IAHR Conference, ‘River Flow’, Louvain de la Neuve, Belgium 2002

1 INTRODUCTION

Exchange processes between dead zones, as formed by groin fields or side arms, and the main flow channel of a river system have a significant influ-ence on the mass transport in rivers. The mass ex-change with dead zones increases longitudinal dis-persion and leads to a reduction of the transport velocity in the river channel compared to its mean flow velocity. An accurate prediction of travel time, maximum concentration and spreading of a pollutant cloud requires an explicit consideration of the mechanism of these exchange processes. These ef-fects must be included in existing one-dimensional models that are used online as “alarm models” for the management of accidental pollutant releases, as for example in the “River Rhine Alarm Model” (Spreafico & Mazijk 1993). This model was devel-oped by the "International Commission for the Hy-drology of the River Rhine" (CHR) and the "Interna-tional Commission for the Protection of the Rhine" (ICPR) after the accidental Sandoz spill in 1986, where a large amount of toxic chemicals (dioxins) was released into the river Rhine. For this kind of predictive model, much effort and expense must be spent on calibration by means of extensive in-situ tracer measurements. In the case of the River Rhine Alarm Model, which uses a one-dimensional ana-lytical approximation for the travel times and the concentration curves, a dispersion coefficient and a lag coefficient have to be calibrated. The model works well for cases of similar hydrological situa-tions. However, variations in discharge, and thus,

changes in water surface levels, lead to increased er-rors if the same calibrated parameters are used for different hydrological characteristics. Hence, predic-tive methods that are appropriate under variable flow conditions are needed.

To address this problem a series of laboratory ex-periments has been conducted. Experiments by Lehmann et al. (1999) show that the mass transport between dead zone and main stream is dominated by large coherent structures that are generated at the head of a groin. These structures are advected within the mixing layer and transfer tracer mass from dead zone to main stream and vice versa (Figure 1).

In the present study, in addition to surface velocity measurements using Particle Image Velocimetry (PIV), dye experiments were conducted for the pur-pose of analyzing the depth integrated mass ex-change. These concentration measurements were evaluated using a grayscale analysis. For this method, the time dependent decrease of dye in a groin field was recorded to calculate the mass ex-change. Because both methods give similar results, future studies can be conducted using the simpler and faster surface velocity measurements.

Since groins are often built into the river with an inclination angle in respect to the main flow, addi-tional sets of experiments were conducted to study the influence of different inclination angles on ex-change processes. Three cases with angles normal (90°) to the flow, backward inclination (-64°) against the flow, and forward inclination (+64°), re-spectively, were chosen (Figure 9).

Laboratory concentration measurements for determination of mass exchange between groin fields and main stream

Martina Kurzke, Volker Weitbrecht & Gerhard H. Jirka Institute for Hydromechanics, University of Karlsruhe, 76128 Karlsruhe, Germany

ABSTRACT: Laboratory experimental studies with different groin field geometries have been performed and evaluated using a grayscale analysis of dye transport patterns to determine their influence on mass exchange between the main stream and the recirculation zone. A special focus of this paper is on the problems and solu-tions that were encountered with the grayscale analysis method for calculating the time-dependent dye con-centrations inside the groin field. Evaluating the concentration decrease over time, the mass exchange be-tween the ‘unpolluted’ main stream and the ‘polluted’ dead zone could be determined. The results from these depth integrated concentration measurements were compared with results from surface velocity measurements by means of Particle Image Velocimetry.

2 EXPERIMENTS

In order to quantify the mass exchange between main stream and dead zone, laboratory experiments were conducted in a laboratory flume (20m x 1.8m). The bottom slope of the flume is adjustable so that nearly uniform flow conditions can be achieved. The water depth was 4.6cm, and the main stream mean flow velocity was 0.16m/s, which led to a bulk Rey-nolds number of about 7500. To simulate the flow in typical dead zones, a series of 15 groins, made of perspex with a heavy core, were aligned on one side of the flume. These elements could be placed at various positions, so that the groin field aspect ratio (width/length) could be varied from 0.17 up to 3.33. The shape of the groins was chosen to be very sim-ple since earlier investigations suggested that there was no significant influence of the groins’ shape on the exchange processes (Lehmann et al. 1999). For these experiments the outline of a groin was chosen to be a rectangular box (0.475m x 0.05m x 0.05m) with an attached half cylinder (diameter = 0.05m) leading to a total groin-length of 0.5m.

