Rhodamine WT tracer experiments to check flowmeasurements in sewers

Mathieu Lepot a,b,c,n, Adrien Momplot a, Gislain Lipeme Kouyi a, Jean-Luc Bertrand-Krajewski a

a University of Lyon, INSA Lyon, LGCIE (Laboratory of Civil & Environmental Engineering), F-69621 Villeurbanne cedex, Franceb Sepia Conseils, 53 rue de Turbigo, 75003 Paris, Francec Water Management Department, Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1 (Building 23), 2628 CN Delft, The Netherlands

a r t i c l e i n f o

Article history:Received 11 October 2013Received in revised form28 July 2014Accepted 19 August 2014Available online 30 August 2014

Keywords:Flow measurementUncertaintySewer systemRhodamine WTTracer experiment

a b s t r a c t

Flow meters are widely used in urban hydrology to assess discharges, volumes and transport of pollutantloads but may deliver wrong or biased results if they are not checked appropriately. In order to helpoperators to check flow meters and their discharge values, an operational protocol based on RhodamineWTtracer experiments is proposed, tested and applied to various case studies. It includes a detailed uncertaintyassessment, the reduction of the uncertainty in the injected mass of tracer and a complete data processing.Using Rhodamine WT as a tracer offers the following advantages: (i) low injection volume and mass,allowing tracer experiments even for high flow conditions, (ii) absence of Rhodamine WT in wastewater,which ensures low and stable background signal, (iii) on-line data acquisition at short time step with aportable fluorimeter. Tests show that the protocol provides accurate flow measurements when compared toreference values (electromagnetic flow measurements and salt tracer experiments), with repeated tracerinjections giving discharge values with relative standard uncertainties of approximately 5%. Field applica-tions confirm it is an efficient approach to improve the quality of flow measurements in sewers. After anin situ flow meter is checked for various values of discharge, a correction function can be established ifnecessary for each specific measurement site if there is no alternative solution to improve the measure-ments by changing the location and position of the sensor or by replacing it by a more appropriatetechnology. In its present state, the protocol can be applied as a routine method. As a complement, CFDmodeling is applied to one of the case studies to explain the causes of bias in flow meter measurements.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The increasing need for knowledge on the transfer of water andpollutants in urban hydrology and regulatory requirements haveled researchers and managers to install a growing number of flowmeters in sewer systems, overflow structures, stormwater tanksand other infrastructures. In spite of technological developments,flow meters used under free surface flow conditions in sewersystems may provide, in some cases, wrong measurements, parti-cularly in the following typical cases which are critical for velocitysensors like e.g. Doppler sensors: (i) very low flows with waterdepth less than approximately 10 cm (dry weather flow or verymoderate rainfall events), (ii) high flows with water depth higherthan 50–60 cm and high turbidity, (iii) complex cross sectiongeometries like man entry sewers equipped with sidewalks,(iv) positions of velocity sensors different from the central bottom

line of sewer pipes in fully developed flow conditions which maygenerate wrong interpretation of received signals. For such cases,discharge values provided by sensors need to be carefully checkedby independent methods like tracer experiments, exploration of thevelocity field with current meter or portable electromagnetic flowmeter or CFD modeling of velocity fields e.g. [1–3].

Tracer experiments are well known, especially with salt [1,4,5].However, salt, even if it is easily measured on line by meansof calibrated conductivity sensors, is not an ideal tracer for sewersystems. Indeed, there are at least two main drawbacks: (i) thepresence of a significant and fluctuating background level ofconductivity, and (ii) the need to inject a large mass of tracer incase of high flows or storm events and/or in wide cross sections.Tracers which cannot be measured on line (like e.g. lithiumchloride) are not considered for practical reasons. The use offluorescent tracers is of course not new [6], however only fewroutine applications are reported [4,7,8,9], especially for sewersystems.

This paper presents an operational protocol to check in situ flowmeters in sewers by means of tracer experiments with RhodamineWT, with examples of application. It is structured as follows:

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/flowmeasinst

Flow Measurement and Instrumentation

http://dx.doi.org/10.1016/j.flowmeasinst.2014.08.0100955-5986/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author at: Water Management Department, Faculty of CivilEngineering and Geosciences, Delft University of Technology, Stevinweg 1(Building 23), 2628 CN Delft, The Netherlands.

E-mail address: m.j.lepot@tudelft.nl (M. Lepot).

Flow Measurement and Instrumentation 40 (2014) 28–38

materials and experimental sites are presented in Section 2.1. Aftera reminder of the tracer diffusion theory, the protocol is detailedstep by step in Section 2.2, with complements about CFD modelingused for comparison in Section 2.3. In Section 3, two series ofexperiments are presented and discussed. The first series has beendesigned to test and compare the proposed protocol to referencemethods: an electromagnetic flow meter set up on a pressurizedpipe (Section 3.1) and salt tracer experiments (Section 3.2). In thesecond series, the protocol has been applied in combined sewers tosolve practical problems: a divergence between two flow meterslocated along the same sewer reach (Section 3.3) and the correctionof a rating curve for low water levels (Section 3.4). Final conclusionsand perspectives are then given.

2. Materials and methods

2.1. Materials and experimental sites

Tracer experiments were carried out with the following equip-ment: a fluorimeter (Turner Designs, SCUFA), an ultrasonic waterlevel sensor (Mobrey, MSP422), a data logger (Allborn, AllmenoV2290-5), Turner Designs Rhodamine WT commercial (21.33%w/w) or diluted solutions, adjustable laboratory pipettes for tracerinjection (Nichiryo, Nichipet EX 0,5–10, 10–100 and 100–1000 mL)and a laptop.

