lateral cavity
3D-PTV experiments for open-channel flow past a
Academic year 2019-2020
Master of Science in Civil Engineering
Master's dissertation submitted in order to obtain the academic degree of
Counsellor: Ir. Lukas Engelen
Supervisor: Prof. dr. ir. Tom De Mulder
Student number: 01508183
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lateral cavity
3D-PTV experiments for open-channel flow past a
Academic year 2019-2020
Master of Science in Civil Engineering
Master's dissertation submitted in order to obtain the academic degree of
Counsellor: Ir. Lukas Engelen
Supervisor: Prof. dr. ir. Tom De Mulder
Student number: 01508183
copyright terms have to be respected, in particular with regard to the obligation to state explicitly the source when quoting results from this master dissertation.”
Joran Haegebaert Ghent, May 2020
Finishing this master’s dissertation has been a long process, which would not have been possible without the help and support of many people. Therefore, I would like to express my gratitude to all those who helped me complete this work successfully.
I would like to thank my supervisor, prof. dr. ir. Tom De Mulder, to introduce me to this interesting topic. With his great passion and enthusiastic support, he made me realize the beauty and brilliance of fluid mechanics and hydraulics. Also, a special thanks to ir. Lukas Engelen, for the daily support, his unconditional patience and extensive knowledge which helped me to complete this master’s dissertation in a successful way. Not only did he provide me with all the necessary expertise related to experimental research, he also guided me through the difficult times and supported me with encouraging words.
I would also like to thank all my high school friends and friends and fellow students at Ghent University, who made these five years in Ghent an absolute pleasure. When starting the study of Civil Engineer in 2015, I did not expect to end up which such a group of close friends.
I would also like to thank Gilles Rogge, a true friend and fellow student, with whom I have spent a lot of time the last months working together in the Hydraulics Laboratory on our master’s dissertations. Without him, these final months would have been a lot more lonesome. Also, I would like to thank him for the help and support on parts of this master’s dissertation.
To my parents, my brother, my grandparents and family, for their endless support during my studies at Ghent University. In special, I would like to thank my parents, with whom I have been living together very closely these last months, which was not always easy for them, especially when progress was going slow.
Joran Haegebaert
3D-PTV experiments for open-channel flow past a
lateral cavity
Joran Haegebaert Student number: 01508183
Supervisor / Counsellor:
Prof. dr. ir. Tom De Mulder / ir. Lukas Engelen
Master’s dissertation submitted in order to obtain the academic degree of Master of Science in Civil Engineering
Academic year 2019-2020
Keywords: Particle Image Velocimetry, 3D Particle Tracking Velocimetry, open-channel cavity flow, validation, shallow mixing layer
In the Hydraulics Laboratory of Ghent University, 3D Particle Tracking Velocimetry (3D-PTV) measurements have been performed to study free-surface flow past a lateral cavity. 3D-PTV measurements result in a full three-dimensional Lagrangian description of the flow field, which is advantageous when studying the highly turbulent, three-dimensional flow structures in the lateral cavity and at the cavity interface. This work employs Particle Image Velocimetry (PIV) measurements to validate the 3D-PTV results and to compare the advantages, disadvantages and applications of both techniques. As the current Particle Image Velocimetry set-up results in a two-dimensional Eulerian description of the flow, the Lagrangian 3D-PTV measurements are interpolated on a regular, Eulerian grid to allow an adequate comparison. The comparison is concentrated on the time-averaged flow description, as well as the possibility to describe turbulent flow properties, study the characteristics of the mixing layer and estimate the mass exchange between the main channel and lateral cavity. Using the large spatial resolution and Eulerian flow field description obtained with the PIV measurements, a detailed study of the flow properties in the shallow shear layer at the cavity interface is performed. This includes an analysis of the dominant processes, such as vortex shedding in the mixing layer and the presence of surface oscillations (seiches) in the lateral cavity. To study the propagation of vortices in the shallow shear layer, multiple vortex identification techniques are compared. Use is made of Proper Orthogonal Decomposition (POD) and phase-averaging to study the coherent structures and periodic phenomena in the cavity interface.
