Numerical Evaluation of Hydraulic Transientsin a Combined Sewer Overflow Tunnel System

Case Study: Numerical Evaluation of Hydraulic Transientsin a Combined Sewer Overflow Tunnel System

M. Politano1; A. J. Odgaard, M.ASCE2; and W. Klecan3

Abstract: The potential for hydraulic transients in the West Area Combined Sewer Overflow Tunnel System of the City of Atlanta wasinvestigated by numerical modeling. Different design alternatives were evaluated to mitigate pressure oscillations, backflows, and floodingduring storm events. A dynamic transient model was developed to simulate the transition from gravity flow to pressurized flow that wouldoccur during a storm event. The model is able to simulate pressurization with pipe-filling bore or gradual-flow regime transition.Numerical results compare well with experimental data on single pipe flows. Following a brief description of the model, the paperdiscusses the pressure transients simulated during the filling of the tunnels for both the original and improved designs.

DOI: 10.1061/ASCE0733-94292007133:101103

CE Database subject headings: Hydraulic transients; Numerical models; Drainage; Case reports; Georgia; Combined seweroverflow; Tunnels; Pressure; Municipal wastes.

Introduction

This study was conducted to support the design of the West AreaCombined Sewer Overflow CSO Storage Tunnel facilities of theCity of Atlanta. CSO combines sewage and surface runoff repre-senting a mixture of raw sewage, urban storm water, and resus-pended sewer sediment that present environmental concernsUSEPA 1995; He et al. 2006.

CSO systems are usually designed to operate on gravity free-surface flow during low-precipitation events. At higher rates ofprecipitation, the flow regime in parts of the system may transi-tion to pressurized flow. The pressurization usually starts at thedownstream end of the system due to the tunnel slope. As thetunnels fill, an air-water interface or pressurization front travelstoward the upstream end of the system Fig. 1. The regime withboth gravity and pressurized flows, called mixed flow, is highlydynamic Yen 1986, 2001. If inflow rate is significantly largerthan outflow rate, the speed with which the pressurization wavemoves upstream can be very significant. At the very end of thefilling process, when the upstream end of the tunnels get com-pletely filled, the velocity of the pressurization wave is so largethat it may cause pressure transients and backflow in the tunnels,

overflow at the shafts, flooding, damage to the sewer system inthe form of blowoff of dropshaft and manhole covers, and possi-bly even geysering water jets shooting vertically up into theatmosphere.

Many experimental and numerical studies on hydraulic tran-sients in conduits have been conducted over the years. Ghidaouiet al. 2005 has presented a comprehensive review of waterham-mer modeling and practice for full pressurized flows. Unsteadygravity flows in sewers have been traditionally modeled usingone-dimensional 1D continuity and momentum equations Yen1986. Recently Len et al. 2006 proposed a Godunov-typescheme to model unsteady gravity flows in sewer systems. Anappropriate model for mixed flows must be able to compute tran-sients in both pressurized and gravity flow regimes and predictthe pressurization front. Reviews of mixed flows has been madeby Li and McCorquodale 1999 and Fuamba 2002. Gomez andAchiaga 2001 conducted an experimental and numerical studyof two pressurization fronts developed from upstream and down-stream ends of a pipe. Pressure oscillations induced by trapped airin a horizontal pipe were studied both experimentally and numeri-cally by Zhou et al. 2002. Vasconcelos and Wright 2005 intheir experimental studies focused on surge intensity in a conduit.The writers found that the transients are maximized when a hy-draulic bore with high-pressure head fills the pipe cross section.

Two of the most common approaches to model mixed flowsare 1 the Priessman slot method; and 2 the interface trackingmethod ITM. The Priessmann slot method has been usedby among others Garcia-Navarro et al. 1994, Ji 1998, andTrajkovic et al. 1999. This method uses the Saint-Venant equa-tions throughout the flow domain. It simulates the pressurizedflow portion, assuming a hypothetical narrow slot at the crown ofthe pipe. The major drawback with this method is that it assumesventilated flow everywhere in the system and therefore cannotsimulate subatmospheric flow conditions. In addition, it is nu-merically unstable when the slot width must necessarily be smallto represent a large pressure-wave speed.