Initial testing experiments were carried out in two sites:

� A pilot scale open channel in the Laboratory of Fluid Mechanicsand Acoustics (LMFA) of INSA Lyon. The channel is 9 m long,0.25 m wide, with a 0.03% slope. A control valve and an

electromagnetic flow meter (Krohne, Aquaflux F/6) are installedon the return flow pressure pipe: (i) the flow is set to 5 L/s, (ii) thewater depth is constant (9 cm) along the channel: the down-stream level is set to the normal level by means of a swivel wall.

� The Django Reinhardt 1.6 m circular sewer in Chassieu (Lyon,France), with a slope of 1%. This pipe drains storm and coolingwaters from a 185 ha industrial catchment. The discharge isdetermined from simultaneous measurements of water depthby an ultrasonic sensor (Milltronics, XRS-5) and of mean flowvelocity by a Doppler sensor (Nivus, OCM Pro). The DjangoReinhardt sewer is one of the OTHU (Field Observatory onurban drainage – OTHU, www.othu.org) measurement sites.From upstream to downstream of the experimental reach, thewater depth varies from 2 to 7 cm, providing appropriatemeasurement conditions for the fluorimeter [10].

Later on, tracer experiments have been carried out for applica-tion in two combined sewers:

� The first one is a man entry trunk sewer in the center of GreaterLyon, with a double sidewalk (Fig. 1): two measurement pointsalong the sewer have been used. The upstream point (QuaiArloing, mean slope of 0.3%) is located immediately down-stream a pumping station; the downstream point (Quai desEtroits, mean slope of 0.2%) is located approximately 3.7 kmdownstream the first one. During the experiments, dischargesranged from 250 to 480 L/s (corresponding to water levelsbetween 0.22 and 0.35 m) in the upstream site and from 320 to550 L/s (corresponding to water levels between 0.55 and0.65 m) in the downstream site.

Nomenclature

α, β angles of the Doppler sensor, degbi coefficients variousC concentration of tracer, kg/m3

CCORR concentration of tracer after calibration, correctionand data processing, kg/m3

CINJ concentration of the injected tracer solution, kg/m3

cM tracer concentration measured by the fluorimeter,kg/m3

CM estimated true tracer concentration from the calibra-tion function, kg/m3

csV tracer concentration of standard solution, kg/m3

CsV estimated true tracer concentration of standard solu-tion from the calibration function, kg/m3

dk distance between the Doppler sensor and the pointk, m

dt data acquisition time step, sg gravity acceleration, m/s2

h water level, mH hydraulic diameter, mI slope of the sewer reach, m/mK number of injections –

KX longitudinal dispersion coefficient, m2/sMINJ injected mass of tracer, kgυ kinematic viscosity, m2/sP pressure, Paρ fluid density, kg/m3

QCORRECTED discharge corrected by a correction function, m3/sQRHO,F discharge evaluated from K injections, m3/sQRHO,i discharge evaluated from injection i, m3/s

QTEST discharge given by the tested flow meter, m3/sRH hydraulic radius, ms standard deviation variousS wet cross section, m2

t time, sTD start time of the tracer pulse transit dateTF end time of the tracer pulse transit dateu(CCORR) standard uncertainty in CCORR, kg/m3

u(CINJ) standard uncertainty in CINJ, kg/m3

u(cM) standard uncertainty in cM, kg/m3

u(csV) standard uncertainty in csV, kg/m3

u(MINJ) standard uncertainty in MINJ, kgu(QRHO,F) standard uncertainty in QRHO,F, m3/su(QRHO,i) standard uncertainty in QRHO,i, m3/su(QTEST) standard uncertainty in QTEST, m3/su(VINJ) standard uncertainty in VINJ, m3

v average velocity, m/svn friction velocity, m/svi time averaged velocity along the direction i, m/sv0iv

0j Reynolds stresses, m2/s2

vMC averaged computed velocity in the Doppler measure-ment cone in the central position, m/s

vML averaged computed velocity in the Doppler measure-ment cone in the lateral position, m/s

vRHO averaged velocity estimated by tracer experiment, m/sVINJ injected volume of tracer solution, m3

vk computed velocity at point k, m/sW width of the free surface, mx distance from the injection point, mxi space coordinates in the direction i, mz vertical free-surface elevation, m

M. Lepot et al. / Flow Measurement and Instrumentation 40 (2014) 28–38 29

� The second site is a 500 mm circular sewer (mean slope of0.014%) in Genas, East of Greater Lyon, France. Tracer experi-ments were used to establish a rating curve for water depthslower than 10 cm. Two probes have been used to measureflows: an ultrasonic water level and a Doppler were both set upin a manhole. For practical reasons due to limited access intothe sewer, boundary conditions are not known in this reach.

2.2. Methods

2.2.1. Theoretical backgroundFlow measurement by tracer injection requires the checking of

in situ both hydraulic and chemical conditions in order to ensurereliable experiments and results. The main required conditionsand assumptions to perform tracer experiments are as follows:(i) constant background fluorescence and turbidity signals, mea-sured by the fluorimeter and a turbidity sensor before and afterthe transit of the tracer pulses, (ii) constant discharge, which isestimated by means of continuous measurement of the waterlevel, assuming that the flow is permanent and uniform during thefew minutes of the experiments, (iii) negligible adsorption oftracer on suspended solids which are present at significantconcentrations in sewers, and (iv) no inflow or outflow along themeasurement reach to ensure the tracer mass balance.