The main focus of this study was the investiga-tion of the influence of the inclination angle of the groins with respect to the main flow on exchange processes as well as the verification of results from (surface) velocity measurements using (depth inte-grated) dye experiments. Therefore, both measure-ment methods were conducted under the same flow conditions. This paper will take a closer look at the concentration analysis. For a detailed description of the velocity measurement evaluation with Particle Image Velocimetry (PIV), see Weitbrecht (2001a; 2001b).

The idea behind the concentration measurements was to observe the dilution of tracer mass in one single groin field after an instantaneous planar tracer injection. The problem with this kind of measure-ments lies in generating an instantaneous volume source without disturbing the flow field. During former investigations, the dead zone was separated

by a gate from the main stream while the tracer was injected and mixed up. The gate was then removed to observe the exchange processes (Westrich 1977). The problem with this setup was the strong distur-bance of the system during the early stage of the ex-periment due to undeveloped flow conditions in the mixing zone and the groin field. In another study (Uijttewaal et al. 2001), the tracer was spilled by hand into a groin field without any separation be-tween main stream and groin field. Using this tech-nique, the flow was almost undisturbed, leading to a realistic representation of the processes in the mix-ing zone. However, the problem with this setup was the difficulty to reach a well mixed situation as the initial condition for the experiment.

For the present study, a special injection device (Figure 2) was developed to reach an initially homo-geneous dye concentration throughout the groin field. With this device the tracer could be injected from above into the dead zone through a large num-ber of injection points, leading to a uniform distribu-tion of the tracer throughout the entire area. The main part of the injection device was a rectangular box (1,4m x 0,6m x 0,02m), which was connected to a moving frame mounted upon the flume’s walls. The bottom side of the box consisted of a 3cm x 3cm array of thin needles, through which the tracer could be injected into the flow without penetrating the wa-ter surface.

The device was controlled by a vacuum-pressure-system (Figure 2) with which the dissolved tracer could be pumped from the different reservoirs into the injection tank and into the high pressure reser-voir. From the high pressure tank an exact amount of tracer could be injected into the water body. After the tracer was injected into the water body, the injec-tion tank was pushed to the other side of the flume to allow the CCD-camera to observe the flow field. The frame rate was set to 4Hz, and 2500 pictures were captured with a spatial resolution of 256 * 320 pixels and a color depth of 12-bit (the full resolution is 1024 * 1280 pixels, however a binning factor of 4 in the x and y directions is applied during the captur-ing process). For every setup the experiment was re-

Figure 1: Dye experiment in the groin field and PIV data of an instantaneous velocity field (WEITBRECHT 2001b)

IAHR Conference, ‘River Flow’, Louvain de la Neuve, Belgium 2002

peated three times. For experiments where the ex-change processes were slower, either the frame rate was reduced to 2Hz or more pictures were taken. To evaluate the depth integrated concentrations, the lo-cal grayscale intensities (Figure 4) in the region of the groin field were analyzed. To get exact results, the gray values were calibrated with different known dye concentrations, and the possible change of background illuminations during the experiment was taken into account.

Figure 2: Schematic sketch of the tracer injection device, in-cluding the filling tanks and the control section (WEIT-BRECHT 2001b)

As tracer material, we used food dye (Amaranth

85, E 123), which is a very intense red color and provides a very stable aqueous solution. That means that the problem of deposition during or between the measurements did not exist. Such an outfall of solid material, like it happens with the use of potassium permanganate, would raise serious problems. In our case the needles of the injection device could be clogged by this material. In addition accumulation of solid particles in the flexible tubes would increase pressure losses and thus, change the flow conditions in the whole injection device. For reasons of repro-ducibility and accuracy, this had to be avoided.

3 ANALYSIS

To evaluate dye dependent concentrations a program was generated in Matlab®. This program was devel-oped to convert grayscale (intensity) values into concentrations. During this process, the intensity matrix (= picture) had to undergo several steps of conversions to allow for changes in background concentrations and illumination during the experi-ment.