The ITM separates the gravity and pressurized flows in twoflow-regime domains and integrates across the interface as itmoves. This approach can simulate negative pressures and allow a

1Assistant Research Engineer, IIHR-Hydroscience and Engineering,Univ. of Iowa, 300 South Riverside Dr., Iowa City, IA 52242-1585.E-mail: [email protected]

2Professor and Research Engineer, IIHR-Hydroscience andEngineering, Univ. of Iowa, 300 South Riverside Dr., Iowa City,IA 52242-1585. E-mail: [email protected]

3Discipline DirectorTunnels, Jordan, Jones and Goulding in aJoint Venture with Hatch Mott MacDonald and Delon Hampton andAssociates, 6801 Governors Lake Parkway, Norcross, GA 30071. E-mail:[email protected]

Note. Discussion open until March 1, 2008. Separate discussions mustbe submitted for individual papers. To extend the closing date by onemonth, a written request must be filed with the ASCE Managing Editor.The manuscript for this paper was submitted for review and possiblepublication on July 6, 2005; approved on April 10, 2007. This paper ispart of the Journal of Hydraulic Engineering, Vol. 133, No. 10, October1, 2007. ASCE, ISSN 0733-9429/2007/10-11031110/$25.00.

JOURNAL OF HYDRAULIC ENGINEERING ASCE / OCTOBER 2007 / 1103

free-surface interface to develop only in ventilated points. Song etal. 1983, Cardle and Song 1988, and Guo and Song 1990treated the moving interface as a shock wave. They validated theirshock-fitting model against experimental data in pipelines andused it to simulate the flow in several sewer systems. Numericalresults of the shock-fitting model compared well with experimen-tal data for hydraulic jumps in ducts Ze-Yu 1996; Ze-Yu andChang-Zhi 1997. Wang et al. 2003 used the same model tosimulate mixed flow with air pockets. Fuamba 2002 used theshock-fitting model with three different approaches to simulatethe portions of tunnels with gravity or pressurized flows, obtain-ing good agreement with measurements.

The shock-fitting model is especially useful and works wellwhen the energy contained in the inflow is sufficient to create apipe-filling bore. The principal drawback of this model is that itneeds to maintain a bore even if the pressurization takes placewith gradually varied flow. Another disadvantage is that the flownear the interface is calculated with the characteristic method,which, at the moving interface, requires interpolations in an itera-tive calculation. These interpolations do not conserve mass, andsignificant errors can occur, in particular if the grid is coarse. Toovercome these problems, a refined grid must be used, and thecomputation becomes intensive.

To date, modeling of pressurization with gradual flow regimetransition has not been reported. The model presented in thisstudy is based on ITM and it includes a novel treatment of theair-water interface when the energy contained in the inflow isinsufficient to create a pipe-filling bore. The model is validatedwith experimental data in pipes.

In this paper, the model is used for an analysis of hydraulictransients occurring during tunnel filling and for development ofrecommendations for design changes to reduce adverse effects oftransients in the West Area Combined Sewer Overflow CSOStorage Tunnel facilities of the City of Atlanta.

Mathematical and Numerical Model

For the purposes of the hydraulic model, the drainage system isconsidered a network of 1D ducts connected by 0D componentssuch as shafts, junctions, pump, expansions/contractions, etc. Themixed flow in the ducts is modeled as two separate flow regimesgravity or pressurized flows using the ITM. The components arethe boundary conditions of the system.

Modeling of Gravity and Pressurized Flow RegimesThe continuity and momentum equations for pressurized flowsread as follows Streeter and Wylie 1967:

Ht

+a2

gVx

+ VSo + VHx

= 0 1

gHx

+ VVx

+Vt

+ S f = 0 2

The Saint-Venant equations for gravity flows are Streeter andWylie 1967

yt

+c2

gVx

+ Vyx

= 0 3

gyx

+ VVx

+Vt

+ gS f So = 0 4

where the friction slope is given by S f = fVV /2D for pressurizedflows and S f =n2VV /Rh4/3 for gravity flows. The gravity wavespeed is defined as c=gA /T. The cross-sectional area normal tothe flow for circular ducts is

