow front. Air phase modeling was similar tothe approach adopted by Zhou et al. (2002a). However, althoughrelated, this modeling framework is not directly linked to the sud-den entrapment of air pockets, and does not provide further insightinto this problem.

Despite these previous investigations on air-water interactionsduring rapid filling events in closed conduits, there are importantknowledge gaps that still require further clarification. Towards sucha clarification, a conceptual representation of the air pocket entrap-ment mechanism caused by the reflection of open-channel bores onsystem boundaries is described next. Consider an open-channelbore that approaches a dropshaft located in the lowest elevationof a storm-water tunnel system. The hydraulic grade line (HGL)upstream from this bore gradually rises and touches the conduitcrown, creating a gradual flow regime transition front, as describedin the experiments by Trajkovic et al. (1999). As the inflow frontarrives at the dropshaft and causes the water level to rise, pipe-filling bores are generated, and one of these leads to entrapmentof a large air pocket. This condition is illustrated in Fig. 1, whichpresents a snapshot of a HGL profile extracted from an actual sim-ulation output of the rapid filling of a storm-water tunnel. Whereasthe entrapped air pocket that results from this filling scenario maytrigger significant pressure surges, as noted by Martin (1976) andothers, it is hypothesized that the pocket compression process isattenuated by nearby shafts that mitigate these surges.

To the authors, knowledge, no previous experimental investiga-tion has addressed air pocket entrapment events with respect to

attenuation caused by nearby structures. A common assumptionis that neglecting such attenuation may lead to significant pressureover-prediction. However, uncertainties regarding flow conditionsfollowing such sudden entrapments pose difficulties for improve-ments on numerical models to simulate extreme flows in storm-water tunnels. As noted by Vasconcelos et al. (2006), the accuracyof numerical models to simulate filling of storm-water tunnelsmay be severely compromised when air pockets are not properlyrepresented.

Another relevant consideration is the minimum pressure antici-pated following air pocket entrapment. Low pressures may damagethe lining of storm-water storage tunnels, which can result in otheradverse structural impacts to those tunnels. Results presented byMartin (1976) and related studies indicate that negative pressuresfollowing pocket entrapment and compression may be very signifi-cant in the absence of pressure attenuation structures. However, it isuncertain whether those negative pressures are anticipated in con-ditions for which pressure surge relief is provided.

Objectives

The primary goal of this work is to investigate flow conditions instorm-water storage tunnels following sudden air pocket entrap-ment, with respect to surge attenuation. This investigation aimsto provide greater insight on the underlying physics of air-waterinteractions involving entrapped air pockets, which in turn is usefulin improving current modeling approaches to this problem. Specifi-cally, this research determines the magnitudes of pressures follow-ing sudden flow obstructions that result in pocket entrapment, withand without pressure surge relief.

To achieve this goal, an experimental setup was developed inwhich flow parameters—such as air pocket volume, inflow rates,and system slopes—were varied. Results from experiments werecompared with predictions of a numerical model constructed withthe lumped-inertia approach that incorporates the fundamental fea-tures of the flow. The comparison aimed to assess the feasibility ofincorporating the findings from the experimental phase into morecomplex, spatially discretized numerical models.

This research may also be useful in assessing unsteady pressuresfollowing maneuvers at downstream gates in free-discharge waterpipelines. This is attributable to the similarity between the configu-ration used in these experimental investigations and such pipelinesin cases for which cavity outflow conditions are observed, asdescribed in Hager (1999) and Vasconcelos and Wright (2008).

Methodology

Experimental Methods

The experimental apparatus includes a 101.6 mm diameter clearpolyvinyl chloride (PVC) pipeline, with length L ¼ 12.0 m forhorizontal and adverse slopes, and L ¼ 10.6 m for favorableslope experiments. At the upstream end, a 0.66 m3 reservoir(plan area ¼ 0.50 m2) supplied flow to the pipeline that dischargedfreely into a 0.62 m3 reservoir at the downstream end. A recircu-lating line with pumps closed the hydraulic circuit. Initial, steadyflow conditions were such that pressurized flows existed at the up-stream portion of the pipeline, whereas the free-discharge conditionenforced the existence of an air cavity at the downstream end. Var-iable flow rates and pipeline slopes ensured a wide range for thecavity volume. Upon rapid maneuver (within 0.20� 0.03 s) of theknife gate valve at the downstream end of the pipeline, the airpocket became entrapped between a backward moving bore and

Fig. 1. Air pocket entrapment in storm-water tunnels at a certain timestep in a real-life tunnel rapid filling simulation

1082 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / DECEMBER 2012

J. Hydraul. Eng. 2012.138:1081-1089.

Dow

nloa

ded

from

asc

elib

rary

.org

by

RM

IT U

NIV

ER

SIT

Y L

IBR

AR

Y o

n 09

/03/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

the gradual flow regime transition further upstream. Pressure trans-ducers were located at two positions: at the pipe crown in the down-stream end of the apparatus and at the pipe invert, 6.0 m from theupstream end. A MicroADV probe was used to measure flowvelocities 3.0 m from the upstream end, a point that always flowedin pressurized conditions. Fig. 2 is a sketch of the apparatus.