3D-PTV experiments for open-channel flow past a
lateral cavity
Joran Haegebaert
Supervisor / Counsellor: Prof. dr. ir. Tom De Mulder / ir. Lukas Engelen
Abstract - In the Hydraulics Laboratory of Ghent University, 3D Parti-cle Tracking Velocimetry (3D-PTV) measurements have been performed to study free-surface flow past a lateral cavity. 3D-PTV measurements result in a full three-dimensional Lagrangian description of the flow field, which is advantageous when studying the highly turbulent, three-dimensional flow structures in the lateral cavity and at the cavity interface. This work em-ploys Particle Image Velocimetry (PIV) measurements to validate the 3D-PTV results and to compare the advantages, disadvantages and applications of both techniques. As the current Particle Image Velocimetry set-up re-sults in a two-dimensional Eulerian description of the flow, the Lagrangian 3D-PTV measurements are interpolated on a regular, Eulerian grid to al-low an adequate comparison. The comparison is concentrated on the time-averaged flow description, as well as the possibility to describe turbulent flow properties, study the characteristics of the mixing layer and estimate the mass exchange between the main channel and lateral cavity. Using the large spatial resolution and Eulerian flow field description obtained with the PIV measurements, a detailed study of the flow properties in the shal-low shear layer at the cavity interface is performed. This includes an anal-ysis of the dominant processes, such as vortex shedding in the mixing layer and the presence of surface oscillations (seiches) in the lateral cavity. To study the propagation of vortices in the shallow shear layer, multiple vortex identification techniques are compared. Use is made of Proper Orthogonal Decomposition (POD) and phase-averaging to study the coherent structures and periodic phenomena in the cavity interface.
Keywords - Particle Image Velocimetry, 3D Particle Tracking Velocime-try, open-channel cavity flow, validation, shallow mixing layer
I. INTRODUCTION
A. Research topic
Flow past lateral cavities (Figure 1) has been the research topic of many recent investigations, due to the ecological, eco-nomical and operational importance. Along the cavity interface, a shear layer develops, while inside the cavity, one or multiple recirculating gyres have been observed (mainly depending on the cavity aspect ratio W/L, i.e. the ratio of its width W to its length L). For an approximately square cavity, with an aspect ratio close to one, flow inside the cavity is characterized by a large rotating cell, occupying most of the cavity. In the cen-ter of this recirculating cell, a slow-moving, ellipsoidal core or dead zone is observed. Mass exchange of sediments, nutrients or pollutants between the main channel and the lateral embay-ment does not only influence the ecological conditions of the cavity and the main stream, but it also has an impact on sedi-mentation processes, affecting local water depths and requiring regular maintenance dredging.
The free-surface flow past a lateral embayment has been found to be highly three-dimensional (Uijttewaal et al., 2001; Tuna et al., 2013; Akutina, 2015; Engelen and De Mulder, 2019;
J. Haegebaert is a Civil Engineering student at Ghent University (UGent), Ghent, Belgium. E-mail: Joran.Haegebaert@ugent.be
Fig. 1. Schematic depiction of flow past a lateral cavity (Akutina, 2015)
Geerinck, 2019) and therefore, recent studies have opted to use 3D Particle Tracking Velocimetry (3D-PTV), which allows to determine the three-dimensional velocity components of the flow in a Lagrangian way. Next to 3D-PTV, this work also em-ploys Particle Image Velocimetry (PIV), which is able to acquire velocity components in two dimensions.
For both PIV and 3D-PTV, seeding particles are (usually) added to the flow. In PIV experiments, a thin laser sheet is adopted to illuminate these tracer particles, which are then cap-tured by a single camera at a high sampling frequency. After-wards, these images are post-processed and correlation tech-niques are applied to obtain an average particle displacement for a so-called interrogation area. By multiplying the average displacement with the sampling frequency, the velocity vector in two dimensions is obtained for each interrogation area.
In 3D-PTV experiments, the seeding density of tracing par-ticles is usually much smaller than the seeding density adopted in PIV, while the particle diameter is in general and order of magnitude larger. In contrast to PIV, 3D-PTV adopts a light source to illuminate the entire observation volume at once. The smaller seeding density allows to identify and track individual particles. By viewing the observation volume with at least two cameras, performing a calibration of both the interior and exte-rior camera parameters, and searching for correspondences be-tween particles in the images of the different cameras, the three-dimensional coordinates of individual particles can be deter-mined. Special tracking algorithms have been developed which allow to track individual particles through multiple consecutive images, from which particle velocities can be derived.