A = D2 sin/8; cos/2 = 1 2y/D if y D/2D2 sin/2/4; cos/2 = 2y/D 1 if y D/25

The two partial differential equations 1 and 2 or 3 and4 are converted into four total differential equations using thecharacteristic method Streeter and Wylie 1967. The resultingequations for the positive characteristic line C+ and negative char-acteristic line C are

Pressurized Flow:

Cp+

dxdt

= V + a

dHdt

+a

gdVdt

+ VSo + aS f = 0Cpdxdt

= V a

dHdt

a

gdVdt

+ VSo aS f = 0 6

Fig. 1. Control volume for the moving interface

1104 / JOURNAL OF HYDRAULIC ENGINEERING ASCE / OCTOBER 2007

Gravity Flow:

Cfs+

dxdt

= V + c

dydt

+c

gdVdt

+ cS f So = 0Cfsdxdt

= V c

dydt

c

gdVdt

cS f So = 0 7

Interface Tracking MethodThe flow conditions near the air-water interface are calculatedusing either the shock-fitting model or a mass and momentumbalance in a control volume.

The shock-fitting model is appropriate when the energy con-tained in the inflow is sufficient to pressurize the flow through apipe-filling bore with high energy loss. The water depths andvelocities near the moving interface are obtained using two alge-braic shock-boundary conditions plus three characteristic equa-tions. Details of this model are found in Cardle and Song 1988.

If the velocity changes are more gradual, the acceleration ofthe flow between two adjacent sections can be neglected. Ex-amples of such a flow condition include pressurization in subcriti-cal flow after hydraulic jumps, and pressurization with moderateinflow rates in long, sloped, partially full conduits. In this case,the flow near the interface can be simulated using momentum andmass balance on a moving control volume surrounding the inter-face. Fig. 1 shows a generic control volume where a smoothpressurization takes place between Nodes I1 and I. Node I isin pressurized flow and Node I1 in gravity flow. The dottedline indicates the water surface. The interface moves toward NodeI1 by either an increase in pressure head or decrease in velocityin Node I due to a valve closure or pump failure downstream, orby an increase in velocity in Node I1 due to increase in inflowrate. As the pressurization wave moves towards I1, the waterelevation at this node rises. When the water level at I1 reachesthe crown of the pipe, the interface is shifted upstream and is nowlocated between Nodes I2 and I1. The mass and momentumequations in a control volume between Nodes I1 and I are

dAI1 Addt

x = AI1VI1 AdVI 8

0 = AI1VI12

AIVI2 + gyI1AI1 HI zI D/2Ad

+ xSoAI1 + Ad/2 9where y=yD /2+Cg. Eqs. 8 and 9 together with the positivecharacteristic equation for gravity flow, Cfs

+, and the negative

characteristic equation for pressurized flow, Cp, determine waterdepth and velocity at the stations adjacent to the interface as theinterface advances upstream. This method allows for accuratetracking of the interface conserving mass. The model can be usedfor depressurization using the corresponding variables in eachnode and the characteristic equations Cfs and Cp+.

Boundary ConditionsA component with Nc connections have 2Nc unknown variables,which can be determined using one mass conservation equation,Nc1 momentum equations, and Nc characteristic equations. De-tails of the component equations are given in Politano andOdgaard 2004.

All the shafts overflow if the water elevation reaches theground level. It is common to assume that overflowed water istemporarily contained at ground level at the top of the shafts Ji1998, and that the overflowed water reenters the system whenable. However, in the CSO system simulated herein, the overflowis diverted and cannot reenter the system; therefore the waterlevel in the shafts drops as soon as the pressure in the tunneldecreases.

The model equations are discretized using a fixed-grid methodwith a first-order finite-difference approximation. The resultingnonlinear equations are solved using the Newton-Raphsonmethod. The time step is selected as the smaller of two values,either that determined by the Courants criteria or the time it takesto produce pressurized flow in the subsequent node of the ITMmodel.

Comparison with Experimental Results

The model was validated with measurements of mixed flows incircular pipes by Cardle et al. 1989 and Trajkovic et al. 1999.