Two key parameters have to be determined for each tracerexperiment. The first one is the length of mixing, defined as thedistance between injection and measurement points ensuring ahomogeneous tracer concentration through the measurementcross-section. This length typically ranges from 75 (if the injection

is done at the center of the sewer) to 150 (if it is done along thewall of the sewer) times the largest hydraulic scale such as waterlevel, width of free surface in the cross-section, etc. [5].

The second one is the mass of tracer to be injected. Accordingto [4], it can be determined by solving the equation of longitudinaldispersion (Eq. (1)):

∂C∂t

þv� ∂C∂x

¼ Kx �∂2C∂x2

ð1Þ

with C the tracer concentration (kg/m3), v the mean flow velocity(m/s), KX the longitudinal dispersion coefficient (m2/s), t the timeelapsed since the injection of tracer (s) and x the distancemeasured from the injection point (m). The most importantquestion is the setting of KX which is assumed to be constantalong the measurement reach and depends on the geometry of thecross section. In this study, KX was calculated from two equations:Eq. (2) given in [4] and Eqs. (3a) and (3b) given in [9]:

Kx ¼ 6� h�ffiffiffiffiffiffiffighI

pð2Þ

Kx ¼ 5:92� vvn

� �1:43

� WH

� �0:62

ð3aÞ

vn ¼ffiffiffiffiffiffiffiffiffiffigRHI

pð3bÞ

with h the water depth (m), g the acceleration of gravity (m/s2),I the sewer slope (m/m), vn the friction velocity (m/s), RH thehydraulic radius (m), W the width at the free surface (m) and H(m) the hydraulic diameter (ratio between the wet cross-sectionarea and the width at the free surface).

Eq. (2) is applicable for simple cross sections (like e.g. circularor egg-shape sections) and strait measurement reaches. Eqs. (3a)and (3b) are recommended for more complex sections (like e.g.complex sections with lateral sidewalks) and meandering reaches[9]. Other methods for computing KX are proposed in [9] and canbe used depending on the characteristics of the section and of themeasurement reach.

The analytical standard solution (Eq. (4)) of Eq. (1) is often usedin order to estimate initial values of the mass of tracer to beinjected.

C x; tð Þ ¼ MINJ

S � ffiffiffiffiffiffiffiffiffiffiffiffiffi4πKxt

p � e� x� v�tð Þ24Kxt ð4Þ

withMINJ the mass of tracer (kg) to be injected and S the wet cross-section area (m2). The mean velocity u in Eq. (4) can be measuredby either the flow meter to be checked (case of the experimentsdescribed in this paper) or by another sensor.

According to [11], measurements of RhodamineWT concentrationsin water are sensitive to various factors such as temperature (thisinfluence is corrected automatically by the fluorimeter), dissolvedoxygen, light, pH (if it is lower than 5 or higher than 10), water level,chlorine and turbidity. For practical reasons, only turbidity wasmeasured continuously during the tracer experiments reported in thispaper. It generally appeared almost constant during the few minutesof each tracer experiment. Other factors are negligible under usualconditions encountered in sewers, provided some precautions areapplied like storage of Rhodamine WT in the dark, dilution ofcommercial solutions with deionized water, slow stirring duringhandling and experiments. Downstreamwastewater treatment plants,the presence of residuals of treatment chemicals like e.g. ferric chloridemay interfere with RhodamineWTmeasurements. It is important thatthe experimenter checks all possible sources of errors and interfer-ences before performing tracer experiments.

Fig. 1. Cross section at the downstream site Quai des Etroits (source: Greater Lyon).

M. Lepot et al. / Flow Measurement and Instrumentation 40 (2014) 28–3830

2.2.2. Operational protocolThe proposed operational protocol is divided in nine steps

(Fig. 2). In the following, standard uncertainties correspond to thedefinition given in international standards [12,13].

1. Fluorimeter calibration. In the laboratory, two successivecalibrations of the fluorimeter are recommended. The firstsimple one based only on three points according to themanufacturer protocol [10] is indeed not sufficient to assessuncertainties in measurements and calibration function. There-fore a second step calibration is performed, using a set of N¼14(in this study) Rhodamine WT standard solutions with con-centration csV ranging from 0 to 130 g/m3, with a step of10 g/m3, obtained by successive dilutions of the RhodamineWT commercial solution. The commercial solution has a massconcentration equal to 21.3372.5%. Dilutions are made withdemineralized water. Standard uncertainties u(csV) (in g/m3)are determined for each standard solution. From n¼60 (in thisstudy) repeated measurements for each standard solution, themeasured concentrations cM delivered by the fluorimeter andtheir standard uncertainties u(cM) (in g/m3) are computed.Uncertainties in concentrations of standard solutions csV andin measurement results cM are accounted for in the determina-tion of the calibration function (Eq. (5)) (see Fig. 3), by applyingthe Williamson regression method which minimizes the sum Sas given by Eq. (6) [14–16]. Variances and covariances of thecalibration function coefficients bi are calculated analytically forstraight lines or by means of Monte Carlo simulations forpolynomials of higher degrees [17].

cM ¼ ∑iMAX

i ¼ 0bi � csV i ð5Þ

with iMAX the degree of the polynomial calibration functionfrom 1 to 3, and bi the calibration coefficients.