B. Objectives of the master’s dissertation
The objectives of this master’s dissertation are twofold. First of all, Particle Image Velocimetry (PIV) measurements are adopted as an extra validation of 3D Particle Tracking Velocime-try (3D-PTV) measurements. As such, next to the static and
ments is obtained. Secondly, the properties of turbulent struc-tures in the mixing layer at the cavity interface and the coupling with surface oscillations in the cavity are studied.
II. EXPERIMENTAL SET-UP
A. Cavity facility and flow conditions
In the Hydraulics Laboratory of Ghent University, Belgium, a small-scale cavity facility has been constructed which consists of a flume with a total length of 2.5 m and a main channel width bof 0.08 m. The main channel has a rectangular-shaped cross-section and is connected to a lateral cavity with the upstream cavity corner 2 m downstream of the flume inlet. The square cavity has a streamwise length L and transverse width W of 0.08 m and a constant bed level, which is equal to the bed level of the main channel. At the downstream end of the main channel, a weir was installed to control the water level and water depth hinside the flume. In order to obtain steady flow conditions and limit surface distortions, use was made of calming tanks at both ends of the flume, a diffuser to fill the upstream tank, a honeycomb mesh and floating body at the flume inlet, etc.
Four flow conditions with varying bulk velocities Uband
wa-ter depths h were investigated. Table 1 summarizes the flow conditions used in the different experiments. These were chosen to resemble real rivers as close as possible (i.e. a small depth-to-width ratio h/b, large Reynolds numbers Re and sufficiently small Froude numbers F r). Reynolds numbers in Table 1 were computed with an average water density ρf of 1000 kg/m3and
a kinematic viscosity νf of 0.993 × 10−6 m2/s (average water
temperature of 20◦C). Due to the COVID-19 pandemic, and the
associated measures taken at Ghent University, it was not possi-ble to perform the 3D-PTV experiments for cases Q3 and Q4.
Table 1. Overview of experimental flow conditions
Q[l/s] h[m] Ub[m/s] Re[-] F r[-] h/b[-]
Q1 0.16 0.015 0.13 5871 0.35 0.19
Q2 0.30 0.015 0.25 10 825 0.64 0.19
Q3 0.35 0.025 0.18 10 867 0.35 0.31
Q4 0.27 0.015 0.22 9797 0.58 0.19
B. Particle Image Velocimetry set-up
PIV measurements were performed at three elevations above the bed. For all experiments, measurements were performed at a distance of 2 mm, 7.5 mm and 13 mm above the bed (cor-responding to z/h = 0.13, z/h = 0.50 and z/h = 0.87 for flow cases Q1, Q2 and Q4 and z/h = 0.08, z/h = 0.30 and z/h = 0.52 for Q3). Although more valuable information would be collected if experiments were performed at the same relative elevations above the bed for all flow cases, time restric-tions and the time-consuming positioning of the laser did not allow the repositioning of the laser sheet for flow case Q3.
A 1000 mW laser with a wavelength of 450 nm (Z-Laser ZQ1) was adopted. The digital camera was positioned below the cavity facility and viewed the entire cavity, as well as the entire main channel next to the cavity. A monochrome CMOS sensor camera (Basler Ace, 10 Bit) with a resolution of 1920 × 1200 pixels was used, resulting in an average spatial resolution
formed for each flow case and each elevation above the bed. The optical magnification factor of the camera was determined using a calibration plate on which equidistant crosses were applied.
Hollow glass spheres with an average particle diameter dpof
10 µm (ρp= 1100kg/m3) were used as seeding particles. The
analysis and post-processing of the images were executed using the free and open-source software OpenPIV (OpenPIV, 2014), which includes an implementation of the Window Displacement Iterative Method (WiDIM) algorithm. After a thorough compar-ison between the obtained results using different parameters, an overlap ratio of 0.5 and a minimum window size of 36 pixels were adopted, resulting in a spatial resolution of approximately 1.7 mm × 1.7 mm for the different measurement planes. C. 3D Particle Tracking Velocimetry set-up
In the 3D-PTV experiments, four cameras were positioned in a square arrangement approximately 600 mm from the cavity and under an angle of around 15◦with the vertical. The cavity
and main channel were illuminated by an LED panel, positioned next to the main channel. In order to increase contrast and facil-itate the identification of the flow tracers, the walls of the main channel and the cavity were covered with black tape, while a black cover was installed just above the free-water surface. In the current experiments, tracer particles with a diameter of 160-212 µm and a density ρp =1060 kg/m3were used, which were
found to have a limited velocity lag with respect to the smallest flow structures (Stk ≤ 0.1) (Tropea et al., 2007).