There are some important distinctions between the experimentalsetup used in this research and others previously applied in researchsuch as that of Martin (1976) and Zhou et al. (2002a). In thosestudies, prior to air pocket compression, the flow rate in the pipelinewas zero. In the experiments described in this paper, the initial flowrate was set to a steady, non-zero value with a gradual transitionbetween pressurized and free surface flows. Upon valve maneuver,the pocket entrapment yielded by such a configuration is assumedto be more representative of entrapments anticipated in actualstorm-water tunnels. A second distinction is related to pressure re-lief mechanisms. In both of the previously mentioned papers, thepressure surge relief during air pocket compression was providedby air escape through orifices positioned at the downstream end. Inthis paper, when pressure surge relief was provided, the outlet gatevalve was partially closed, leaving a bottom gap that allow for onlywater to escape. The authors estimate this escape to be morerepresentative of the relief caused by water accumulation in anearby shaft as entrapped pockets are compressed. For scenariosin which no pressure surge relief was provided, the experimentwas anticipated to provide results that were similar to those pre-sented by Martin (1976) and Zhou et al. (2002a) with no relief;specifically, low-frequency pressure oscillations with peak pres-sures much higher than the pressure head driving the flow.

The experimental procedure was as follows:1. With the desired slope set in the pipeline, the pumps were

started; correspondent flow valves were opened, feeding theupstream reservoir and creating steady flow conditions atthe clear PVC pipeline.

2. Flow rate was chosen such that the upstream end of the pipe-line was in the pressurized regime, whereas the downstreamend discharged freely, characterizing a gradual flow regimetransition.

3. Initial pressures at both calibration manometers were read,along with the head at the upstream reservoir.

4. Air pockets volumes were calculated by measuring the dryperimeter of the air cavity at regular intervals on the clearPVC pipe crown. Interval sizes ranged between 0.05 m forsmallest air pockets to 0.30 m for the largest air pockets. Thesemeasurements were later used to determine the initial airpocket volume through numerical integration.

5. With digital camcorders (1920 × 1080 resolution,30 frames=s) turned on, pressure acquisition was initiatedusing two piezo-resistive pressure transducers (MEGGIT-ENDEVCO 8510-50C, maximum pressure 345 kPa, 0.4%accuracy), sampling at a frequency of 100 Hz.

6. Velocity acquisition was initiated with a MicroADV probe(Nortek Vectrino), sampling at a frequency of 25 Hz.

7. Flow was obstructed (partially or completely) by quickly man-euvering the knife gate valve at the downstream end of thepipeline, and visual observations and remarks were made toaid subsequent camera data analysis.

8. After the pressure pulses disappeared, pump flow was stopped,valves closed and pressures reached an equilibrium level. Finalpressure levels at the manometers were read to calibrate read-ings from pressure transducers.

The experimental variables systematically varied included:(1) five pipeline slopes: two adverse (0.027 and 0.013), one hori-zonal and two favorable (−0.005 and −0.010); (2) up to five flow

ratesQ per slope, with a normalized rangeQ� ¼ Q=ffiffiffiffiffiffiffiffigD5

pranging

from 0.20–0.57; and (3) three valve obstructions: 100, 89 and 81%of the pipe cross sectional area. Over 51 distinct experimentalconditions were tested, and the range tested is presented in Table 1.All experimental runs were repeated at least twice to ensureconsistency in the results.

Numerical Methods

The interactions of air and water following the sudden entrapmentof air pockets are highly complex, characterizing a two-phase flowthat cannot be exactly described in a one-dimensional modelingframework. However, since the goal of this research is to describethe pressure variation with respect to time, particularly the ability topredict the maximum and minimum pressures following such anentrapment, one-dimensional approaches may be adequate andcomputationally convenient. This convenience is explained bythe relatively simple manner in which these air-water interactions

Fig. 2. Experimental apparatus used in the experimental program

Table 1. Range of Experimental Variables Considered in the Experimentsof Air Pocket Compression

Experimental variable Tested range

Flow rates (m3=s) 2.08–5.45 L=s (Q� ¼ 0.202–0.532)Pipeline slope 0.027, 0.013, 0.00, −0.005 and −0.01Valve obstruction 100, 81, and 89% of cross section

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / DECEMBER 2012 / 1083

J. Hydraul. Eng. 2012.138:1081-1089.

Dow

nloa

ded

from

asc

elib

rary

.org

by

RM

IT U

NIV

ER

SIT

Y L

IBR

AR

Y o

n 09

/03/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

would be incorporated in tunnel flow models without adding ex-cessive computational effort, although still being able to provideuseful predictions.