S¼ ∑N

i ¼ 1

1u2 csVð Þ � CV �csVð Þ2þ 1

u2 cMð Þ � CM�cMð Þ2� �

ð6Þ

with CM and CV respectively the measured and standard con-centrations estimated by the Williamson regression (in g/m3).In Fig. 3, three calibration functions of the fluorimeter areshown: straight line, polynomials of second and third degrees.Between 0 and 130 g/m3, the response of the fluorimeter isalmost linear, a straight line calibration function is thereforeappropriate. Other calibrations made with more concentratedstandard solutions (up to 300 g/m3, not shown in this paper)revealed, in agreement with [10], that linearity is not verifybeyond 130 g/m3. Consequently, 2nd or 3rd degree polynomialfunctions are necessary in such cases.

2. Study of injection pipettes. In the laboratory, standard uncer-tainties u(VINJ) in volumes VINJ delivered by adjustable injectionpipettes were experimentally estimated by means of repeated(n¼25 in this study) measurements of the mass of watercorresponding to each volume VINJ. Values of u(VINJ) rangedfrom 0.6 to 3 mL for VINJ values between 10 and 100 mL for a10–100 mL pipette.

3. Tracer solutions. In the laboratory, two operational tracersolutions are prepared by dilution of the commercial solution,with dilution ratio respectively equal to 10 and 100.

4. Determination of MINJ and of its standard uncertainty. The aim is todetermine the pair of variables (concentration CINJ and volume VINJ)and consequently the mass MINJ to be injected and its standarduncertainty u(MINJ), by accounting for hydraulic conditions (flowvelocity, water depth, wet cross-section area) and the acceptable

Fig. 2. Scheme of the proposed protocol.

M. Lepot et al. / Flow Measurement and Instrumentation 40 (2014) 28–38 31

maximum Rhodamine WT concentration in the measurementsection to remain in the range of the fluorimeter calibration. Fromall possible pairs, the pairs (CINJ, VINJ) leading to a downstreammaximum concentration close to the expected value are thenfurther evaluated and the pair providing the lowest standarduncertainty u(MINJ) is eventually selected. During this study, theselected pairs (CINJ, VINJ) varied from (2.133 w/w, 200 mL) at theLMFA to (21.33 w/w, 4.7 mL) in the Greater Lyon.

5. Injection and on-line measurement. After injection of the tracermass MINJ in the flow, the Rhodamine WT concentration ismeasured by the fluorimeter and recorded at the downstreammeasurement section with a time step dt¼1 s. The recordedtime series is the raw signal.

6. Raw data correction. The inverse of the calibration function(Eq. (5)) is used to transform the raw time series into acorrected time series containing the most likely true valuesof the Rhodamine WT concentration and of its standarduncertainty.

7. Data processing. The corrected signal time series are analyzed inorder to estimate the background concentration, the beginningand the end of the tracer pulse transit, to correct some errorsand smooth the signal if necessary due to measurementartefacts, Tyndall and hidden effects due to suspended parti-cles, and possible additional fluorescence due to other sub-stances in the effluent [8]. The last three elements constitutethe background noise which consistency must be checked bycareful observation of the signal before and after the tracerpulse transit. The start (TD) and end (TF) times of the tracerpulse transit are identified from the corrected signal, when thesignal becomes significantly different from (respectively equalto) the background noise, the uncertainties being accounted for[18]. Artefacts, random measurement errors or abnormal dis-ruption of the signal are detected by tests on ascending anddescending gradients. At the end of this processing, the signalis noted CCORR (g/m3) for further calculations. Fig. 4 illustratesthe data processing: TD and TF are detected automatically whenthe signal is significantly different from background noiserepresented by horizontal lines. Artefacts, marked by circles,are then manually corrected.

8. Computation of discharge and of its uncertainty. The discharge QRHO,i

(m3/s) is computed for each injection i by means of Eq. (7).

QRHO;i ¼CINJ � VINJR TF

t ¼ TDCCORR tð Þ � dtð Þ

ð7Þ

The standard uncertainty u(QRHO,i) (m3/s) can be calculated by thelaw of propagation of uncertainties [12] (Eqs. (8a)–(8c)):

u QRHO;i� �¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

u2 MINJ� �þu2 Measurementð Þ

qð8aÞ

u2 MINJ� �¼ u2 CINJ

� �� VINJ2þu2 VINJ

� �� CINJ2

R TFt ¼ TD

CCORR tð Þ � dtð Þ 2 ð8bÞ

u2 Measurementð Þ ¼ ∑TF

t ¼ TD

u2 CCORR tð Þð Þ

� CINJ � VINJR TFt ¼ TD

CCORR tð Þ � dtð Þ 2

264

3752

ð8cÞ

with u(CINJ) the standard uncertainty in the injected concentration(g/m3) and u(CCORR (t)) the standard uncertainty in the correctedmeasured concentration (g/m3) evaluated from the fluorimetercalibration experiment.In the case of K repeated injections to measure a given dischargewith calculations made as just described above, the final value ofthe flow QRHO,F (m3/s) is the mean of K flow values (Eq. (9))and its standard uncertainty u(QRHO,F) (m3/s) is calculated withEq. (10).