Both an interior and exterior camera calibration were per-formed. To obtain the focal distance, principle point and image distortion parameters of each camera, a checkerboard pattern was adopted (interior camera calibration). The exterior cam-era parameters were obtained by performing a so-called multi-plane calibration. Therefore, use was made of a black-coated aluminium plate on which a grid of 14 × 25 white dots with a diameter of 0.5 mm was engraved. This calibration plate was positioned at 10 elevations above the bed, each 1.5 mm apart, creating an imaginary 3D calibration object. Using the imple-mented multi-plane calibration procedure in the free OpenPTV-software (OpenPTV Consortium, 2014), the orientation and po-sition of each camera were determined using 5 of these planes. The 5 remaining planes were used as part of a static validation. For the 3D-PTV experiments, a sampling frequency fs of 100
Hz was adopted. After preprocessing the images, particle detec-tion and particle tracking were performed using the OpenPTV-software. Afterwards, broken trajectories were linked using the linking algorithm as proposed by Xu (2008).
D. Validation and error analysis
For both PIV and 3D-PTV, different error sources are present during the experiments. Therefore, an assessment was made of the final uncertainty on the velocity measurements and/or parti-cle positions.
During PIV experiments, three main error sources can be dis-tinguished (Raffel et al., 2018; Sciacchitano, 2019). First of all, errors can be caused by the different system components, such as errors due to the installation and misalignment of the laser
nation, image noise, etc. The main error source related to the system components will be due to the peak-locking effect (i.e. detected particles are biased towards integer pixel values) and which depends on the sub-pixel localisation algorithm. For the sub-pixel localisation procedure implemented in the WiDIM al-gorithm, peak-locking was estimated to cause an uncertainty on the velocity measurements of approximately 1.5 mm/s (Jahan-miri, 2011; Sciacchitano et al., 2013; Raffel et al., 2018). Also, out-of-plane velocities of tracing particles result in an additional perspective error, which was estimated as 0.1-0.2 mm/s (Ma and Jiang, 2018). A second source of uncertainties in the PIV measurements is related to errors due to the flow itself, such as velocity gradients and velocity fluctuations. However, as men-tioned by Jahanmiri (2011) and Mignot et al. (2016), the domi-nant error source due to the flow is the existence of gradients in the seeding density. This error was estimated to be half of the peak-locking error, i.e. 0.75 mm/s (Jahanmiri, 2011). Finally, also errors can be introduced due to the evaluation technique and post-processing algorithms adopted. For the current exper-iments, post-processing parameters were carefully fine-tuned to achieve reliable and accurate results, such that the additional er-ror is deemed to be sufficiently small. The total uncertainty on the PIV measurements is therefore estimated as 2.35-2.45 mm/s. For the 3D-PTV experiments, the residual calibration error was calculated, whereas also a static and dynamic validation was performed. The calculation of the residual calibration error in-volves calculating the residual errors on the theoretical positions of the white dots on the 5 planes of the multi-plane calibration unit. This was done by using the original calibration images as input images for the particle detection procedure and comparing the results with the theoretical particle coordinates. The resid-ual calibration errors in x-, y- and z-direction were calculated as 0.033 mm, 0.019 mm and 0.046 mm, respectively. The static validation was executed in a similar way by adopting the 5 re-maining planes and resulted in a similar error, such that it can be concluded that the positions of new, independent particles can be determined accurately. In addition, a dynamic (‘dumbbell’) val-idation was performed, in which two seeding particles are glued on a black-coated rod, which is moved through the observation volume with approximately the same velocity of the seeding par-ticles. In theory, the distance between the two seeding particles remains constant, while the velocity component of the particles on the axis connecting both particles should be equal to zero. By calculating the variation in particle distance and the veloc-ity component on the axis connecting both particles, an assess-ment of the dynamic positional error and the particle velocity error can be obtained. Figure 2 shows the obtained probabil-ity densprobabil-ity function of the obtained velocprobabil-ity error. An average (absolute) velocity error of 0.76 mm/s was obtained.