Before every experiment, 50 reference pictures of the setup were captured to take background concen-trations into account. The water in the flume was circulating through the system. Therefore, dye from former experiments could still be found in the water.

The intention was to calculate the time dependent concentration decrease in the groin field. Therefore, an area of interest (AOI) had to be chosen (solid-lined rectangle in Figure 4) to eliminate areas that were outside of the groin field. Since the main inter-est lay in the mean concentration but not the actual concentration at every single location within the groin field, a binning of the matrix elements was possible to save not only memory space but also time to calculate the concentrations. Studies with different binning factors showed that if the binning factor is selected too big, leading to a small amount of matrix elements, errors that result from calibra-tion errors were weighted too strong. On the other hand could a small binning factor increase the num-ber of elements where the calibration does not fit perfectly. Within that range, binning leads to a cer-tain smoothing effect. Therefore, during this study, it was tried to use a medium size binning factor that would lead to a matrix of about 100 elements. Typi-cal binning factors ranged from 4 to 12. This means that in case of a binning factor of 4, 4 elements in x as well as y direction (leading to a total of 16 ele-ments) were summarized into one new element (one element is equivalent to 16 pixels, which have been merged already during the process of capturing the pictures as discussed in section 2). Figure 3 shows a typical distribution of concentration areas inside the groin field due to the chosen binning factor.

The subprogram responsible for the binning did not only return the binned matrix, but also a so-called “weighted matrix”. This weighted matrix was necessary to avoid an overrating of the edges of the AOI due to fewer elements that were combined into one element, when taking the average of the matrix in a later step.

Each element of this resized matrix was then sub-tracted from its counterpart of the mean matrix of the 50 reference pictures. This means that the actual concentration analysis was done with the intensity differences between reference and experimental pic-tures, not with absolute intensity values.

Figure 3: Representation of a binned groin field as it used for the concentration analysis. Each square (in this example an area of about 8cm x 8cm) corresponds to one element of the binned matrix.

To adjust for variations in illumination, a refer-ence-AOI outside the groin field was chosen (Figure 4). The mean value of this “unpolluted” area of the current concentration picture was then compared with the mean value of same area of the averaged reference recordings. In case of differences in inten-sity values, the percentage difference was taken into account for all the elements of the matrix, which means that the new matrix was equivalent to the old matrix multiplied by the ratio of the reference inten-sity value to the intensity value of the current con-centration picture:

conc

refnilil rAOI

rAOIMatrixMatrix ⋅= (1)

where Matrixil = Matrix with compensation for illu-mination changes; Matrixnil = Matrix without com-pensation for illumination changes; rAOIref= inten-sity value of the reference AOI of the (mean) reference picture; and rAOIconc= intensity value of the reference AOI of the concentration picture. Studies showed that this method was much more ac-curate than subtracting or adding absolute values. When counter checking with the reference pictures, which should have shown values of exactly 0.00mg/L for all 50 shots, values from -0.015mg/L to +0.015mg/L were encountered. However, most of the values were much smaller than |0.01| mg/L, and the average value was found to be -0.003mg/L for all three test runs. Studies with the calibration pic-tures showed divergences of less than 5% from the actual concentration value for the concentrations that were encountered during the experiments. Higher concentrations showed an increased divergence from the actual value than lower concentrations. Figure 4 shows the selected reference AOI as a dotted-lined polygon in the upper left hand corner.

Figure 4: Selected AOIs drawn into a grayscale concentration picture. The dotted rectangle in the upper left hand corner rep-resents the reference AOI.

For easier fitting of a concentration curve (equa-tion 3) as well as for presentation purposes, the ma-trix was then inverted. To avoid negative intensity values a constant value of 2500 was added to every element of the matrix (Figure 5). By doing so, high

intensity values that are presented in a light color, correspond to low concentrations. This means that concentration increases with decreasing (modified) intensity values (curve (3) in Figure 5).