QRHO;F ¼∑K

i ¼ 1QRHO;i

Kð9Þ

u QRHO;F� �¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

K2 ∑K

i ¼ 1u2 QRHO;i

� �þ14t2 0:975;K�1ð Þs2 QRHO;ið Þ

sð10Þ

with t(0.975, K�1) the Student coefficient with K�1 degrees offreedom and a confidence level of 95%, and s²(QRHO,i) the square ofthe standard deviation of the K values of QRHO,i (m3/s).An alternative approach to estimate the mean discharge and itsuncertainty is the Monte Carlo simulation method [13]. Ourexperience indicates that equivalent results are obtained for thecases presented in this paper.

9. Verification of the tested flowmeter. The values QTEST provided bythe tested flow meter and QRHO,F are then compared. If inequal-ity (11) is verified, the difference between the two values islower than its extended uncertainty. In this case, one mayconclude (with a level of risk of approximately 5%) that thetested flow meter and the tracer experiment give not sig-nificantly distinguishable discharge values. By considering the

Fig. 3. Example of calibration functions of the fluorimeter.

M. Lepot et al. / Flow Measurement and Instrumentation 40 (2014) 28–3832

tracer experiment value as the reference value, the tested flowmeter is considered as unbiased and is validated for this case. Ifnot, the flow meter is not reliable and adjustment and/orcorrection are needed.

QRHO;F�QTEST

�� ��r2�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiu2 QRHO;F

� �þu2 QTESTð Þq

ð11Þ

with u(QTEST) the standard uncertainty (m3/s) in QTEST calculatedaccording to standard methods [12,13,19].

2.3. CFD modeling

As a complement to the application of the proposed protocol inthe site Quai des Etroits, CFD modeling [20] has been carried out inorder to provide another assessment of the Doppler sensorresponse according to its location, aiming to evaluate the hypoth-esis that the location of the sensor is the main factor explainingthe systematic underestimation of flow rates. The discharge issimulated by applying the RANS (Reynolds time-Average NavierStokes) method with the commercial code ANSYS FLUENT [21].The RANS approach for incompressible fluids is based on theresolution of (i) the continuity equation in the whole domain withthe Eulerian approach (Eq. (12)) and (ii) the momentum equationfor steady flow condition (Eq. (13)) [22].

∂vi∂xi

¼ 0 ð12Þ

vj∂vi∂xj

¼ �g∂z∂xi

�1ρ

∂P∂xi

þ ∂∂xj

v∂vi∂xj

�v0iv0j

� �ð13Þ

with indexes i and j¼1, 2 and 3, where xi (m) represents the threespace coordinate axes, vi (m/s) the time-averaged velocity alongaxis i, z (m) the vertical free-surface elevation, P (Pa) the pressure,ρ (kg/m3) the fluid density, ν (m2/s) the kinematic viscosity andvi'vj' (m

2/s2) the Reynolds stresses with the “prime sign” referringto time fluctuations.

Solving Eqs. (12) and (13) requires a turbulence model to set theReynolds stresses. In order to obtain an accurate representation ofthe velocity field, the Reynolds Stress Model (RSM) has been chosen[23]. The wall law is the scalable wall function [24]. The domain isdefined as a 14 m long reach in order to get a fully developed velocityprofile at the point where the Doppler sensor is located. Theboundary conditions are given in Table 1. CFD modeling results

strongly depend on choices, options and conditions defined by thesoftware user. However, as a fully detailed presentation of the CFDmodeling aspects (choice of turbulence models, mesh, discretizationscheme and solver, etc.) is beyond the scope of this paper, the readerwill find more information in [25–27].

Once the convergence of the CFD model is obtained for all cases(all residual quantities are lower than 0.0001), the velocity field isfully developed beyond a distance of x¼9 m from the inlet. In thecross-sections beyond x¼9 m, a 1.4 m long cone with an apertureangle α¼151 and a beam angle β¼151 (sensor characteristics givenby the manufacturer technical manual) represents the domaintheoretically explored by the Doppler sensor (Figs. 5 and 6). A seriesof seven circular cross sections in the cone between 0.2 and 1.4 mfrom the Doppler sensor are used to simulate the Doppler sensormeasurement process (Fig. 5). For each circular cross section l, thecomputed velocity vk (m/s) projected in the direction of the Dopplersensor in each mesh cell k is used to estimate the theoretical meanflow velocity vML (m/s) in the cone as it should be measured by thesensor from its lateral position 14 cm above the sewer pipe invert(Fig. 7 left). vML is determined by Eq. (14) which was derived frominvestigations carried out by [28].

vML ¼∑n

k ¼ 1vkdk

4

∑nk ¼ 1

1dk

4

ð14Þ

where dk is the distance between Doppler sensor and point k, and nthe total number of points in all cross-sections.

Similar calculations are also carried out for the case where theDoppler sensor is positioned centrally on the pipe invert (theore-tical best sensor position, Fig. 7 right) and no longer along the wall.From the CFD modeling results, it is then possible to estimate thetheoretical mean flow velocity vMC (m/s) in the cone as it shouldbe measured by the sensor from its central position in the sewerpipe again by Eq. (14).

For the three discharge cases, the mean flow velocity vRHO iscalculated from both the discharge QRHO (m3/s) and the wet crosssection S (m2), by means of Eq. (15):

vRHO ¼ QRHO

S hð Þ ð15Þ

with h (m) the water depth measured during the tracer experimentsand S(h) (m2) the relation established for the sewer geometry.

Fig. 4. Automatic identification of start and end of the Rhodamine WT transit pulse.

M. Lepot et al. / Flow Measurement and Instrumentation 40 (2014) 28–38 33

Uncertainties in all variables are estimated by means of the lawof propagation of uncertainties [12]. It is then possible to comparevRHO, vML and vMC.