III. VALIDATION OF3D-PTVMEASUREMENTS WITHPIV MEASUREMENTS
In the Hydraulics Laboratory of Ghent University, a 3D-PTV set-up has been adopted to study free-surface flow past a lateral cavity. The PIV experiments that were performed in the same experimental facility allow to compare the results obtained with
Fig. 2. Probability density distribution of 3D-PTV velocity error ∆u
these 3D-PTV measurements with another type of flow mea-surement. To compare the Lagrangian flow description obtained with 3D-PTV with the Eulerian results of PIV, a binning proce-dure is applied to the 3D-PTV results, in which the entire flow domain is subdivided into three-dimensional cuboid-shaped vol-umes, bins or voxels and the velocity of all detected particles within such a cuboid-shaped volume is assigned to the center of the bin. A larger binsize will facilitate and accelerate the con-vergence of the data, but as such reduce the obtained spatial res-olution. A binsize of 2.5 mm in the horizontal directions and a binsize of 1.5 mm in the vertical direction resulted in an accept-able compromise between convergence and spatial resolution. A. Time-averaged velocity and turbulent flow characteristics
Figure 3 shows the spatial distribution of the absolute dif-ference in time-averaged longitudinal |∆u| and transverse |∆v| velocity obtained with PIV and 3D-PTV for flow case Q1 at z/h = 0.87. The larger difference in longitudinal velocity (and to a lesser extent also in transverse velocity) on either side of the main channel axis, as well as the very local spots with an increased discrepancy in the main channel, are ascribed to some slight damage to the bottom of the flume and are therefore not necessarily related to an inaccuracy of the 3D-PTV measure-ments. Multiple factors are thought to contribute to the larger difference near the channel walls. First of all, light reflections in the 3D-PTV experiments at the cavity walls hinder the detection and tracking of seeding particles close to the flume walls, as well as causing possible spurious velocity vectors due to wrong
par-Fig. 3. Contour plot of |∆u|/Uband |∆v|/Ubat z/h = 0.87 for Q1
Secondly, previous work (Engelen and De Mulder, 2019; Geer-inck, 2019) has shown an increased calibration error near the cavity walls, decreasing the accuracy of the 3D-PTV measure-ments. Moreover, due to the limited spatial resolution (binsize of 2.5 mm in the horizontal direction), large velocity gradients near the flume walls are more difficult to identify. Finally, due to the adopted set-up, in which the cameras are positioned slightly outwards with respect to the observation volume, the observa-tion volume in the camera images is partly obstructed by the flume walls. As such, particles are less easily identified in all camera images, reducing the accuracy of the 3D-PTV results.
The lateral cavity shows in general a slightly larger discrep-ancy between PIV and 3D-PTV, especially in the cavity center and corners. The difference in the main recirculating gyre re-mains quite limited. These observations are mainly related to the low particle density in the lateral cavity center and corners. Moreover, suboptimal illumination (due to the larger distance between the cavity and the LED panel) and the influence of set-tled particles in low turbulent areas in the 3D-PTV experiments, as well as velocity gradients and the highly three-dimensional flow field in the lateral cavity contribute to an increased discrep-ancy between PIV and 3D-PTV. The large velocity gradient and three-dimensional flow field, combined with the possibility of a slight shift between the adopted coordinate systems are thought cause the larger discrepancy in the mixing layer.
At z/h = 0.50, similar results are obtained. However, at z/h = 0.13, a more significant difference in longitudinal ve-locity is observed. Next to light reflections, which are aggra-vated due to the proximity of the channel bed, the large velocity gradients near the bottom are expected to be the main cause of these discrepancies. A small uncertainty on the exact elevation above the bed of the laser, together with the finite thickness of the laser sheet and the adopted vertical binsize will therefore cause a significant difference in (longitudinal) velocity. Flow case Q2 shows similar results, in which the effect of large ve-locity gradients is even more pronounced. Moreover, also near the lateral cavity wall, an increased difference was observed for flow case Q2 which could probably be attributed to the influ-ence of surface oscillations on the velocity measurements, slight differences in flow conditions or suboptimal post-processing of either the PIV or 3D-PTV measurements. Post-processing the results with more advanced software and making a distinction between the parameters of the main channel and lateral cavity (in which significantly smaller flow velocities exist) could be used in future research to investigate these discrepancies.