The numerical model presented in this paper is a two-phase,lumped-inertia model (Wylie and Streeter 1993) that uses ideas pre-sented in Li and McCorquodale (1999) and Zhou et al. (2002a).The idea is to combine the water phase momentum equation, a con-tinuity equation for the air phase, and the ideal gas law to describechanges in the air phase pressure, air volume, and the system flowrate over time. This modeling approach was selected because inthese previous studies it succeeded in providing estimates for maxi-mum and minimum pressures involving air compression. This suc-cess is probably explained by the dominant effect of air pockets indetermining the unsteady flow pressures with respect to other prob-lem features, such as pipe wall elasticity and water compressibility.This enables application of the lumped-inertia approach with goodaccuracy.

The momentum equation expresses water flow rate Q upstreamfrom the air pocket region. The length of the rigid column used inthe model, rather than disregarding the water mass initially in freesurface conditions under the downstream air cavity (as sketched inFig. 2), accounts for that water mass in the overall system inertiathrough the expression L ¼ ðLpipe.A − VairÞ=A, where A = crosssectional area of the conduit; Lpipe = length of the pipeline; andVair = air phase volume. Another important assumption of the pro-posed model is that the outflow rate can be described by an orifice-like equation that depends on the air pressure upstream from thegate. Using the lumped-inertia model assumptions, one may writea mass balance equation to compute the change in air pocket vol-ume by tracking the values of Q and the outflow rate through theorifice; no air ventilation is assumed to occur through the orifice.As a result, the proposed system of equations describing the flowbecomes the following:

dQdT

¼ gAL

�Hres − ðHair −HatmÞ −

��fLDþ Kloss

�QjQj2gA2

��(1)

dVair

dT¼ −Qþ CdAorif

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2gðHair −HatmÞ

p(2)

dHair

dT¼ k

Hair

Vair

dVair

dT(3)

where g = gravity acceleration; T = time;Hres = pressure head at theupstream end of the pipeline; Hair and Hatm = air phase and atmos-pheric pressure head, respectively; f and Kloss = the Darcy frictioncoefficient (assumed to be 0.025) and the summation of the localloss coefficients, respectively; Cd = the water discharge coefficientacross the knife gate valve; Aorif = water discharge cross-sectionalarea at the knife gate valve; and k = the polytropic coefficient(assumed to be 1.2 in this paper). The authors acknowledge thelimitations of assuming a constant friction factor in this model.A number of relevant factors may play a role in defining the actualenergy damping of these flows, including frequency-dependentfriction (Wylie and Streeter 1993), viscoelastic effects in plasticpipes (Soares et al. 2008), and thermofluid dynamics effects(Lee 2005). Although the results of numerical modeling indicatethat the observed energy damping is stronger than that obtainedwith the constant friction factor, this aspect of the problem itselfrequires separate investigations that is beyond the scope ofthis paper.

The initial conditions used in the model were obtained as de-scribed next. Q and Hres were obtained by direct measurement,whereas the authors assumed Hair ¼ Hatm. The authors further

assumed that, during the simulation, the water level in the upstreamtank was constant even in scenarios for which the outflow was com-pletely blocked. Considering the plan area of that tank is over60 times larger than the cross sectional area of the pipeline, theauthors found that this simplification introduced an underestima-tion of the value of Hres towards the end of the simulation of rang-ing from 3–7% of the total head, which was not considered aprimary factor in model accuracy. As noted, the initial Vair valuewas obtained by numerical integration of the dry perimeter of theair pocket at the pipe crown at regular intervals. The set of ordinarydifferential equations were solved applying a fourth-order Runge-Kutta, as presented in Press et al. (1989).

Results and Discussion

Pressure Hydrographs Following Various ValveManeuvers

The authors anticipated that the experimental conditions involvingcomplete obstruction would yield low-frequency oscillations withpeak pressures that were higher than the pressure head driving theflow. This is reflected in the results, as it is shown in the typicalpressure hydrographs measured at the downstream end for the hori-zontal slope.

