FLOW PATTERNS AND EXCHANGE PROCESSES IN DEAD ZONES OF RIVERS VOLKER WEITBRECHT & GERHARD H. JIRKA

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1 FLOW PATTERNS AND EXCHANGE PROCESSES IN DEAD ZONES OF RIVERS VOLKER WEITBRECHT & GERHARD H. JIRKA Institute for Hydromechanics, University of Karlsruhe Karlsruhe, Germany ABSTRACT This paper presents the results of an experimental work conducted in the framework of a research project that deals with the effect of dead zones (groyne fields, harbours) on the longitudinal dispersion in rivers. The objective is an improved prediction of travel time, maximum concentration and skewness of a tracer cloud than is possible with existing alarm models. The exchange processes between main stream and dead zones have major influence on the longitudinal stretching of a tracer cloud traveling down a river. The main physical process that governs the exchange of dissolved matter between the dead zone and the main stream are coherent two-dimensional structures that are generated at the head of a groyne. These structures are growing in horizontal direction during their travel between two groynes because the flow is very shallow. Planar velocity measurements with PIV (Particle-Image-Velocimetry) have been performed in a large shallow water table (5.5 m x 15 m) at the Institute for Hydromechanics at the University of Karlsruhe to analyze the turbulent flow characteristics in a river in the presence of groynes. The mass exchange is related to the aspect ratio (width/length) of a dead zone and to the position of the groynes in relation to the main flow direction. With the aid of PIV it is possible to measure instantaneous velocity fields with a high spatial resolution so that the coherent structures which are mainly responsible for mass exchange can be determined by calculating vorticity fields. These measurements give detailed insight to the mean flow conditions and the turbulent flow characteristics in the dead zones. In a further step a dimensionless mass exchange parameter as has been defined by Valentine & Wood (1977) was extracted from the velocity data. KEY WORDS Longitudinal dispersion, recirculating flows, particle-image-velocimetry INTRODUCTION Accidental pollution spills of dissolved matter in rivers occur frequently. The knowledge of how fast these pollution clouds get transported and dispersed is of great importance. As a result of the Sandoz accident in 1986 where a large amount of toxic chemicals were released into the river Rhine the International Commission for the Hydrology of the River Rhine (CHR) developed a prediction model (Spreafico & Mazijk 1993) for travel times and maximum concentrations for such accidental scenarios. For this kind of predictive model, much effort and funding must be spent on calibration by means of extensive tracer measurements. In case of the river Rhine-Alarm-Model which uses a one-dimensional analytical approximation for the travel times and the concentration curves, a dispersion coefficient and a lag coefficient have to be calibrated. If this calibration procedure is complete the model works well for cases of similar hydrological situations. However, variations in discharge and thus

2 changes in water surface level lead to increased errors if the same calibrated parameters are used for different hydrological characteristics. Dead zones along the flow path of a river such as groyne fields, harbors and side channels have a major influence on the longitudinal dispersion in rivers. Exchange processes between dead zones and the main channel influence the transport velocity of the tracer cloud and also the dispersive character of the flow due to fact that dissolved material gets trapped in such dead zones. This leads to a certain lag of the tracer cloud in comparison to the mean flow velocity in the main channel and hence to additional longitudinal dispersion. For regular channels with known spanwise velocity distribution, the one-dimensional longitudinal dispersion can be predicted with the aid of Fischer s theory (Fischer 1979), where the expression of Elder (1959) for horizontal shear flow in channels is extended for natural rivers with horizontal velocity distribution. To determine the effect of additional dispersion due to exchange processes between dead zones and main stream, it is of great interest to know the behavior of the flow dynamics in a river in the presence of dead zones. Due to the fact, that the flow is very shallow, which means that the horizontal dimension of the flow is much larger than the vertical, large coherent structures emerge at the head of a groyne. These structures are responsible for the mass transport between the main stream and the dead zone. With the aid of PIV (Particle Image Velocimetry) measurement technique, it is possible to detect these structures because this technique provides a view of the instantaneous velocity fields. In addition, the knowledge of flow velocities at every single point allows to calculate the instantaneous rate of mass exchange. EXPERIMENTS The Institute for Hydromechanics is equipped with a shallow water table that has a smooth horizontal bottom and dimensions of 15 m long and 5.5 m wide (Fig. 1). A uniform flow with water depth of 4.6 cm and mean flow velocity about 0.16 m/s was regulated with the aid of a diffuser and damping screens at the inlet region of the tank. The Reynolds Number based on water depth in the main flow region is therefore in the order of In order to simulate the flow in typical dead zones, a series of 15 groynes made of Perspex with a heavy core are produced, so that these elements can be placed at variable positions. The shape of the groynes was chosen to be very simple due to the fact that earlier investigations suggest that there is no significant effect of the groynes shape to the exchange processes (Lehmann et al. 1999). The outline of the groynes is a combination of a rectangular box (0. 5 m x 0.05 m x 0.05 m) with an attached half cylinder (diameter = 0.05 m). 15 m W W/L = 0.34 L W/L = m α W/L = 0.40 W/L = 1.11 α = + (10, 18, 26 ) α = + ( 10,26), + 18 Inlet with diffusor Damping screens 3-D positioning system Fig. 1: Top view of shallow water table with schematized groyne fields Fig. 2: Schematized illustration of all tested formation

