velocity fields within sewers: an experimental study

Flow Measurement and Instrumentation 17 (2006) 282–290www.elsevier.com/locate/flowmeasinst

Velocity fields within sewers: An experimental study

Frederique Larrarte∗

Laboratoire Central des Ponts et Chaussees, Division Eau et Environnement, Route de Bouaye, BP 4129, 44341 Bouguenais Cedex, France

Received 15 June 2005

Abstract

Measuring the flow rate through sewer networks is necessary for a number of reasons. To achieve such measurements, precise knowledge ofthe hydrodynamic conditions of each potential measurement location proves critical. A research project is currently being conducted to improvethe representativeness of flow rate measurements recorded in man-entry sewers. Three objectives are being pursued as part of this project:

◦ assisting with the selection of a suitable measurement section;◦ designing for proper sensor implementation in a given section; and◦ setting up an appropriate system for processing the raw data provided by sensors.

This project relies upon numerical simulations; moreover, experimental devices have been developed and utilized to collect measurement datafor purposes of model validation. This paper will describe such experimental devices and presents the results obtained after several months ofinvestigation.c© 2006 Elsevier Ltd. All rights reserved.

Keywords: Velocity; Spatial sampling; Sewers

1. Introduction

While sewer systems have existed for many centuriesin European countries, legal requirements have becomeincreasingly stringent as a result of the May 1991 EuropeanCommunity Directive and the January 1992 French waterpolicy law, which stipulates that any town producing adaily pollutant load in excess of 900 kg must be equippedwith a wastewater collection network. Moreover, wastewatercollection systems are now recognized as an integral partof the wastewater pollution control process. Like anyindustrial process, wastewater collection requires measurementcapabilities for the real-time control of flows, as well as forperformance evaluation.

Sound sewer network management and minimization ofthe pollution loads discharged into rivers through combinedsewer overflows necessitate more in-depth knowledge ofthe flow rates and pollutant loads conveyed into the sewersystem. Exact knowledge of discharge volumes makes use of

∗ Tel.: +33 2 40 84 58 82; fax: +33 2 40 84 59 98.E-mail address: [email protected].

0955-5986/$ - see front matter c© 2006 Elsevier Ltd. All rights reserved.doi:10.1016/j.flowmeasinst.2006.08.001

the representativeness of velocities, as measured by sensors,with respect to the average velocity over a cross section.Various European research teams are currently working onsuch topics. In sampling velocity fields, [1] proposed anarray of acoustic Doppler sensors, yet this technique onlyyields a limited number of measurements in a cross-sectionand, furthermore, selecting the location of these points is notstraightforward. [2] used the CFD tool in order to calibrateflowmeters.

Our laboratory is involved with a research project aimed atimproving the representativeness of measurements recorded inman-entry sewers [3]. Three objectives are being pursued in thisproject:

◦ assisting with the selection of a suitable measurementsection;

◦ designing for proper sensor implementation in a givensection; and

◦ setting up an appropriate system for processing the raw dataprovided by sensors.

Since very little data are available for either oval or circularchannels, the current research project combines experimentalinvestigation inside actual man-entry sewers along with

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F. Larrarte / Flow Measurement and Instrumentation 17 (2006) 282–290 283

Nomenclature

b width of the free surface (m)F =

U√

gRhFroude number

g gravitational acceleration (m s−2)

h water level (m)hmax maximum water level (m)hmin minimum water level (m)I slope of the bottom (m m−1)

K Manning–Strickler coefficient (m5/2 s−1)

Re =U Rh

υReynolds number

Rh hydraulic radius (m)Sm wetted area of the vertical cross-section (m2)

Si elementary area (m2)

U flow velocity (m s−1)

Vi (ti ) local velocity measured at time ti (m s−1)

Vm mean velocity (m s−1)

Vms(ti ) Manning–Strickler velocity at time ti (m s−1)

Vms Manning–Strickler velocity calculated with thewater level at time ti (m s−1)

ν water viscosity (m2 s−1)

numerical modeling. Numerical models offer considerablepotential in representing the evolution of flow rates within asewer network, yet the one-dimensional computations, nowquite common in urban hydraulics, are unable to depict all thecomplexity associated with the hydraulic phenomena occurringin narrow (i.e. a free surface width/height ratio of less than 5)or compound channel flows, such as the dip phenomenon andsecondary currents. A three-dimensional Navier–Stokes solverhas therefore been used for this project. The experimentalcomponent provides the measurements necessary to validatethe numerical component. This paper focuses on obtainingfield data on observed velocities across a sewer section; it willdescribe the experimental devices employed and presents theresults derived after several months.