Cardle et al.s 1989 measurements were made in a 48.8 mlong 0.1626 m I.D. circular pipe with slope So=0.001. An ad-vancing interface was generated by a sudden gate closure at thedownstream end of the pipe. The variation in piezometric headwas measured in three points along the pipe, P1, P2, and P3,located at 9.1, 21.3, and 39.6 m, respectively, from the down-stream end of the pipe. The water level in the downstream reser-voir was at elevation of 0.15 m and the inflow rate was0.0068 m3/s. As seen in Fig. 2, there is good agreement betweenmeasurements and predicted piezometric head in the three points.However, the piezometric head in the measured jump as the in-terface advances past the three points is not as abrupt as pre-dicted. This might be because the gate closure in the experiment

Fig. 2. Comparison of measurements Cardle et al. 1989 andpredicted piezometric head in pipe flow following downstream gateclosure


occurred over a finite time, while the model assumes a suddenshutoff of all the flow.

Fig. 3 shows a comparison between measurements and com-puted piezometric heads in a circular pipe 10 m long, 0.10 m I.D.,on a slope So=0.027 Trajkovic et al. 1999. The points of mea-surements are located at 0.6 m P1 and 4.5 m P2 from thedownstream end. At the upstream end, a tank with overflow keptthe water level constant. The pressurization wave is generatedfrom a steady supercritical gravity flow condition due to suddenclosure of a sluice gate at the downstream end. In this case, thebore itself does not pressurize the pipe; the pressurization takesplace from a subcritical gravity flow condition. As seen in Fig. 3,the main features of the mixed transient flow are predicted by themodel; there is good agreement between experimental and nu-merical results. As in the previous simulation, the model overpre-dicts the height of the bore because of the assumption of suddenshutoff of flow at the downstream gate. After 30 s, a sudden re-opening of the valve caused a negative depressurization wave atthe downstream end. This situation is not expected to occur in theCSO system and was not contemplated in the numerical modelpresented in this paper. Future improvement of the model willinclude the prediction of negative and/or simultaneous waves.

West Area CSO Tunnel System

The model was used to predict the hydraulic transients in theWest Area CSO Tunnel System for the City of Atlanta. As shownin Fig. 4, the system consists of two 7.3-m diameter tunnels, onerunning from North Avenue to a Pump Station, the other fromClear Creek to a junction with the North Avenue tunnel. Thelengths of the tunnels, as originally designed, are 7,116 and6,349 m, respectively. To facilitate the conveyance to the pumpstation, the tunnels are laid on a slope of 0.001. The flow to thetunnels is received through three dropshafts: a 3.3-m diameterdropshaft at North Avenue, a 4.7-m diameter dropshaft at ClearCreek, and a 3.9-m diameter dropshaft at Tanyard. The Tanyarddropshaft is located at the upstream end of a short 3.4-m diametersubbranch to the Clear Creek branch. Three 12.2-m diameter con-struction shafts are located along the tunnels. The total storagecapacity of the system is about 5.7 105 m3.

The simulations were performed using the 25-year hydrographshown in Fig. 5. The initial condition was mixed flow with

the tunnels 60% full. Water was admitted to the system throughthe dropshafts and pumped out at the pump station at a rateof 3.72 m3/s. The distance between two grid points wasx=12.2 m. The Mannings roughness coefficient n=0.015 andthe speed of the pressure wave in water, a=762 m/s, were used.

The velocity and pressure were calculated as a function of timeat all grid points and plotted at key points. Simulations of theoriginal tunnel system design showed severe pressure oscillations,backflows, and overflows. An alternative network configurationwas proposed to mitigate these problems. Simulations showedthat the most effective and feasible improvements were 1 to letthe 12.3-m diameter Clear Creek and North Avenue constructionshafts be part of the flow system functioning as surge tanks and2 to design a 7.3-m diameter bypass shaft just upstream of thepump station. The improvements were so significant that consid-erations were subsequently made to increase the elevation of theoverall tunnel system by 12.2 m. The final simulations were madewith the tunnels at this higher elevation. An additional simulationwas made to determine at what time during the filling the inflowgates should be activated and closed to prevent overflow andbypass.