3. Results and discussion

3.1. Laboratory flow measurements

For the experiments at LMFA, the flow in the pilot scale channelwas set equal to 5 L/s with a 95% confidence interval equal to [4.9,5.1], i.e.7 2% of the nominal value. Six injections were performed.The mean flow calculated from the six tracer experiments is equalto 5.23 L/s and its 95% confidence interval is [5.00, 5.46]. Thedifference between set and measured flows is 0.23 L/s and itsextended uncertainty corresponding to a 95% confidence intervalis 0.25 L/s. According to Eq. (11), both discharge values arecoherent and not significantly different each other, which validatesthe Rhodamine WT tracer experiments. However, the extendeduncertainty is relatively large for controlled laboratory conditions.This may be due to the fact that, on this pre-existing hydraulicbench, the distance between injection and measurement points isslightly less than the recommended length of mixing, leading topossible heterogeneities in the Rhodamine WT concentration atthe measurement point.

3.2. Comparison between rhodamine WT and salt tracer experiments

Comparative tracer experiments with salt (used as reference)and Rhodamine WT have been carried out at Chassieu during dryweather low flow conditions. Injection volumes were respectively20 mL of Rhodamine WT commercial solution and 200 mL of de-icing salt at a concentration of 180 g/L. Five injections of salt andRhodamine WT were performed alternately.

Results are shown in Fig. 8: discharges are represented byvertical bars for each injection, average values and their 95%confidence intervals are represented by continuous and dashedhorizontal lines respectively. With salt, the measured dischargesvary between 2.03 and 2.62 L/s, the average discharge is 2.33 L/sand its 95% confidence interval is [2.30, 2.36]. With RhodamineWT, the measured discharges vary between 2.02 and 2.62 L/s, theaverage discharge is 2.28 L/s and its 95% confidence interval is[2.19, 2.39]. The difference between the average discharges is0.06 L/s and its enlarged uncertainty is 0.12 L/s. Salt and Rhoda-mine WT experiments thus provide equivalent results whenuncertainties are accounted for.

In Fig. 9, average discharges measured by (i) Rhodamine WT,(ii) salt tracer experiments and (iii) the in situ flow meter areshown with their 95% confidence intervals on the left graph. Theright graph shows the differences V between pairs of mean valuesand their extended uncertainties u(V): V�RS is the differencebetween Rhodamine WT and salt tracer experiments mean dis-charges, V�RF between Rhodamine WT tracer experiments andthe in situ flow meter, and V�FS between the in situ flow meterand salt tracer experiments, and Unc(V�xx) for their respectiveextended uncertainties.

The in situ flow meter located at the outlet of the sewer systemindicated a discharge value QTEST close to 1 L/s, compared toapproximately 2.3 L/s obtained by both types of tracer experi-ments. The difference of 1.3 L/s (i.e. 130% of the value QTEST)indicates that the flow meter does not deliver reliable resultsunder these low flow conditions, where the water level is close to2 cm. With such a low water level, the Doppler sensor itself is

Table 1Boundary conditions for CFD modeling. The three cases have been defined according to the results obtained with tracer experiments. The associated water depth is measuredby means of the ultrasonic sensor installed in the sewer.

Discharge QRHO (L/s) 550 480 320Upstream condition: uniform velocity set at inlet boundary Vuc (m/s) 0.69 0.602 0.401Downstream condition: water depth imposed at the outlet hdc (m) 0.7 0.65 0.56Roughness set for walls k (m) 0.00167 0.00167 0.00167

Flow direction

Doppler measurement cone

sensor β

α

Fig. 5. Doppler sensor measurement cone, with the seven circular cross sectionsused to estimate the mean velocity within the measurement cone from the CFDmodeling velocity field.

Fig. 6. Velocity field and vectors obtained by CFD modeling at the same location asthe in situ Doppler sensor located on the right side wall, in case of dischargeQRHO¼550 L/s and water level h¼0.7 m. The color scale indicates the values of thevelocities along the x-axis, perpendicularly to the wet cross section (here labeledU-velocity), while gray arrows indicate magnitudes and directions of velocitiesalong the y-axis and z-axis (here labeled V-W spanwise velocities). The Dopplermeasurement cone contains the Prandtl secondary flows.

14 c

m

Fig. 7. Scheme of the position of the Doppler sensor in the sewer and of itsmeasurement cone. Left: lateral position 14 cm above the pipe invert in Quai desEtroits; right: theoretical best central position on the pipe invert.

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intrusive and modifies the local velocity distribution around itsbody [2]. The water level is not sufficient to deliver a correctvelocity value. In addition, in the Chassieu sewer, the water depthand velocity sensors are located a few meters one from each other,which was not appropriate as the observed in situ hydraulicconditions corresponded to permanent but non-uniform flow,which led to an additional error in the determination of the valueof QTEST.

3.3. In situ flow meter checking with rhodamine WT tracerexperiments

The field tests were carried out during two consecutive morn-ings at the Greater Lyon sites Quai Arloing and Quai des Etroits.These sites were selected as the Metrology Department of theGreater Lyon suspected that in situ flow meters were not deliver-ing reliable values. According to the previous tests of the protocolat LMFA and in Chassieu, the tracer experiment values measuredin Quai Arloing and Quai des Etroits were assumed to be truevalues. Results of the field tests are presented in Fig. 10: discharges

measured with a 6 min time step by the in situ flow meters aregiven on the x-axis, and the discharges measured by the tracerexperiments are given on the y-axis, respectively on the left andright graphs for Quai Arloing and Quai des Etroits.