2. Experimental site and set-up

The experimental site chosen is located in an area called“Cordon Bleu”, a few kilometers upstream of the treatmentplant on the City of Nantes’ main sewer line (northwesternFrance). All wastewater generated from the northern part of theurban district is conveyed through this line, i.e. a populationequivalent of 600,000. Several reasons explain why this facilityis convenient for the purposes of our study. First, it is easilyaccessible thanks to a 2.86 m height and an oval channel with abench (see Fig. 1). Second, a number of sensors are already inplace within the main sewer (Fig. 2).

2.1. Continuously-monitored data

One water level gauge has been placed at the site’s upstreamextremity and another 130 m downstream at the other extremity(Fig. 2). For both devices, water height is calculated using thetime necessary for an ultrasonic signal emitted by the sensor

Fig. 1. Scheme of cross section and definition of parameters.

located at the upper sewer invert to reach the free surface andthen return. Over one stretch, continuous velocity monitoring iscarried out with an ultrasonic Doppler flowmeter that indicatesmaximum flow velocity (Fig. 2). Data are recorded every 6 min.

2.2. Velocity field samplers

An initial sequence of measurements has been conductedunder dry weather conditions using a fix-drop set-up. In orderto obtain a velocity map normal to the flow, the verticalcross-section was discretized into sampling points. At eachpoint, water velocity was measured three or four times withan electromagnetic velocimeter accurate to within ±2 mm/s(Fig. 3). After several trials, we found that the most efficientmanner to proceed consisted of taking measurements from topto bottom and then from the bench to the opposite wall.

Since the experimental area lies on a combined sewer,the water level, velocity and flow rate all substantiallyincrease during rainfall events (Fig. 4). For safety reasons,measurements using the fix-drop set-up can only be carried outduring dry weather periods, even though maximum flow ratesoccur during rainy periods.

A new experimental device has thus been developed topermit operations from the ground level in order to conductmeasurements regardless of the water level. Considerable carehas been taken not to interrupt wastewater flow for lengthyperiods. For this reason, some of the equipment is left in placewithin the sewer, and a number of elements are added for eachspecific measurement campaign. The atmosphere in the sewer isquite corrosive, hence the permanent device needs to be robust.The additional elements must be easy to handle since theyneed to be conveyed through the manhole (typically 1 m wide).Based on such considerations, a 2D sampler, called “Cerberes”,has been built (Fig. 5).

This machine differs from those proposed in [1] given thatthe sensors may be moved over the cross-section. “Cerberes”allows for up to three simultaneous measurements alonga vertical profile with three acoustic Doppler velocimeters

284 F. Larrarte / Flow Measurement and Instrumentation 17 (2006) 282–290

Fig. 2. Instrumentation layout over the experimental area.

Fig. 3. Fix-drop device during dry weather measurements.

located every 20 cm on a vertical jack. It seems particularlydifficult to perform instantaneous measurements [4] usingthese portable flowmeters. Each result actually represents themean value of two replicates, with each replicate being themean value of the instantaneous velocity gauged over a 10 speriod. This procedure complies with the NF EN ISO 748Standard [5]; it also complies with Doppler flow measurementguidelines [6] and the testing protocol for flowmeter technicalparameters [7]. Moreover, verification has been made hereinthat these flowmeters operate within a rather small volume,

3 cm long by 1.5 cm diameter, positioned 10 cm in front ofthe transducer.

These sensors are remote-controlled from the groundlevel. Once velocities have been simultaneously measured at3 points, the carriage is moved 10 cm to perform 3 additionalmeasurements. When velocities are measured on a verticalprofile, the carriage is shifted to the next profile location and soon. It thus becomes possible to scan the entire wetted area fromthe bottom to a maximum level of 1.5 m (which encompassesroughly 90% of the situations encountered during a given year).With “Cerberes”, 5–10 min are required to obtain a verticalvelocity profile (depending on water level and clogging, withgreater frequency when levels are high).

Fig. 6 shows that by using “Cerberes”, it is possible toperform a considerably greater number of measurements over ashorter time period than with the fix-drop set-up. Map durationincreases linearly with the maximum water level (the outliercorresponded to the first “Cerberes” high water map, andthe measurement team was not properly trained in remote-controlled measurement operations).