Fig. 3 presents pressure hydrographs at the downstream end ofthe pipeline for horizontal slope condition following total valveobstruction. As anticipated, higher flow rates (Q�) yield smallerair cavities volumes (V�

air ¼ Vair=D3) at the downstream end. Upon

Fig. 3. Pressure hydrographs at the downstream end following totalobstruction (horizontal slopes)

1084 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / DECEMBER 2012

J. Hydraul. Eng. 2012.138:1081-1089.

Dow

nloa

ded

from

asc

elib

rary

.org

by

RM

IT U

NIV

ER

SIT

Y L

IBR

AR

Y o

n 09

/03/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

valve maneuver, an air pocket entrapment occurred and pressureoscillations were detected, with larger magnitudes and smaller peri-ods for the smaller pocket volumes. The pressure peaks rangedfrom H� ¼ H=D ¼ 24–120, results that were much larger thanthe initial pressure head at the upstream reservoir. Significant neg-ative pressures were detected (down to an absolute minimum ofH� < −50, or −5.1 mH2O) in those obstructions without pressuresurge relief. Pressure hydrographs obtained with the upstreampressure transducers were generally the same in nature; however,the magnitude was somewhat smaller. In experiments involvingsmall air pockets, the pressures at the upstream transducer was gen-erally 20–30% smaller, whereas for larger air pockets, the discrep-ancy was approximately 10%. For brevity, results are not shown inthis paper.

Results with partial valve obstruction were significantly differ-ent from those obtained with total valve obstruction in that the pres-sure peaks were significantly diminished. As illustrated in Fig. 4,for the horizontal slope experiments, for 81% partial obstruction,the pressure peaks were generally between 17 and 26% of thoseobtained with correspondent total obstruction results. For 89% par-tial obstruction, the pressure peaks were within 42–58% of thoseobtained with total obstruction. Such smaller pressures have astraightforward explanation in that the flow rate variation uponvalve maneuver was not as prominent as in total obstruction con-ditions, as is discussed in a subsequent paragraph.

Another significant difference was the absence of pressure os-cillations, a result that was not initially anticipated. The hydro-graphs presented in Fig. 4 illustrate that, upon rapid partialobstruction, there was a single pressure peak followed by a new,although higher, steady pressure level. This signifies that the sys-tem rapidly adjusted to a new steady state characterized by a sig-nificant head loss across the partially obstructed valve. A limiting

condition between the oscillatory pattern observed in total obstruc-tions and the single pressure pulse pattern was detected with thefavorable slope (−0.010) and 89% valve obstruction. In this sce-nario, the observed pressure oscillations were of shorter duration,i.e., under T� ¼ T=ðL= ffiffiffiffiffiffi

gDp Þ < 0.3, than those measured for total

obstruction conditions.An additional very relevant observation in the partial obstruction

experiments was the absence of negative pressure in almost allexperiments involving partial valve obstruction. This result thatmay have some relevant and practical implications for structuraldesign of storm-water tunnels in scenarios for which air pockets arepotential issues.

The results obtained in this research are very dependent on geo-metric characteristics of the hydraulic system, inflow conditionsand the mechanisms by which air pockets become entrapped. Itis thus difficult to directly extend these findings into actual tunneldesign applications. However, in a qualitative fashion, the authorsanticipated that pressure surge pattern in real-lfe filling scenariosshould be dependent on the proximity of pressure relief structures.If there is proximity between the location where air pockets becomeentrapped and pressure relief structures (e.g., dropshafts), thesingle-pulse pressure pattern is possibly a more realistic represen-tation of the interactions between a compressed air pocket and thewater pressurized flow.

Velocity Hydrographs

Velocity measurements by the MicroADV probe located 3.0 mfrom the upstream end of the apparatus closely reflected the pres-sure results. Measurements for total valve obstruction runs indi-cated a damped oscillatory pattern for the flow velocity thatbecame zero after T� > 0.5. In contrast, the velocity hydrographsobtained for the partial obstructions of 89 and 81% indicated nooscillatory pattern, but instead a residual and quasi-steady velocityafter the maneuver was performed. After valve maneuvering, theresidual flow velocity ranged from 18–24% of the initial velocityfor the scenarios with 89% obstruction, and 36–52% for the sce-narios with 81% obstruction. The results presented in Fig. 5 wereobtained with the horizontal slope, but are representative for theother tested slopes.

Velocity measurements were also useful for two other purposes.The first was to calibrate the discharge coefficient of the knife gatevalves in partial obstruction conditions, a necessary step for numeri-cal modeling analysis. The second reason was to determine the ini-tial flow rate through velocity measurements (and hence an estimateof the initial system inertia) prior to the valve maneuver, and withthis to establish the role of the initial system flow rate/velocity inthe magnitude of the pressure surges observed. As noted, previousstudies on the compression of air pockets used configurations inwhich the flow was initially zero. Because the initial conditionin the present study was a steady flow characterized by a gradualflow regime transition, determination of the role of the initial sys-tem inertia was possible and relevant in the context of this research.

Role of Air Pocket Volume and Initial System Inertia inPressure Peak Magnitudes

A summary from all pressure peaks measured in the experiments asa function of the initial air pocket volume is presented in Fig. 6. Inagreement with the findings of previous investigations, such asMartin (1976) and Izquierdo et al. (1999), pressure peak magni-tudes decreased with increasing air pocket volume. This statementis valid for all tested conditions, including the magnitude of down-surges and the pressure peaks for partial obstruction experiments.