Although not shown, the spatial distribution of the differ-ence in root-mean-square velocities and turbulent kinetic energy show similar results and could therefore be related to the abomentioned causes. Moreover, neither the time-averaged flow ve-locities or the turbulent flow properties showed any significant bias towards positive or negative values, such that no systematic errors in either PIV or 3D-PTV measurements are present. B. Evolution of the mixing layer thickness δm
Due to interactions between the fast-moving flow in the main channel and the slow-moving recirculating gyre inside the
lat-ity wall. The thickness of the mixing layer can be estimated as δm(x) = (U2(x)−U1(x))/|∂u(x)/∂y|max(Chu and Babarutsi,
1988; Uijttewaal and Booij, 2000) with U2and U1characteristic
flow velocities in the main channel and cavity, respectively, and |∂u(x)/∂y|maxthe maximum transverse gradient in
longitudi-nal velocity. Figure 4 shows the evolution of the shallow shear layer width along the cavity interface for Q1 (z/h = 0.87). The mixing layer thickness increases towards the downstream cavity wall until x/L ≈ 0.8, whereafter the thickness decreases due to a local increase in maximum velocity gradient (caused by the impingement of the shear layer on the downstream cavity wall, causing an adverse pressure gradient) (Mignot et al., 2016).
In general, both PIV and 3D-PTV show a good agreement. The (limited) spatial resolution in areas with large velocity gra-dients and the associated uncertainty in the determination of U1,
U2and |∂u(x)/∂y|maxare thought to be the main contributors
to the observed discrepancy.
Fig. 4. Evolution of mixing layer thickness δmfor Q1 (z/h = 0.87)
C. Mass exchange coefficient k
Mass transport across the cavity interface is often character-ized by the mass exchange coefficient k = E(z, t)/2Ubin which
E(z, t) = 1/LR0L|v(x, z, t)|dx represents the time-averaged exchange velocity. Figure 5 shows the vertical profiles of k for both Q1 and Q2. In general, the obtained profiles are in good agreement with literature, in which an increased mass exchange coefficient near mid-depth is observed. However, it is observed that the magnitude of k is quite dependent on the adopted mea-surement technique. A possible explanation for the observed differences can be related to suboptimal post-processing of the PIV results, as the PIV measurements seem to underestimate the local ejection or outflow near the downstream cavity cor-ner, causing a more significant difference in the time-averaged exchange velocity.
Fig. 5. Vertical profiles of the mass exchange coefficient k(z)
A. Vortex shedding
A description of the flow properties in the shallow mixing layer can contribute to a better understanding of the phenomena contributing to mass exchange between the lateral cavity and main channel. This study was mainly executed using the results of the PIV measurements. Previous work (Mignot et al., 2016; Perrot-Minot et al., 2018, 2020) showed that vortices in the mix-ing layer are shed at a dominant frequency fpwhich can be
de-termined by calculating the power spectral density of the trans-verse velocity fluctuations v0across the cavity interface. Figure
6 shows the obtained frequency spectra for flow cases Q1 and Q2 at z/h = 0.13, z/h = 0.50 and z/h = 0.87.
A comparison of the vortex shedding frequencies at different measurement planes for a single flow case suggests the exis-tence of a different vortex shedding behaviour depending on the Froude number. For flow case Q2, characterized by high Froude numbers, the dominant vortex shedding frequency is constant over the entire water depth (fp = 1.15Hz), creating vertical or
slightly inclined vortical columns extending over the complete water depth. However, flow case Q1 (low Froude number) is characterized by non-uniform vortex shedding in which vortices are created at the upstream cavity wall at different frequencies depending on the elevation above the bed (i.e. fp= 2.40Hz at
z/h = 0.87and fp= 1.25Hz at z/h = 0.13). At z/h = 0.50,
no dominant vortex shedding frequency is observed (multiple frequencies characterized by more or less equal signal power are noticed), such that it is assumed that two regions of uniform vortex shedding exist which are separated by a transitional area. Similar observations were made for flow past a seamount with varying Froude numbers (Perfect et al., 2018). However, it was
Fig. 6. Power spectral density of velocity fluctuations v0in mixing layer
the average main channel longitudinal velocity Uzat elevation z
above the bed, for flow case Q1 is approximately constant in the two regions of uniform vortex shedding.