At Quai Arloing, which is located just downstream a pumpingstation, the results suggest that the in situ flow meter eitheroverestimates or underestimates the true discharges measured bytracer experiments. Indeed, all in situ measured values are around350 L/s (Fig. 10 left). This phenomenon is mainly due to the factthat, downstream the pumping station, discharges are varyingvery fast over a few minutes, depending on the pumping regime(starts and stops of pumps): this is detected and measured bytracer experiments, but not by the in situ flow meter whichaverages values over a few number of 6 min time steps accordingto the settings of the Greater Lyon Scada system. However, themean discharge value calculated from 8 successive injections withEq. (9) is consistent with the average flow recorded by the in situflow meter. Indeed, according to Eq. (11), the difference betweenthe average discharges (5 L/s) is less than its extended uncertainty(60 L/s). Nevertheless, it is important to note that the main

Fig. 8. Comparison of discharges obtained in Chassieu with five injections of Rhodamine WT (left) and salt (right).

Fig. 9. Left: mean discharges in Chassieu obtained from five injections of Rhodamine WT and salt, and measured by the in situ flow meter during the five injections; right:differences between measurements techniques and their standard uncertainties.

M. Lepot et al. / Flow Measurement and Instrumentation 40 (2014) 28–38 35

contribution to the extended uncertainty in the difference is dueto the uncertainty in flow meter values.

At Quai des Etroits, tracer experiments results indicate that thein situ flow meter systematically underestimates the true dis-charges, with a bias increasing approximately linearly with thetrue value of the discharge. The underestimation is ranging from18.8% for a true discharge of 270 L/s to 54.6% for 350 L/s (Fig. 10right). This is consistent with the problem suspected by theMetrology Department. The hypothesis is that the underestima-tion is due to the positioning of the Doppler sensor, as no otherreasonwas found after the checking of the complete measurementchain (from the sensor to the Scada system) by the MetrologyDepartment. Indeed, the sensor, to avoid sedimentation, is notlocated just on the sewer invert along the central axis of the pipe,but is fastened 14 cm above the invert on the left wall of thesection (see Figs. 5 and 7).

Based on the experimental data, an empirical equation is thenestablished by regression to correct the values delivered by thein situ flow meter (Eqs. (16a) and (16b). It corresponds to thecontinuous line drawn on Fig. 7 right. Eq. (16b) avoids unrealisticnegative values for low values of QTEST.

QCORRECTED ¼ �434:89þ2:79� QTEST ð16aÞ

QCORRECTED ¼ max QCORRECTED;QTESTð Þ ð16bÞ

According to the Greater Lyon modeling expertise [29], thedaily volume at Quai des Etroits should be approximately 20%greater than the daily volume at Quai Arloing, due to connectionsof sewers draining wastewater from sub-catchments betweenboth sites. For the two days of the tracer experiments (29 and30 November 2010), a comparison was done between on the onehand the daily upstream volumes (Vu) as measured by the in situflow meter and increased by 20% (Vuþ20) and on the other handthe downstream daily volumes measured by the in situ flow meterwithout correction (Vd) and with correction (Vdc) according toEq. (16). Results are shown in Fig. 11. The top graph in Fig. 11shows that Vd is less than Vu (which is impossible in reality) anddramatically lower than Vuþ20. It also appears that Vdc is slightlylower than Vuþ20. The left side of the down graph shows thedifference between Vd and Vuþ20 and its enlarged uncertainty.Clearly, Vd is far from the expected estimated value Vuþ20. On theright side of the down graph, the difference between Vuþ20 andVdc is given with its enlarged uncertainty: the difference is lowerthan its enlarged uncertainty and it is acceptable to conclude thatVdc is not significantly different from the theoretical value Vuþ20

expected to be measured at Quai des Etroits. This is an indirect

Fig. 10. Comparison of discharges by Rhodamine WT tracer experiments and in situ flow meters at Quai Arloing (left) and Quai des Etroits (right).

Fig. 11. Daily volume analysis at Quai Arloing and Quai des Etroits.

M. Lepot et al. / Flow Measurement and Instrumentation 40 (2014) 28–3836

confirmation (according to Greater Lyon modeling results) thatthe proposed correction by means of Eq. (16), even if not veryaccurate, is a valuable practical improvement for the operator.

Results of both tracer experiments and CFD modeling are givenin Table 2. For the three cases, vML is significantly lower than vRHO:the CFD simulated Doppler sensor measurement process system-atically underestimates the velocity compared to tracer experi-ments. This underestimation ranges from 0.07 to 0.123 m/s inabsolute values, or from 12% to 19% compared to vRHO. In addition,the differences vRHO�vML are equal to at least 3 times theirstandard uncertainty: their probability to be due to measurementuncertainties is thus very low. In the lateral position, the sensordelivers velocity measurements which are systematically biased.This is due to the fact that it explores mainly a region of the flownear the wall where velocities are lower than in the central part, asillustrated in Fig. 6 showing the position of the sensor and the CFDvelocity field for the case QRHO¼550 L/s and h¼0.7 m. The meanvelocity in the sensor measurement cone is estimated by CFDequal to 0.61 m/s, while the true mean velocity through the crosssection is 0.69 m/s, i.e. an underestimation of 12%. Similar CFDresults are obtained for the two other cases (480 and 320 L/s) andare thus not shown here.