A practical metrological problem stems from driftingmaterial coming in contact with the flow and clogging thesensors. This clogging greatly affects results and provesdifficult to detect since the sensors are not visible. It has beendecided to replicate the measurement, within a minute, at each

Fig. 4. Ranges of water levels, velocities and rates in the experimental area.


Fig. 5. “Cerberes”: the 2D remote-controlled device.

measurement point. If the difference exceeds 0.05 m/s, theflowmeter is to be removed from the water and cleaned. In somecases, we were not able to perform any measurements at all,e.g. during a storm event occurring after a long dry period, thesensors were clogged by fallen leaves.

3. Results and discussion

The sewer used for these experiments features an ovalsection with a bench. The flow can be considered as fullyturbulent and sub-critical since:

• the Reynolds number Re =U Rh

υis greater than 10+5,

• the Froude number F =U

√gRh

= 0.4,

where U is the flow velocity, Rh the hydraulic radius whoserange lies between 0.3 and 0.6, g the gravitational acceleration

Table 1Hydraulic characteristics of the experimental area

Dry weather Rain weather

h10 (m) 0.60 Low rainfall h (m) 0.92V 10 (m s−1) 0.60 Low rainfall V (m s−1) 0.88h50 (m) 0.77 Medium rainfall h (m) 1.12V 50 (m s−1) 0.76 Medium rainfall V (m s−1) 0.92h90 (m) 0.89 Heavy rainfall h (m) 1.26V 90 (m s−1) 0.81 Heavy rainfall V (m s−1) 0.94

g = 9.81 m s−2 and ν the water viscosity with ν =

10−6 m2 s−1.Using the continuously-monitored data, it was possible to

characterize hydraulic conditions inside the sewer. Dry weatherperiods are defined as full days without any rain, along withstabilized velocity and water level cycles (Fig. 4). During suchdays (see Table 1), x% of the water levels are lower than hx ,where V x is the velocity measured in the area when water levelequals hx . All other days are defined as rainy days. Low rainfallamounts correspond to a cumulative rainfall depth over 72 h ofless than 5 mm and make up 40% of all rainfall events, whereasmedium rainfalls correspond to a cumulative depth of between5 and 10 mm (20% of all events) and heavy rainfalls correspondto a cumulative depth of greater than 10 mm (40% of all events).

For dry weather situations, the water level duringmeasurements remains below the bench, with the section beingnearly trapezoidal. In other cases, the water level rises abovethe bench and the section becomes compound.

Velocity measurements have been obtained for a wide arrayof situations, from summer dry weather periods to water levellowering after a storm. Table 2 lists the conditions, wherebyhmin and hmax are respectively the minimum and maximumwater levels during the measurement period, and Vms (hmin)

and Vms (hmax) the Manning–Strickler velocities calculatedwith the respective water levels. The Manning–Stricklervelocity is defined by:

Vms = K R2/3h I 1/2

with K = 70 being the Manning–Strickler coefficient for high-quality concrete walls, and I the bottom slope. In all cases,the ratio of maximum water level hmax over the free surface

Fig. 6. Evolution of the map duration as a function of the maximum water level.


(a) Water level from 0.60 to 0.68 m. (b) Water level from 0.66 to 0.75 m.

(c) Water level from 0.71 to 0.78 m. (d) Water level from 0.74 to 0.81 m.

Fig. 7. Fix-drop measurements, isovelocity map for dry weather situations.

Table 2Experimental situations

Set-up hmin hmax Vms Vms b Range(hmin) (hmax)

(m) (m) (m/s) (m/s) (m)

Fix drop 0.56 0.61 0.67 0.69 1.60 h10Fix drop 0.60 0.68 0.69 0.72 1.61 h10–h50Fix drop 0.66 0.75 0.71 0.75 1.63 h10–h50Fix drop 0.66 0.75 0.71 0.75 1.63 h10–h50Fix drop 0.69 0.75 0.73 0.75 1.63 h10–h50Fix drop 0.67 0.76 0.72 0.76 1.63 h10–h50Fix drop 0.68 0.76 0.72 0.76 1.63 h10–h50Fix drop 0.71 0.78 0.74 0.76 1.63 h10–h50Fix drop 0.70 0.79 0.73 0.77 1.63 h50Fix drop 0.74 0.81 0.75 0.77 1.64 h50–h90Cerberes 0.65 0.69 0.71 0.73 1.62 h10Cerberes 0.72 0.74 0.74 0.75 1.62 h50Cerberes 0.77 0.81 0.76 0.77 1.64 h50Cerberes 0.91 0.91 0.81 0.81 2.07 h90–lowCerberes 0.84 0.95 0.78 0.81 2.08 h90–lowCerberes 0.86 0.97 0.79 0.81 2.09 h90–lowCerberes 1.00 1.02 0.82 0.82 2.10 LowCerberes 1.01 1.06 0.82 0.83 2.11 LowCerberes 0.92 1.17 0.81 0.85 2.14 Low–mediumCerberes 1.16 1.22 0.84 0.86 2.15 Medium–high