Fig. 4. Pressure hydrographs at the downstream end following thepartial obstructions (horizontal slopes); a single repetition for each caseis represented

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / DECEMBER 2012 / 1085

J. Hydraul. Eng. 2012.138:1081-1089.

Dow

nloa

ded

from

asc

elib

rary

.org

by

RM

IT U

NIV

ER

SIT

Y L

IBR

AR

Y o

n 09

/03/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

Although there is significant scatter in the results, for experi-mental conditions involving total valve obstructions and smallentrapped air pocket volumes (V�

air < 0.5, normalized by D3), pres-sure peaks H� (normalized by D) were on the order of 100–150,with maximum downsurges of −50. For total obstruction runs,peak H� values decreased steadily to values ranging from 15–25for large air pocket volumes (V�

air > 2.0), depending on the pipelineslope. This decrease rate was not uniform, given that the peaksurges were also related to the initial flow rate in the system priorto the gate maneuver, as subsequently explained.

With respect to the 89% partial obstruction runs, maximum H�reached 95 between all experimental runs, whereas for 81% ob-structions, the maximum H� was 34. Even with the scatter inthe results for small pocket volumes, significant attenuation inthe peak pressures is noticeable for the partial obstruction scenar-ios. These results highlight the practical value of these findings fordeep storage tunnel design, and the importance of accounting forthe relief provided by nearby structures during air-water interac-tions. Similarly to the total obstruction scenario, peak H� valuesalso decreased steadily with larger initial air pocket volumes.The rate of pressure decrease is not uniform between the differentpipeline slopes, with the steepest decrease rate associated with the0.027 adverse slope and the shallowest decrease rate with the−0.010 favorable slope.

A likely explanation for the differences in the decline rate of H�with V�

air between different slopes is linked to the required flow rate

to maintain a certain cavity volume at the downstream end of thepipeline. For scenarios in which the pipeline features an adverseslope, a relatively small flow rate is able to maintain an air cavityof a certain volume at the pipeline outlet prior to the valve maneu-ver. In contrast, a much larger flow rate would be required to main-tain the same air cavity volume for favorable slopes as themaintenance of pressurized flow conditions require larger pipeflows. As a result, upon valve maneuvering, the results show thatconfigurations with adverse slopes can trigger significantH� valueseven with relatively small flow rates and initial system inertia,attributable to the small initial air pocket volume. Fig. 7 confirmsthis observation. Conversely, experiments using favorable slopeswere always characterized by larger flow rates. This larger systeminertia was converted into relatively significant pressure surge evenin scenarios for which large air pockets were compressed, explain-ing the slower decrease rate of the pressure peaks for favorableslopes observed in Fig. 6 as V�

air increased.The correlation between peak H� and normalized flow rate Q�

for favorable slope experiments was not as strong as those observedfor the horizontal and adverse slopes. At these slopes, air cavities

Fig. 5. Velocity hydrographs measured by the MicroADV followingtotal and the partial obstructions (horizontal slopes); a single repetitionfor each case is represented

Fig. 6. Consolidation of the pressure peak results obtained for allslopes and valve obstructions as a function of air pocket volumes

1086 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / DECEMBER 2012

J. Hydraul. Eng. 2012.138:1081-1089.

Dow

nloa

ded

from

asc

elib

rary

.org

by

RM

IT U

NIV

ER

SIT

Y L

IBR

AR

Y o

n 09

/03/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

at the downstream end could only be sustained for larger flow rates(Q� > 0.5). Within a much narrow range of flow rates, the size ofcavities in favorable slopes could vary from a maximum of V�

air >4.5–8 down to values as low as 0.3. Consequently, as presented inFig. 7, a small change in Q� from 0.50–0.55 resulted in an increasefrom three- to four-fold in peak H� values. This was not observedfor the other tested slopes. A stronger correlation between Q� andH� was noticed both for horizontal and adverse slopes. This is alsoconfirmed when a correlation observed between V�

air and Q� in theexperiments is derived. As presented in Fig. 8, there is generally agood parabolic fit (expressed in terms of the coefficient of deter-mination R2) between Q� and H� measurements for horizontal andadverse slopes. The same was not true for the favorable slopes.

Numerical Modeling Results

The experimental results were compared with the predictions of theproposed numerical model. The objective of this comparison wasto assess whether one-dimensional models could reproduce thegeneral characteristics of the air-water interactions, particularlythe pattern of pressure variation over time and maximum/minimumpressure values.