For the purpose of calculating concentrations from intensity values, a calibration of the evaluation program was needed. Therefore, 50 pictures of dif-ferent known concentrations were taken before each setup. The pictures for the different concentrations were averaged to get a statistical mean value for every element of the intensity matrix independent of possible variations in illumination. Since the correla-tion between concentration of a solute in water and intensity is not linear, as many calibration steps as possible should be conducted. As the curvature of the calibration curve (equation 3) changes with changing background concentrations (i.e. less curva-ture at higher background concentrations), it is not possible to overlay a given calibration curve with just a few newly taken calibration points to create the new one. This problem affects the results of the experiments with W/L-ratios of 0.59 and 0.77 as well as 1.0 (Table 1: sets 5, 4, and 11, respectively). Here, the background concentrations were rather high, and since only a few calibration steps were taken, the number of resulting data points might not have been sufficient to grasp the right curvature of the calibration curve. However, after realizing the problem of background concentrations, this was kept at a minimum by adding bleach to the circulating water at the end of every experimental day.

Figure 5: Schematic sketch of (1) original intensity-concentration dependence, (2) original curve multiplied by negative one, and (3) final curve with a constant value of 2500 added to curve (2).

To convert the given intensities to concentrations, a fitting curve for the calibrated data points had to be found. Former studies suggested the dependency be-tween concentration and intensity value as (Leh-mann et al. 1999)

IAHR Conference, ‘River Flow’, Louvain de la Neuve, Belgium 2002

( ) j,iIntB

j,i IntCe1Aconc j,i ⋅++−= ⋅ (2)

where A, B, and C = coefficients determined during the calibration; conci,j = concentration of element i,j of the actual concentration picture; and Inti,j = inten-sity value of element i,j of the actual grayscale pic-ture.

However, further investigations revealed a prob-lem in the determination of the coefficients A, B, and C of equation 2. Figure 6 shows the different calibration curves for different elements of the gray-scale picture. The reason for these differences are changes in the brightness of the picture due to shadow effects. The result of these changes in brightness is that the calibration curve of every ele-ment has its own characteristic trait in curvature.

Figure 6: Schematic representation of intensity-dependent con-centrations

Since every data set stands for one element of the

intensity matrix, those variations in curvature mean that all coefficients have to be calculated for every element of the matrix. However, the coefficients A, B, and C of equation 2 are calculated iteratively from given concentration and intensity values, and good starting guesses speed up the calculation. With differing curvatures, good starting values are diffi-cult to find, leading to an increased computing time as well as an increased chance of errors. The as-sumption of a reverse dependency led to equation 3:

( ) j,iconcD

j,ij,i concEeCconcBAInt j,i ⋅++⋅+= ⋅ (3)

where A, B, C, D, and E = coefficients from calibra-tion process; Inti,j = intensity value of element i,j; and conci,j = concentration of element i,j.

Although it seems that even more coefficients have to be calculated iteratively with this equation, studies showed an almost constant value of the coef-ficient D for every element of the matrix. Further-more, the coefficient E represents the curve for infi-nite x (i.e. concentration) values, where there is no influence of the exponential part of the equation. This means that this coefficient can be estimated from the slope between the two data points with the highest concentrations. With D and E set, only the

coefficients A, B, and C have to be determined itera-tively. Studies showed much faster computing times and less errors when fitting a curve through the data sets with equation 3 than with equation 2. So, even though the actual concentrations have to be calcu-lated iteratively, equation 3 has not only proven to be the most representative fitting curve for the given data, but also assured minimal computing times.

Figure 7: Time dependent concentration reduction. Examples show the concentration curve for one run (reduced data points) with an inclination angle of 90° and +64°, respectively.

For given intensities from the concentration ex-

periments and given coefficients from the calibra-tion, the concentrations at any given time could be calculated iteratively for the groin field. Since the main interest lay in the change of concentration over time, but not at the different concentrations at vari-ous locations in the groin field, the average of the concentration matrix was used for the following analysis. To get the mean concentration of the whole groin field, the weighted matrix that was calculated during the binning process was multiplied with the concentration matrix. Afterwards, this newly created matrix was divided by the number of elements of the

matrix to get the mean value. With this averaged concentration value, the exchange coefficient could then be calculated.

The following paragraph gives a short summary of the steps that were taken to get the averaged con-centrations of the groin field at different times that were needed to calculate exchange rates.