width b lies between 1.6 and 2.2, which corresponds to a narrowchannel and, as previously noted in [8], maximum velocity canbe expected below the free surface, as a consequence of theso-called “dip phenomenon”. The range column pertains to thedaily hydraulic conditions in Table 1.

Figs. 7 through 10 present the iso-lines Vi (ti )/Vms(ti ),where local velocities Vi (ti ) are divided by Vms(ti ); theManning–Strickler velocity is calculated with the continuously-monitored water level recorded at time ti in order to makethese measurements comparable. As would be expected underhydraulic conditions with such narrow channels, the maximumvelocity indeed lies below the free surface. Velocity profilesdisplay a parabolic shape similar to those presented in [9] closeto rectangular channel walls, with an aspect ratio of less than3. Ref. [10] located the maximum velocity at 0.6h, with hbeing the water level. [11] illustrated the dip phenomenon withvelocity fields in a rectangular cross-section and demonstratedthat maximum velocity increases towards the free surface asthe width-to-height ratio increases. This finding is analogousto results in [12] on a rectangular channel. In the actual sewerherein, uncertainty on the location of maximum velocity hasbeen evaluated at 0.10 m due to the experimental vertical mesh.Fig. 11 shows that the location of maximum velocity may beconsidered both linearly increasing with the highest water leveland independent of the set-up. Flooding of the bench generatesa vertical translation on the order of 10%. These results areconsistent with the work in [13], which indicates velocitydistributions with a maximum velocity located between 0.5and 0.7hmax. This paper reveals the presence of inclinedsecondary currents, which we could not properly measure since“Cerberes” does not allow for conducting measurements on thebench.



(c) Water level from 0.77 to 0.81 m. (d) Water level constant at 0.91 m.

Fig. 8. “Cerberes” measurements, isovelocity map for dry weather situations.


Fig. 9. “Cerberes” measurements, isovelocity map for just submerged bank situations.

In order to neutralize flow rate evolution while scanninga cross-section, an adimensional mean velocity Vm/Vms iscalculated using an area method, as follows:

Vm/Vms =1

Sm

∑ (Vi (ti )

Vmsi (ti )Si

)(1)

where Sm is the wetted area of the vertical cross-sectionfor the maximum water level hmax, Si the elementary area,Vi (ti ) the local velocity measured at time ti , and Vmsi (ti ) theManning–Strickler velocity calculated with the water level attime ti .

A comparison of Figs. 7(b) and 8(b) shows the lack ofinfluence of the particular set-up on the ratio.

In this sewer configuration, flow remains sub-critical, yet thewater level changes between the first and last measurements,as seen in Table 2. Moreover, under high water conditions,the sewer exhibits a compound section. According to Table 3,even under such conditions, the ratio of mean velocity toManning–Strickler velocity remains between 0.90 and 1.02.This finding indicates that the Manning–Strickler law forcompound sections calculated from continuously-monitoredwater level data yields a good approximation of flow velocity,which could then be used as an initial condition in the numericalpart of this research.

From Fig. 12, it is observed that the maximum waterlevel exerts no influence on velocity field heterogeneities since



Fig. 10. “Cerberes” measurements, isovelocity map for a submerged bank situations.

Fig. 11. Location of the dip phenomenon as a function of the b/hmax ratio.