When considering the CFD simulation of the sensor measure-ment process in the central axis position, vMC remains system-atically lower than vRHO, but differences are reduced compared tovML (Table 2). For the case shown in Fig. 6, the mean velocity in thesensor measurement cone is estimated by CFD equal to 0.63 m/s,which is closer to the true value of 0.69 m/s. This sensor positionimproves the measurement, but differences remain 2 to almost

6 times greater than their standard uncertainties. This is explainedby the fact that, with angles α and β equal to 151 (Fig. 5), the sensorexplores mainly the region of the flow near the pipe invert wherevelocity profiles have their lowest values. This implies that, even ifthe sensor is in the central axis position, tracer experiments arenecessary to correct raw measurements which may be affected bysystematic biases. The above CFD modeling results explain, at leastpartly, the bias in the flow meter values detected by the proposedprotocol.

3.4. Correction of a rating curve by means of rhodamine WT tracerexperiments

The second field test briefly illustrates another application ofthe proposed protocol. It took place in Genas for the SyndicatIntercommunal d'Assainissement Grand Projet (a group of threemunicipalities in the East of Lyon). The operator had initiallyinstalled autonomous water level measurement sensors (IJINUS,M011501A) at some points of interest in the sewer system. Ratingcurves Q¼ f(h) were then fitted for each point of interest by usingadditional measurement campaigns using flow meters (Hydreka,Mainstream 4). From the campaign data sets including water levelh, flow velocity u and discharge Q, it appeared that, for waterlevels lower than 10 cm corresponding to most frequent dryweather conditions, the rating curves were not compatible withthe calibrated Manning Strickler formula which was correct foruniform and steady flows for higher water levels. The hypothesiswas that, for low water levels, the flow meters did not deliveraccurate results. Rhodamine WT tracer experiments were thuscarried out with the proposed protocol.

Fig. 12 shows the results obtained for only one point of interest(they are similar for the other points). The right graph is a zoom ofthe left one for water levels lower than 10 cm. The initial ratingcurve (dashed line) was derived from the field campaign data set(black dots). Tracer experiments gave the pairs of values (h, Q)shown as circles: they are clearly above the points measured bythe in situ flow meter. Based on the tracer experiments results, acorrected rating curve for low water levels was then established,shown as the continuous green line in Fig. 12.

Table 2Comparison of velocities obtained from tracer experiments and CFD modeling fortwo positions of the Doppler sensor, with standard uncertainties in brackets for allvariables (all velocity values have been rounded to 2 digits).

Discharge QRHO (L/s) 550 (9) 480 (7.5) 320 (5)Mean velocity vRHO (m/s) 0.69 (0.01) 0.65 (0.01) 0.50 (0.01)Mean velocity vML (m/s) 0.61 (0.02) 0.52 (0.02) 0.43 (0.02)vRHO�vML 0.08 (0.03) 0.12 (0.02) 0.07 (0.02)Mean velocity vMC (m/s) 0.63 (0.02) 0.55 (0.02) 0.41 (0.01)vRHO�vML 0.06 (0.03) 0.10 (0.02) 0.10 (0.02)

Fig. 12. Use of tracer experiments in Genas to correct a rating curve for water levels lower than 0.1 m. Left: complete rating curve; right: zoom for water level o0.1 m.

M. Lepot et al. / Flow Measurement and Instrumentation 40 (2014) 28–38 37

4. Conclusions

The Rhodamine WT tracer experiment protocol for sewerspresented in this paper proposes some improvements and noveltiescompared to basic tracer experiments: the assessment of varioussources of uncertainties, the reduction of the uncertainty in theinjected mass of tracer and the automation of data processing. Itprovides accurate values of discharge, with the following advan-tages: (i) low injection volume and mass, allowing tracer experi-ments even for high flow conditions, (ii) Rhodamine WT is usuallyabsent in wastewaters, which ensures low and stable backgroundsignal, (iii) short time step on line fluorimeter data acquisition. Ithas also some limitations: (i) lack of commercial standard solutionsat various concentrations, (ii) uncertainty of the commercial solu-tion is not very low and in some cases may be the limiting factor todecrease the final uncertainty in the injection mass, (iii) turbiditymay affect the results and should be checked systematically duringexperiments.

The case studies show that the protocol is an efficient approachto improve the quality of flow measurements in sewers. After anin situ flow meter is checked for various values of discharge, acorrection function can be established if necessary for each specificmeasurement site if there is no alternative solution to improve themeasurements by changing the location and position of the sensoror by replacing it by a more appropriate technology. In its presentstate, the protocol can be applied as a routine method. However, itdoes not provide explanation of the observed bias. As a comple-ment, CFD modeling may help to interpret the results and under-stand the causes of bias even it is not yet a usual tool for seweroperators as it requires very specific skills. Further applicationof CFD will allow better locating flow meters in sewer systemsby accounting for both hydrodynamic conditions and sensorspecifications.

Acknowledgments

Authors warmly thank the Greater Lyon for site and dataavailability. The work was partly co-financed by the R2DS programfrom the Ile de France Regional Council (http://www.r2ds-ile-de-france.com/), by the HURRBIS French network of Urban HydrologyObservatories (http://www.graie.org/hurrbis/), by the OTHU project(www.othu.org) and was also part of the FP7 PREPARED researchproject (http://www.prepared-fp7.eu/). Author also thanks ANR(Agence Nationale de la Recherche – French national researchagency)-11-ECOTECH-007-MENTOR project.

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