By plotting the transverse velocity v across the cavity inter-face as function of space and time, additional information about the propagation of vortices in the mixing layer is obtained. It was observed that the vortex celerity c in the cavity interface decreases slightly towards the downstream cavity wall, as was also observed by Perrot-Minot et al. (2018). The average vortex propagation velocity is smaller than the bulk velocity Ubin the
main channel but larger than the average longitudinal velocity Ui in the cavity interface. Moreover, it was observed that both
the vortex wavelength λ and the vortex celerity c for flow case Q2 are significantly larger than for flow condition Q1.
The distinct vortex shedding behaviour between flow case Q1 and Q2 was also observed in the Proper Orthogonal Decomposi-tion (POD) of the transverse velocity fluctuaDecomposi-tions, which showed that the first (dominant) modes for flow case Q2 are almost iden-tical at z/h = 0.13 and z/h = 0.87, while the first modes of flow case Q1 at z/h = 0.13 and z/h = 0.87 indicated a differ-ent number of vortical structures, characterized by differdiffer-ent di-mensions (approximately equal to the calculated wavelengths). B. Flow-induced surface oscillations and coupling with vortex
shedding
For high Froude numbers, surface oscillations have been ob-served in the lateral cavity. One of the excitation mechanisms of these surface oscillations, also called seiches, is the impinge-ment of the coherent structures in the mixing layer on the down-stream cavity wall. This impingement causes the kinetic energy of the vortices to be transformed into potential energy, causing a periodic rise and fall of the local water level. When the vortex shedding frequency matches the natural frequency of the lateral embayment (which can be estimated theoretically), surface os-cillations occupying the entire lateral cavity are created. It was concluded that the observed vortex shedding frequency of flow case Q2 matches closely with the frequency of transverse seich-ing accordseich-ing to the first mode. As such, vortex sheddseich-ing occurs in phase with transverse seiching. The presence of these surface oscillations helps in explaining the different vortex shedding be-haviour that was observed for flow case Q2 compared with Q1. Moreover, the frequency spectrum for flow case Q2 (Figure 6) also indicates the possible existence of higher-order transverse or longitudinal seiching modes.
Previous work (Tuna et al., 2013; Akutina, 2015) also indi-cated that the undulating or flapping motion of the centerline of the mixing layer occurs in phase with the shedding of vortices in case these surface oscillations are present. Although not shown, the calculated frequency spectra and the phase-averaged veloc-ity fields both confirmed these observations. In flow cases where seiching is limited, this in phase behaviour is noticed to be less strong or completely absent.
3D-PTV was adopted to estimate the amplitude of these sur-face oscillations for flow case Q2. To analyze the shape of the free-water surface, floating seeding particles were added in the lateral cavity. After preprocessing the images and determining
ing mode) were fitted to the obtained point cloud. However, the latter was observed to have only a limited effect, due to the large wavelength. On average, a seiching amplitude of approximately 0.047 h, with h the average water depth, was observed. More-over, the reconstructed free-water surface confirmed the hypoth-esis of the presence of a longitudinal seiching component. C. Propagation of vortices in the mixing layer
A combination of POD and vortex identifiers (Γ-criteria (Graftieaux et al., 2001)) is adopted to study the propagation of vortices in the mixing layer. Figure 7 shows the propagation of these coherent structures over approximately a single vortex shedding period (tfp≈ 1) for flow case Q1 at z/h = 0.87. Both
clockwise rotating (blue) as counterclockwise rotating (red) vor-tices are created at the upstream cavity corner and propagate in the mixing layer towards the downstream cavity wall, where they either enter the lateral cavity or are advected in the main channel. As vortices propagate through the mixing layer, inter-actions between different vortices take place. These interinter-actions result in the merging of two vortices into a single vortex (e.g. B1and B2merge into B), while also the reverse phenomenon,
in which vortices undergo a splitting process (e.g. the vortex indicated with D in Figure 7), is observed.