• 50 reference pictures were taken and averaged to

determine the background concentration of the system

• To calibrate the coefficients A, B, C, D, and E of equation 3, 50 pictures each were taken of dif-ferent known concentrations in the groin field

• An area of interest (i.e. the groin field) was se-lected

• The number of elements of this intensity matrix was further reduced by binning

• To take the background concentration into ac-count, this intensity matrix was then subtracted from the (also binned) averaged matrix of the reference pictures leading to Matrixnil (equation 1)

• To adjust for variations in illumination during the experiment, the intensities in a reference field outside the groin field were determined and compared to the averaged reference and the ac-tual dye intensity matrix

• These variations were then adjusted by multiply-ing the ratio of the intensity value of the refer-ence AOI to the reference AOI of the dye picture with Matrixnil

• The corresponding concentrations to the ele-ments of this intensity matrix could then be cal-culated iteratively using equation 3.

For the application that is described in the follow-ing section, only the mean concentration of the groin field (Cb) was needed.

4 APPLICATION

As mentioned in the introduction, the mass exchange between dead zones like groin fields and the main stream has an influence on longitudinal dispersion. Therefore, Valentine & Wood (1979) state that the one dimensional dispersion model that was initiated by Taylor (1954) for pipe flow, and which has been adapted by Elder (1959) for wide open channels, and then by Fischer et al. (1979) for natural channels, does not adequately describe the transport mecha-nisms in rivers when dead zones exist. They showed that the dead zone model, where the one-dimensional convection diffusion equation is linked with a second equation (equation 4) describing the concentration in the dead zone, better represents the

behavior of a pollution cloud in the presence of dead zones.

)CC(Dt

CSbb

b −−=∂

∂ (4)

In this equation, Cb stands for the concentration in the dead zone, Cs for the concentration in the main stream and Db for the ratio between the exchanged volume per time Qe and the dead zone volume Vb. Equation 5 shows the definition of this parameter

WE

hWLEhL

VQ

Db

eb === (5)

Figure 8 illustrates the definitions for the parame-

ters used in equation 5, with E being the exchange velocity.

Figure 8: a) Schematic cross sectional of a river with dead zone, b) definition of a groin field’s geometries

Db is the reciprocal of a typical time scale, which

corresponds to the overturn time of the gyre inside the groin field. Normalization of Db with the mean velocity in the main stream (us) and the width of the groin field (W) leads to a dimensionless exchange coefficient k that has been defined by Valentine & Wood (1977). It expresses the ratio between the ex-change velocity (E) and the main stream velocity (us) (equation 6). Typical values of k have been found to be in the order of 0.015 – 0.04 (Valentine & Wood 1979, Booij 1989, Wallast et al. 1999, Weit-brecht 2001a).

Equation 4 yields the solution Cb = Co exp (-Db t) if we assume the concentration in the main stream to be zero, which is reasonable for the laboratory set-ting. In order to determine Db, this function is fitted to the measured time dependent mean concentration in the groin field. Figure 7 shows this fitted curve as a black solid line. Normalization with us and W fi-nally yields the dimensionless exchange parameter k

s

b

s

b

inb

b

uDW

uD

aAk ⋅

=⋅=,

(6)

where Ab = cross sectional area of the groin field; ab,in = depth of the groin field at the transition zone between groin field and main stream; and us = main stream mean velocity.

IAHR Conference, ‘River Flow’, Louvain de la Neuve, Belgium 2002

5 RESULTS

Three different cases with variation of the inclina-tion angle of the groins in respect to the main stream direction have been evaluated for a W/L aspect ratio of 0.4 (Figure 9, Runs 7, 9, and 10 in Table 1).

In comparing the results of the two experimental methods, the following observations could be made: Runs 2, 9, and 10 led to the exact same dimen-sionless exchange coefficient k for the surface veloc-ity measurements and the depth integrated concen-tration experiments. However, when looking at the results of the other runs in Table 1, slight deviations, but no systematic difference could be found between the k values obtained by the two methods for the various groin field geometries.