The authors provide three comments with respect to the param-eters used in the Eqs. 1, 2 and 3. The value assumed for Aorif isassumed to decrease linearly from A into the final obstruction valuewithin 0.20� 0.03 s (based on frame-by-frame analysis frommovie recordings). Concerning the local losses coefficient Kloss,local losses are primarily caused by the upstream connection be-tween the reservoir and the pipeline, using mm pipes and connec-tion. To match these head losses observed in steady flowconditions, Kloss was set to 2.9 with reference to 50 mm diameter.

The third comment is that the discharge coefficient values usedin the numerical modeling of Cd following the partial obstructionscenarios were calibrated to match the flow rates measured with theMicroADV velocity and transducer pressures at post-valve maneu-vering conditions. Considering the valve opening shape of acrescent moon and with a maximum width (at the bottom) of either8 or 13 mm, the resulting discharge area could be directly calcu-lated. Applying a typical orifice equation and the pressure mea-sured at the upstream side of the discharge point (measuredwith the transducer), the values for Cd obtained were either approx-imately 0.36 (for 81% obstruction) or 0.20 (for 89% obstruction).

Six conditions were selected to perform the comparison be-tween the experimental results and the model, all with the favorableslope of −0.010. The first three scenarios involve a large initial airpocket volume (V�

air ¼ 8.3–8.5), and the remainder cases with asmall initial air pocket (V�

air ¼ 0.31). In both, the initial flow rate(and hence the system inertia) was high (Q� ¼ 0.51–0.54), and thethree obstruction conditions were tested. There are three primaryreasons for the choice of this particular slope to perform the com-parison between experimental results and numerical models. Thefirst is that, for this slope, it was the limiting condition betweenoscillatory and single-pulse pressure patterns that occurred with89% obstruction. For total obstruction, the pattern was oscillatory,whereas for 81% obstruction, the single-pulse pattern was ob-served. The second reason is that this slope provided the widestrange of air pocket volumes (V�

air from 0.3 up to 8.5). The thirdreason is that, simulations performed with other slopes have notprovided further insight in to the problem.

Fig. 9 presents the comparison of the pressure hydrographs ofthe downstream transducer during the initial seconds for the sce-narios with large air pocket volume (V�

air ¼ 8.3–8.5). Consideringthe peak pressure pulse and comparison parameter, there is goodagreement between model predictions and experimental results,with the discrepancy under 6–7%. Moreover, the general trendof the pressure variation over time is well captured in all obstructiontypes. A limitation of the numerical predictions is the inability toincorporate the higher energy dissipation levels observed in the ex-periments, which is particularly noticeable in the full obstructionsimulation results. There is also a small discrepancy in the oscil-lation period that is perhaps linked to slight inaccuracies in thecalculation of air pocket volume.

Fig. 10 presents a comparison between pressure measurementsand prediction results for scenarios involving small initial airpocket volumes (V�

air ¼ 0.31). The general observations formulatedfor the previous cases are also applicable in this research, with thepressure peaks being well captured by the proposed numericalmodel. There is, however, a systematic discrepancy in the timingof the first pressure peak, which tends to occur slightly sooner thanthose predicted by the model. Moreover, for the scenario of totalobstruction, the oscillation period is 20% smaller than that ob-served in the experiments. This may also result from an under-measurement of the air pocket volume, or perhaps limitations ofthe one-dimensional framework used for the numerical model.

In general, the ability of this simplified model to predict withgood accuracy the pressure surges and the general behavior of

Fig. 7. Pressure peak results obtained for all slopes and total valveobstruction as a function of initial flow rate

Fig. 8. Relationship between initial air pocket volumes and initial flowrates for different slopes

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / DECEMBER 2012 / 1087

J. Hydraul. Eng. 2012.138:1081-1089.

Dow

nloa

ded

from

asc

elib

rary

.org

by

RM

IT U

NIV

ER

SIT

Y L

IBR

AR

Y o

n 09

/03/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

the flow following the sudden pocket entrapment is encouraging.Clearly, such a simple framework would need extensive adjustmentsto be incorporated in to more complex, multi-pipe, discretizednumerical models which would be applied in actual simulationsof extreme flows in storm-water storage tunnels. However, with ad-equate calibration from the obtained experimental results or fromavailable field data, such a model can be developed. However,

the description of air pocket motion following its entrapment, nec-essary for numerical model simulations, is still an open questionand is planned for future experiments.

Conclusions and Future Work

This paper presents results of a combined experimental and numeri-cal investigation of rapid filling flows in closed conduits in whichsudden air pocket entrapment occurs. The entrapment events arelinked to the reflection of inflow fronts on system boundaries.The experimental program involved the study of obstruction offlows generating pocket entrapment, in which the initial air pocketvolume, initial flow rate, pipeline slope and obstruction degreewere systematically varied. The goal of performing partial obstruc-tions was to assess changes in pressures in scenarios for which apressure surge relief structure, such as a dropshaft, is nearby thelocation where the pocket was formed. A two-phase flow modelthat incorporate essential features of the problem was proposedand its results compared with the experimental data.