Hydraulic Transients in the Original and ImprovedTunnel System DesignsDuring the early stages of the storm, the flow in the tunnels is inmixed-flow regime; the interface between gravity and pressurizedflow is located in the North Avenue tunnel between the down-stream construction shaft and the Clear Creek branch. Upstreamof the interface, the water surface is below the crown of the tun-nels. As the tunnels fill, the interface propagates upstream. Thevelocity with which the interface travels upstream increases withtime as the inflow rate increases Fig. 5 and the volume availablefor storage becomes increasingly smaller.

Fig. 5 shows the rates of overflow in the dropshafts of theoriginal and improved designs. At about 2 h, Clear Creek andTanyard start to overflow. No overflow occurs in the North Av-enue dropshaft because it is further from the upstream end and theground level is higher. Over a period of about 40 min, the over-flow rate at Tanyard is greater than the inflow rate, meaning thatwater is flowing backward in the branch toward the dropshaft.The overflow in Tanyard is bigger and of longer duration, due inpart to the smaller tunnel diameter of the Tanyard branch. As

Fig. 3. Comparison of measurements Trajkovic et al. 1999 andpredicted piezometric head in pipe flow following downstream gateclosure

Fig. 4. West Area CSO tunnels system configuration for modelingpurposes


shown in the detail in Fig. 5, the overflows in the improved de-sign in both the Tanyard and Clear Creek dropshafts are smaller.

Fig. 6 shows cumulative water volumes as a function of time.The horizontal line designated tunnel system indicates theavailable storage volume of the tunnel system considering theinitial condition of 60% full. At any given time, the total volumeshown represents the total inflow volume less the volume that hasbeen pumped out. In this simulation, the 25-year hydrograph fillsthe tunnels in about 2 h. It is also seen that, given the initialcondition and pumping rate, only about 12% of the net inflow isstored in the tunnel system. When the system reaches capacity inthe original system, most of the water is released through thepump shaft, causing overflows at the pump station. In the im-proved design, the bypass handles most of the excess inflow andprevents overflow and flooding of the pump station. Althoughearly overflow at Tanyard and Clear Creek cannot be completelyprevented with the new design at the 25-year design storm event,both the magnitude of the cumulative volume during the overflowand the duration of overflow are significantly reduced.

Fig. 7 shows the water surface elevation/piezometric headmeasured from the tunnel invert for b the original design anda,c the improved design. Fig. 8 shows the velocities in the tun-nels. Positive velocities denote water flowing toward the pumpstation. As seen in Fig. 7, the interface reaches the North Avenueshaft after approximately 1.7 h, the Tanyard shaft at 1.9 h, and theClear Creek shaft after about 2 h. Note that when the interface orsurge front hits Clear Creek and the system reaches capacity,negative velocities occur in the tunnel at Clear Creek.

This backflow together with the inflow of water to the systemthrough the dropshaft causes the water level in the Clear Creekshaft to rise rapidly. The pressure is immediately transmitted asa pressure wave throughout the rest of the system, causingsignificant pressure oscillations in all of the dropshafts. It is seenthat the hydraulic transients generated when Tanyard and NorthAvenue pressurize are negligible compared with those developedwhen the pressurization wave generated in Clear Creek is trans-

mitted. Because of its upstream location, the Clear Creek drop-shaft reacts with particularly large pressure fluctuations.

As seen in Fig. 7b, in the original design, the pressure headdrops intermittently below the crown of the tunnel, allowing afree surface to develop before the next surge hits the shaft. A totalof five pressurization-depressurization waves occur at this loca-tion over a period of 4 min. As shown in Fig. 8a, the pressureoscillations are coincident with intermittent backflows. Whenthe pressurization wave hits Tanyard, large velocity fluctuationsare generated in the Tanyard tunnel about 4 m/s because ofthe smaller tunnel and dropshaft size. However, at this momentthe system is under pressure and no gravity flow develops in thetunnel.

Fig. 7d shows the piezometric head when the inflow gatesare closed to prevent overflows. The gates start to close when thesystem is 93% full. It is assumed that the gates close in 15 minand the inflow rate decreases linearly over this period of time. The

Fig. 5. Rates of inflows and overflows for 25-year hydrograph

Fig. 6. Cumulative volume in original and improved tunnel system


tunnels are 98% full when the gates are fully closed. After that thewater volume in the tunnels decreases at the rate of pumping.Note that when the gates start to close, the surge front has alreadyarrived at the North Avenue dropshaft; however, the associatedpressure oscillations are small, with little impact on the rest of thesystem.