Run #

W/L Groin length / inclination

angle

k evaluated from velocity measurements

k evaluated from dye

experiments 1 3.33 50cm / 90° 0.015 0.012 2 2.00 50cm / 90° 0.019 0.019 3 1.11 50cm / 90° 0.022 0.026 4 0.77 50cm / 90° 0.023 0.032 5 0.59 50cm / 90° 0.022 0.028 6 0.48 50cm / 90° 0.032 0.033 7 0.40 50cm / 90° 0.033 0.028 8 0.34 50cm / 90° 0.035 0.030 9 0.40 50cm / -64° 0.035 0.035

10 0.40 50cm / +64° 0.022 0.022 11 1.00 50cm / -64° 0.021 0.032 12 1.00 50cm / +64° 0.014 0.015 13 0.17 25cm / 90° 0.025 0.018 14 0.25 25cm / 90° 0.020 0.022 15 0.40 25cm / 90° 0.017 0.020

Table 1: exchange coefficient k from dye experiments and ve-locity measurements

When looking at the influence of the inclination

angle, it can be seen that for groins that are inclined with respect to the main flow direction (runs 9 and 10, Table 1), the exchange parameter is altered com-pared to the right-angled setup of run 7. An explana-tion for the observation of a stronger mass exchange in case of groins that are inclined against the main flow direction (run 9) can be found by comparing the turbulent characteristics in the mixing zones of the three different cases. The maximum rms value of the transverse velocities in the mixing zone for run 9

is about 0.020 m/s, whereas for run 10 it is only 0.015 m/s. An additional reason for a stronger mass exchange in run 9 is the small size of the secondary eddy in the upstream corner of the groin field (Figure 9). Since this part of the dead zone is ex-changing mass with the primary gyre much slower than the primary gyre itself is exchanging mass with the main stream (Lehmann et al. 1999), the size of the secondary gyre is directly proportional to the sheltering effect that will take place. In run 10 the secondary eddy covers the largest volume fraction of the dead zone of all cases. Therefore, a slower mass exchange is encountered for this case, which is rep-resented in a smaller dimensionless exchange coeffi-cient k. This phenomenon of different exchange rates can also be seen in the concentration curve of Figure 7, where the concentration reduction of run 7 is much faster than it is for an inclination angle of +64° (run 10). These findings show that the dimen-sionless exchange coefficient k does not only depend on the W/L aspect ratio, but is also influenced by the inclination angle of the groins. When taking a closer look at the results of the experiments with short groins (25cm), one might wonder why the calculated k values are much smaller than the counterparts with longer (50cm) groins at the same W/L-aspect ratio.

This observation is another indication for the fact that the exchange parameter k (equation 6) is not a constant value. It also shows, that the aspect ratio W/L and the inclination angle are not the only pa-rameters that have an influence on k. In equation 6, k is defined as the ratio between an exchange rate Qe and the dead zone volume Vb. However, with this definition, no information on the geometrical shape of the dead zone or on the shallowness of the flow is included in the determination of k, even though both properties have a strong influence on the mass exchange.

However, since for this study we were only inter-ested in the effects of variations in groin field ge-ometries on mass exchange as well as the compari-son of the results of surface velocity with depth integrated dye measurements, the actual value of the dimensionless parameter was not that important. Nevertheless, further investigations are needed to corroborate equation 6.

Figure 9: Comparison of the averaged flow field of three different groin inclination with the same aspect ratio (W/L = 0.4) (WEIT-BRECHT 2001b)

6 CONCLUSIONS

If the tracer was well mixed at the initial stage of the experiment and the background was low or a suffi-cient amount of calibration steps were taken, the ex-change processes between dead zones and main stream could be determined with dye experiments using a grayscale analysis tool. Counter checking the results of these dye experiments with the results that were obtained from the surface velocity measure-ments, showed similar mass exchange values for both methods. Since velocity measurements are much easier to perform, this verification allows us to analyze future setups with different geometries with this less time-consuming method. However, using the PIV method, the exchange coefficient is calcu-lated with the exchange velocity between the heads of two groins. Therefore, this method can only be used as long as the groins are not submerged.

The application showed that groins, which were inclined against the flow direction, led to slightly higher exchange values than groins that were built into the flume at a 90° angle. If the groins were in-clined with the main flow direction a much larger secondary eddy was generated in the upstream cor-ner of the groin field, leading to significantly smaller exchange values than in the other two cases.

7 ACKNOWLEDGEMENTS

The authors would like to thank G. Kühn, K. Schmidhäußler, and R. Erler for their help in per-forming the experiments. The project is sponsored by the German “Federal Ministry for Education and Research” (bmb+f Grant No. 02 WT 9934/9).

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