Table 3Evolution of the Vm/Vms and Vm/Max(Vi ) ratios

hmax (m) R1 = Vm/Vms R2 = Max(Vi /Vms (ti )) R1/R2 Min(Vi /Vms (ti )) Standard deviation Set-up

0.61 0.92 1.09 0.84 0.62 0.12 Fix drop0.68 0.93 1.08 0.86 0.70 0.11 Fix drop0.75 0.98 1.15 0.85 0.74 0.10 Fix drop0.75 0.98 1.14 0.86 0.72 0.09 Fix drop0.76 0.93 1.09 0.85 0.60 0.11 Fix drop0.76 0.95 1.10 0.86 0.71 0.10 Fix drop0.75 1.02 1.16 0.88 0.76 0.09 Fix drop0.79 0.96 1.10 0.87 0.73 0.09 Fix drop0.78 0.90 1.08 0.83 0.61 0.12 Fix drop0.81 0.95 1.09 0.87 0.65 0.10 Fix drop0.69 0.94 1.07 0.88 0.68 0.10 Cerberes0.74 0.97 1.15 0.84 0.71 0.11 Cerberes0.81 0.94 1.08 0.87 0.64 0.10 Cerberes0.91 0.97 1.12 0.87 0.72 0.10 Cerberes0.95 0.95 1.12 0.85 0.65 0.12 Cerberes0.97 0.97 1.11 0.88 0.76 0.11 Cerberes1.02 0.97 1.15 0.84 0.67 0.11 Cerberes1.06 0.96 1.14 0.84 0.52 0.12 Cerberes1.17 0.95 1.11 0.86 0.60 0.11 Cerberes1.22 0.98 1.14 0.86 0.69 0.10 Cerberes

parameters Vm/Vms , Min(Vi/Vms) and Max(Vi/Vms) remainnearly constant.

The ratio R1/R2 = [Vm/Vms]/Max(Vi/Vms(ti )) measuredexperimentally in the narrow, oval cross-section is just about


Fig. 12. Evolution of Vm/Vms , Max(Vi /Vms (ti )) and Min(Vi /Vms (ti )) as a function of hmax.

Fig. 13. Velocity distribution with dh = hmax − hmin.

constant at 0.86. Ref. [5] displays a ratio of mean velocity tomaximum velocity measured at the free surface of river flowsbetween 0.84 and 0.90. This result proves interesting from ametrological perspective given that ratios lying in the 0.80–0.90range are often used to calibrate flowmeters in sewers.

Fig. 13 presents the velocity distributions for velocityfield measurements performed using “Cerberes”. The 90%confidence interval is equal to 0.05 m/s. It can be observed thatthe distribution is not symmetrical since more than 50% of thevalues are less than 0.96, i.e. the mean value of the Vm/Vmsratio obtained with “Cerberes”. This result stems from theinfluence of the narrow channel with boundary layer effects dueto the walls. The curves are moving slightly to the right as waterlevel increases, which correlates with both the evolution ofvertical velocity profiles that flatten out as water level increasesand the accentuated dip phenomenon.

4. Conclusion

Despite some reliability problems due to the corrosive at-mosphere inside the sewer, the 2D “Cerberes” sampler was in-stalled in an actual sewer and operated successfully. A set ofexperimental cases, providing the velocity maps for low andhigh water levels, is already available for an egg-shaped sewer.

A fairly broad spectrum of flow conditions has been studied andthe dip phenomenon has been clearly demonstrated on commonsewer sections. This outcome would imply that the typical cal-ibration process relying on just a few points must be carefullyconducted in order to appreciate the actual mean and maximumvelocities through the cross-section. For situations involvingcompound sections, vortices similar to secondary currents havebeen observed yet could not be measured. The compound sec-tion Manning–Strickler law calculated from the continuously-monitored water level yields a good approximation of flowvelocity; such an approximation can then be used as an initialcondition in the numerical part of the project.

The experimental data will also be used to validatethe numerical data of the research project dedicated toimplementing sensors inside sewers.

In order to expand our database, our next steps call for:

• continuing the measurement campaign under other typesof hydraulic conditions, such as lower velocities and thepresence of sediment;

• conducting velocity measurements with other configurations(e.g. junctions, edges) in order to quantify velocity fieldheterogeneities and typical sensor representativeness; and

• associating a hydraulic study with sediment transport.


Acknowledgements

This work has been backed by GEMCEA, a Public InterestGroup for Assessing Measurements for Water and Sewerage.The author would like to thank the technical staffs of boththe Laboratoire Central des Ponts et Chaussees — DivisionEau & Environnement, and the Direction de l’Assainissementde la Communaute Urbaine de Nantes (Nantes MetropolitanWastewater Authority) for their valuable contributions to theseexperiments. The author would also like to express gratitude toC. Joannis for the many fruitful conversations held.

References

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velocity fields within sewers: an experimental study

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