The experiments indicated that total obstructions generated verystrong pressure pulses, followed by an oscillatory pattern for thepressure and flows within the conduit. Such conditions also werecharacterized by significant negative pressures, and in essencethese observations are in agreement with previous related studies.However, experiments involving partial blockage demonstratedthat not only are the pressure peaks are reduced, but also thatthe pressure pattern is no longer oscillatory; instead, it is charac-terized by a single pressure pulse. Moreover, the absence ofnegative pressures in the experimental observations may have im-portant structural design implications. The observations in thispaper depend strongly on system geometry characteristics, flowconditions and the actual distance between the location wherepocket compression occurs and pressure relief is provided.Although such factors prevent generalization of the experimentalresults presented in this paper, they are useful to other researchersdeveloping related investigations. Despite the limitations of the pre-sented experiments that include tested geometry, pocket entrapmentmechanism and pressure relief mechanism, it seems clear thatsurges caused by air pocket compression are reduced by nearbypressure relief structures, and it is possible that the negative pres-sures may not even occur. One expects that the results presentedin this paper will help in the development of improved modelingtools that will more accurately assess the interactions betweenair and water phases during rapid filling of existing and proposedtunnel systems.

This research also aimed to provide an experimental verificationof the role of system inertia for the pressure pulse magnitude, inde-pendently of air pocket volumes. For adverse slopes, even airpocket entrapment involving small flow rates, and hence systeminertia, can generate significant pressure peaks because of the smallair pockets. In contrast, much larger flow rates associated with largeair pocket volumes, observed with the favorable slope experiments,resulted in pressure surges that decayed more gradually withincreasing V�

air values.Experimental results compared well with predictions from a

two-phase numerical model. The model was not able to replicatethe energy damping observed in the experiments, a limitation thatwas also reported by Li and McCorquodale (1999) in their two-phase flow model. However, the comparative results are still prom-ising, and will be used in the development and calibration ofinnovative modeling tools that can detect and handle the formationof air pockets during filling events. A current limitation of the pro-posed model is its inability to precisely predict the kinematics of

Fig. 9. Comparison between experimental results and numerical pre-dictions for total and partial obstructions for large air pocket volumesand 1.0% favorable slope

Fig. 10. Comparison between experimental results and numerical pre-dictions for total and partial obstructions for small air pocket volumesand 1.0% favorable slope

1088 / JOURNAL OF HYDRAULIC ENGINEERING © ASCE / DECEMBER 2012

J. Hydraul. Eng. 2012.138:1081-1089.

Dow

nloa

ded

from

asc

elib

rary

.org

by

RM

IT U

NIV

ER

SIT

Y L

IBR

AR

Y o

n 09

/03/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

these entrapped pockets following their entrapment. Although re-lated studies on the balance between drag and buoyancy forces inwater mains were primarily focused on obtaining a threshold veloc-ity that would clear water pipelines from air, the velocity and spreadof entrapped air pocket motions is still poorly understood, and willbe addressed in our future investigations.

Acknowledgments

The authors gratefully acknowledge Auburn University andLimnotech Inc for supporting the development of this research.They also thank the comments from anonymous reviewers thatsignificantly improved the quality of the paper.

Notation

The following symbols are used in this paper:A = conduit cross-sectional area;

Aorif = water discharge cross sectional area at the knife gatevalve;

Cd = water discharge coefficient across the knife gate valve;D = pipeline diameter;f = Darcy friction coefficient;g = gravity acceleration;H = pressure head;H� = normalized pressure head ¼ H=D;Hair = air phase pressure head;Hatm = atmospheric pressure head;Hres = pressure head at the upstream end of the pipeline;Kloss = summation of local loss coefficients;

k = polytropic coefficient (assumed to be 1.2);L = pipeline length associated with water volume;

Lpipe = total pipeline length;Q = flow rate in the pipeline;Q� = normalized flow rate in the pipeline ¼ Q=

ffiffiffiffiffiffiffiffigD5

p;

T = time;T� = normalized time ¼ T=ðL= ffiffiffiffiffiffi

gDp Þ;

Vair = air phase volume; andV�air = normalized air phase volume ¼ Vair=D3.

References

Cardle, J. A., and Song, C. S. S. (1988). “Mathematical modeling of un-steady flow in storm sewers.” Int. J. Eng. Fluid Mech., 1(4), 495–518.

Fuertes, V. S., Arregui, F., Cabrera, E., and Iglesias, P. (2000). “Experimen-tal setup for entrapped air pockets validation.” Publication 2, 8th Int.Conf. on Pressure Surges: Safe Design and Operation of IndustrialPipe Systems, A. Anderson, ed., Wiley, New York, 133–146.