3 In this study, the influence of the aspect ratio (width/length of groyne field) and the angle between the groyne and the main flow direction is analyzed. It could be shown, that for typical European rivers the aspect ratio lies in the range of The mean value for the River Rhine is about 0.5 whereas for the Dutch river Waal it is 0.3. In Fig. 2 all the situations that have been tested are illustrated. Additional experiments with smaller aspect ratios will be conducted in the near future. In a second step, the inclination angle of the groynes to the flow direction was varied for two cases (W/L = 0.40 and 1.11). These values are shown in Fig. 2 and are typical for the River Elbe. The measurement technique used in this study is based on a PIV-System (LaVision), which has been adapted so that a flow field of 1.2 m x 1.4 m could be observed with a high spatial resolution leading to a 60 x 84 vector matrix. The time resolution of 7 Hz is provided by a PCO-Sensicam camera (12 Bit, 1024 x 1280 pixels). A NIKON lens (f-mount) with a focal length of 14 mm is used for an undistorted high quality image. The quality of the velocity measurements with PIV technique highly depends on the optical and physical properties of the particles that are put on the water surface to trace the flow. They must give a strong contrast to the white bottom, the density must be just below the density of the water, and the size has to be in the order of 2-3 mm. Good visualization can be obtained with black polypropylene particles with a special coating to prevent sticking together. Another important requirement for a successful measurement is the distribution of the observed particles on the water surface. The particles have to be distributed uniformly in every subdivision (AOI, Area of Interest) of the flow field. Therefore a particle dispenser (Fig. 3) has been designed, that uses a roller brush within a vibrating silo to scatter the particle homogeneously. Top view Silo Side view PIV-Camera silo with particles Roller brush Groyne Fig. 3: Experimental setup for PIV measurements at the water surface with particle dispenser Every situation has been measured three times for about 30 seconds with 7 Hz, so that the statistics are based on 600 velocity fields. The time scale of the large structures is in the order of 5 to 10 seconds. Due to the fact, that one frame contains a data size of 2.5 MB, this configuration requires a PC with at least 1 GB RAM capacity. Otherwise a single time series would have to be much shorter and it would be impossible to track the large scale coherent structures.

4 VELOCITY FIELDS With the aid of the PIV measurement technique, it is possible to get detailed information about the mean flow velocities and the turbulent characteristics of the flow. In this study we are talking only about low frequency turbulence because these phenomena are dominant in the sense of mass transfer. The following pictures show the streamlines which are generated out of 600 velocity fields. In general the mean flow in a groyne field is dominated by a single large RESULTS eddy (Fig. 4, W/L = 1.11). For aspect ratios of less than 0.5 a second eddy emerges in the upstream corner of the groyne field. For aspect ratios larger than 1.5 the main eddy is splitting into two in the transverse direction. Similar phenomena have been observed by Booij (1986) and Uijttewaal (1999), respectively. In order to analyze the exchange processes, it is of great importance to observe the dynamics of the flow. With simple dye tests (Fig. 5), it can be shown, that the region between the W/L = 0,34 W/L = W/L = 0.40 W/L = 2.00 Fig. 4: Measured mean flow conditions in groyne fields with different aspect ratio Fig. 5: Visualization of coherent structures that are responsible for mass exchange groyne field and the main stream is very dynamic. Large structures are generated at the head of a groyne and are growing in the horizontal direction. The path of these structures is not always the same. Sometimes they get trapped in the dead zone and sometimes they travel further downstream without any additional influence of the particular dead zone. This mechanism governs the mass exchange between main stream and dead zone. The interpretation of exchange processes must be done with the help of instantaneous velocity fields. In Fig. 6 the instantaneous velocity field is plotted in comparison with the corresponding vorticity field. It can be seen that a large structure starts to travel downstream. At this instant it is not obvious if it is going to penetrate fully, partly or not into the groyne field. The vorticity field shows clearly the clockwise rotation of the large structures in the mixing layer. Shear and therefore vorticity is also generated at the groynes and in the shear zone between the two eddies. Here the rotation is mainly anticlockwise