The above simulations show that as the system reaches capac-ity, there is a potential for air entrapment, bubble collapse, andwaterhammer, which are important structural design concerns.

The simulations also show that by allowing the constructionshafts to act as surge tanks, the risk of such problems is reduced.As seen in Fig. 7c, when the improved tunnel system reachescapacity, pressure heads remain above the crown of the tunnel,preventing gravity flow from developing until the system starts todepressurize. In addition, in the improved design, no significantnegative velocities occur at Clear Creek and no backflow is gen-erated at Tanyard Fig. 8b. The simulations show that thebypass has little effect on the transients. This is because nosignificant bypass flow develops before the surge reaches theupstream end of the tunnel system and the entire system is pres-surized. However, the bypass is essential in controlling the ulti-mate water level in the pump station.

Toward the end of the storm, when runoff and inflow ratediminish, the overflow and water level in the shafts decrease, asshown in Fig. 7a. As the water is pumped out, the flow regimein the tunnel becomes mixed again at about 8.8 h. The subsequentpressure variation is smooth and responding to the changes ininflow hydrograph.

Fig. 9 shows the hydraulic grade lines HGL along the tunnelsat different times for the improved design. As seen in Fig. 9a,the North Avenue tunnel keeps a stable increase during the fillingprocess. The pressure wave generated at the Clear Creek drop-shaft when the system is full reaches this channel at 2.01 h. Afterthat, the pressure increases without serious oscillations. Details ofthe oscillations are in Fig. 7c. Similar behavior is observed inthe Tanyard branch. As seen in Fig. 9b, this channel is initiallyempty and starts to fill from the upstream as the water is admittedthrough the Tanyard dropshaft.

The oscillations generated when the system is completely full

Fig. 7. Piezometric heads in b original; a,c improved tunnelsystem; and d gates operating

Fig. 8. Velocities in a original; b improved tunnel system


are very small and affect only the upstream end of this tunnelduring a short period of time. As seen in Fig. 9c, the upstreamportion of the system is subjected to the most severe oscillations.Note the pressurization wave that is traveling upstream at 1.98 h.At this time, the pressure oscillations observed downstream of thesurge wave do not imply gravity flow since the water level isalways above the tunnel invert. Note also that the most significantoscillations occur in the portion of the tunnel upstream of theTanyard branch. The maximum pressure in the tunnels occursbefore the stabilization of the system, at 2.21 h, near Clear Creekdropshaft, and it is approximately 55 m.

Summary and Conclusions

This study has simulated the potential for hydraulic transients inthe West Area CSO tunnel system of the City of Atlanta. Different

design alternatives have been evaluated to mitigate the transients.The simulations were made using a dynamic, transient numericalmodel developed as part of the study. The model is based on theinterface tracking method and includes a novel treatment of theair-water interface when the energy contained in the inflow isinsufficient to create a pipe-filling bore. The characteristic methodis used to solve the regions of the system with pressurized orgravity flows. The numerical model is validated against experi-mental data.

Based on this study, recommendations were made to 1 allowthe upstream construction shafts to act as surge tanks to reduce oreliminate hydraulic transients; and 2 include a bypass near thedownstream end of the system to more effectively prevent over-flows and flooding in the pump station. Both recommendationswere adopted and will be incorporated into the final design of theCSO system of the City of Atlanta.

Notation

The following symbols are used in this paper:A flow area;

Ad tunnel area;a pressure-wave speed;

Cg distance from the center of the tunnel to the centroidof the flow cross-sectional area;

c gravity wave speed;D tunnel diameter;f Darcy-Weisbach friction factor;g acceleration due to gravity;H piezometric head measured from the tunnel invert;n Manning coefficient;

Rh hydraulic radius;Sf friction slope;So slope of tunnel;T top width of flow;t time;

V velocity;x distance along the tunnel;y water depth measured from tunnel invert; andy distance from the water surface to the center of

gravity of the flow area.

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Numerical Evaluation of Hydraulic Transientsin a Combined Sewer Overflow Tunnel System

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