Guo, Q., and Song, C. S. S. (1991). “Dropshaft hydrodynamics undertransient conditions.” J. Hydraul. Eng., 117(8), 1042–1055.

Hager, W. H. (1999). “Cavity outflow from a nearly horizontal pipe.” Int. J.Multiphase Flow, 25(2), 349–364.

Hamam, M. A., and McCorquodale, J. A. (1982). “Transient conditions inthe transition from gravity to surcharged sewer flow.” Can. J. Civil Eng.,9(2), 189–196.

Izquierdo, J., Fuertes, J., Cabrera, E., Iglesias, P. L., and Garcia-Serra, J.(1999). “Pipeline start-up with entrapped air.” J. Hydraul. Res., 37(5),579–590.

Leite, G. M., and Vasconcelos, J. G. (2011). “Numerical modeling ofthe filling of water mains considering air pressurization.” Cognitivemodeling of urban water systems, J. William, ed., ComputationalHydraulics International, Guelph, ON, Canada, 1–21.

Lee, N. H. (2005). “Effect of pressurization and expulsion of entrapped airin pipelines.” Doctoral dissertation, Georgia Institute of Technology,Atlanta, GA.

Li, J., and McCorquodale, A. (1999). “Modeling mixed flow in stormsewers.” J. Hydraul. Eng., 125(11), 1170–1180.

Martin, C. S. (1976). “Entrapped air in pipelines.” Proc., 2nd Int. Conf. onPressure Surges, BHRA Fluid Engineering, Cranfield, U.K.

Politano, M., Oodgard, A. J., and Klecan, W. (2007). “Case study: Numeri-cal evaluation of hydraulic transients in a combined sewer overflowtunnel system.” J. Hydraul. Eng., 133(10), 1103–1110.

Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T. (1989).Numerical recipes in pascal, Cambridge University Press, Cambridge,U.K.

Soares, A. K., Covas, D. I. C., and Reis, L. F. R. (2008). “Analysis of PVCpipe-wall viscoelasticity during water hammer.” J. Hydraul. Eng.,134(9), 1389–1395.

Sturm, T. (2010). Open channel hydraulics, 2nd Ed., McGraw-Hill, NY.Trajkovic, B., Ivetic, M., Calomino, F., and D’Ippolito, A. (1999). “Inves-

tigation of transition from free surface to pressurized flow in a circularpipe.” Water Sci. Technol., 39(9), 105–112.

Vasconcelos, J. G., and Wright, S. J. (2005). “Experimental investigationof surges in a stormwater storage tunnel.” J. Hydraul. Eng., 131(10),853–861.

Vasconcelos, J. G., and Wright, S. J. (2006). “Mechanisms for air pocketentrapment in stormwater storage tunnels.” Proc., 2006 ASCE EWRIWorld Environmental and Water Resources Congress, ASCE, Reston,VA, 1–10.

Vasconcelos, J. G., and Wright, S. J. (2008). “Rapid flow startup in filledhorizontal pipelines.” J. Hydraul. Eng., 134(7), 984–992.

Vasconcelos, J. G., and Wright, S. J. (2009). “Investigation of rapid fillingof poorly ventilated stormwater storage tunnels.” J. Hydraul. Res.,47(5), 547–558.

Vasconcelos, J. G., Wright, S. J., and Lautenbach, D. L. (2011). “Modelingapproaches for the rapid filling of closed conduits with entrapped air.”Proc., 2011 ASCE EWRI World Environmental and Water ResourcesCongress, ASCE, Reston, VA, 3449–3458.

Vasconcelos, J. G., Wright, S. J., and Roe, P. L. (2006). “Improved sim-ulation of flow regime transition in sewers: The two-component pres-sure approach.” J. Hydraul. Eng., 132(6), 553–562.

Wright, S. J., Lewis, J. W., and Vasconcelos, J. G. (2011). “Geysering inrapidly filling storm-water tunnels.” J. Hydraul. Eng., 137(1), 112–115.

Wylie, E. B., and Streeter, V. L. (1993). Fluid transient in systems, PrenticeHall, Upper Saddle River, NJ.

Zhou, F., Hicks, F. E., and Steffler, P. M. (2002a). “Transient flow in arapidly filling horizontal pipe containing trapped air.” J. Hydraul.Eng., 128(6), 625–634.

Zhou, F., Hicks, F. E., and Steffler, P. M. (2002b). “Observations of airwaterinteraction in a rapidly filling horizontal pipe.” J. Hydraul. Eng.,128(6), 635–639.

JOURNAL OF HYDRAULIC ENGINEERING © ASCE / DECEMBER 2012 / 1089

J. Hydraul. Eng. 2012.138:1081-1089.

Dow

nloa

ded

from

asc

elib

rary

.org

by

RM

IT U

NIV

ER

SIT

Y L

IBR

AR

Y o

n 09

/03/

13. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.