5 Fig. 6: Instantaneous velocity field and vorticity field (dark color strong anticlockwise rotation and white color strong clockwise rotation) Main stream h Groyne field Fig. 7: Transverse rms-velocity (max. value = 0,026 m/s (white), mean velocity in main stream = 0,2 m/s) A s E A b Fig. 8: Schematic cross sectional view of river with dead zone In order quantify the mass exchange between main stream and groyne field, the instantaneous transverse velocities were analyzed. In Fig. 7 the velocity fluctuations (rms-velocity) in transverse direction are plotted. Point measurements with Laser-Doppler-Technique showed, that these results are reliable. In this example it can be seen, that the highest turbulent intensities can be found in the mid section between the two groynes. EXCHANGE PROCESSES Longitudinal dispersion in rivers is often modeled with one-dimensional dead zone model where the one-dimensional advection diffusion equation is linked with a second exchange C b equation = D b (Cs C b ) which describes the concentration in the dead zone (Schmid t 1999). C b is the concentration in the dead zone, C s the concentration in the main stream and D b an exchange coefficient. D b is defined by D b = (h/a b ) E with A b the cross sectional area and E the exchange velocity between the dead zone and the main stream (Fig. 8). Normalization of the exchange coefficient D b with the mean velocity of the main stream and the width of the groyne field gives a dimensionless exchange coefficient k (Valentine & B Db Wood, 1977) k =. U s

6 Since the exchange velocity E can be directly observed in the experiments, the dimensionless exchange coefficient can be determined (Fig. 9). Account should be taken of the fact, that the velocities are measured at the water surface and do not represent the depth averaged velocity. It can be seen that the exchange gets smaller if the aspect ratio increases. For very large aspect ratios the exchange coefficient starts to increase again. This phenomenon is not related to the actual mass exchange but to oscillation effects. The whole water body in the dead zone starts to swing back and forth which leads in this case to additional virtual exchange. Fig. 9: Exchange parameter k in relation to aspect ratio CONCLUSIONS Exchange processes between dead zones and main stream are governed by large coherent two-dimensional structures which are generated at the head of a groyne. These structures can be quantified with PIV-measurements at the water surface if adequate particles are chosen and the distribution of these particles is homogeneous. It is possible to determine the mass exchange with the aid of velocity measurements. The mass exchange is related to the aspect ratio of a dead zone and, in case of groynes, of the angle between the groyne and the main flow direction. In case of high aspect ratios oscillation effects occur, which are not part of the actual mass exchange. ACKNOWLEDGMENTS The authors would like to thank G. Kühn and K. Schmidhäussler for their help in performing the experiments. The project is sponsored by the German Bundesministerium für Bildung und Forschung (Grant No. 02 WT 9934/9). REFERENCES: Elder, J. (1959), The dispersion of marked fluid in turbulent shear flow. J. Fluid Mech. 5 Booij, R. (1989), Exchange of mass in harbours, Proc. 23th, IAHR Congresss Ottawa Fischer, H.B., List, E.J., Koh, R.C.Y., Imberger, J. and Brooks, N.H. (1979), Mixing in Inland and Coastal Waters, Academic Press, New York Lehmann, D. W. Uijttewaal, A. van Mazijk, V. Weitbrecht, (1999),Auswirkung von Buhnenfeldern auf den Transport gelöster Stoffe in Flüssen, TU-Delft, Dept. of Fluid Mechanics Schmid, B. (1999), Analytic Solution of the Transient Storage Equations Accounting for Solute Decay, Proceedings 28 th IAHR Congress, Graz, Austria Spreafico, M. and A. van Mazijk (1993), Alarmmodell Rhein. Ein Modell für die operationelle Vorhersage des Transportes von Schadstoffen im Rhein. Bericht Nr. I-12, Kommission für die Hydrologie des Rheins, Lelystad Uijttewaal, W. (1999), Groyne Field Velocity Patterns determined with particle tracking velocimetry, Proceedings 28 th IAHR Congress, Graz, Austria Valentine, E.M. Wood, I.R. (1977), Longitudinal dispersion with dead zones, J. Hydraulics Division, 105(HY8),pp 999 Wallast, I., Uijttewaal, W., Mazijk, A. van, (1999), Exchange processes between groyne field and main stream. Proceedings 28 th IAHR Congress, Graz