The propagation of vortices is associated with large velocity fluctuations (so-called ’sweep’ and ’ejection’) and large negative Reynolds stresses. Although not shown in this paper, flow case Q2 showed the presence of significantly larger coherent struc-tures (with larger wavelength λ).
Fig. 7. Vortex propagation in the mixing layer at z/h = 0.87 for flow case Q1
D. Mass exchange
Tuna et al. (2013) indicated that the presence of surface oscil-lations can significantly increase the mass exchange between the main channel and lateral cavity. This statement was confirmed in the current study, in which an increase of approximately 30 % was observed between flow case Q1 (k3D−PTV = 0.035) and
flow case Q2 (k3D−P T V = 0.046). However, as noted by prof.
Uijttewaal in Akutina (2015), seiching does not necessarily con-tribute to the net mass exchange. Therefore, a Lagrangian de-termination of the mass transport as proposed by Engelen and De Mulder (2019, 2020) may contribute to a better understand-ing of the effect of seichunderstand-ing on the net mass exchange.
PTV measurements performed in a small-scale cavity facility in which free-surface flow past a lateral cavity is studied. The main contributions to the observed differences were described. How-ever, it was concluded that in general, both PIV and 3D-PTV are able to describe time-averaged and turbulent flow proper-ties within the estimated accuracy of the flow measurements. A larger discrepancy was observed between the estimated mass exchange coefficients. Using PIV, the main flow properties in the shallow shear layer were studied. Depending on the Froude number, a distinct vortex shedding behaviour was noted. More-over, strong coupling with surface oscillations was observed.
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Acknowledgements ii
Abstract iii
Extended abstract iv
Table of Contents xi
List of Figures xii
List of Tables xv
List of Symbols and Abbreviations xvi
1 Introduction 1
1.1 Research topic . . . 1
1.2 Objectives of the master’s dissertation . . . 2
1.3 Dissertation outline . . . 2
2 Literature review 4 2.1 Free-surface flow past a lateral cavity . . . 4
2.1.1 Description of the time-averaged flow field . . . 5
2.1.2 Flow instabilities occurring in flow past a lateral cavity . . . 7
2.1.3 Mass exchange . . . 9
2.2 Theoretical description of the measurement techniques used in this work . . . 11
2.2.1 Classification of measurement techniques . . . 11
2.2.2 Particle Image Velocimetry . . . 12
2.2.3 3D Particle Tracking Velocimetry . . . 16
2.3 Comparison between PIV and 3D-PTV . . . 22
3 Experimental set-up 24 3.1 Cavity facility and flow conditions . . . 24
3.1.1 Cavity facility . . . 24
3.1.2 Flow conditions . . . 25
3.2 Particle Image Velocimetry set-up . . . 26
3.3 3D Particle Tracking Velocimetry set-up . . . 29
3.4 Validation and error analysis of the velocity measurements . . . 31
3.4.1 Estimation of PIV uncertainties . . . 32
3.4.2 Validation of 3D-PTV experiments . . . 34
4 Validation of 3D-PTV measurements with PIV measurements 38 4.1 Introduction . . . 38
4.2 Convergence of the flow measurements . . . 38
4.2.1 Convergence of the PIV measurements . . . 38
4.2.2 Convergence of the 3D-PTV measurements . . . 41
4.3.2 Time-averaged velocity field . . . 50
4.3.3 Turbulent flow properties . . . 57
4.3.4 Impact of Eulerian binning procedure on 3D-PTV measurements . . . 59
4.3.5 Comparison of velocity-derived quantities . . . 61
4.4 Conclusion . . . 65
5 Identification of coherent structures 67 5.1 Importance of coherent structures . . . 67
5.2 Vortex identification methods . . . 67
5.2.1 Methods based on the local velocity gradient . . . 68
5.2.2 Methods based on the topology of the velocity field . . . 70
5.2.3 Proper Orthogonal Decomposition . . . 71
5.3 Selection of vortex indicator . . . 72
5.4 Conclusion . . . 76
6 Investigation of the flow properties in the shallow mixing layer 77 6.1 Vortex shedding . . . 77
6.2 Flow-induced surface oscillations and coupling with vortex shedding . . . 84
6.3 Propagation of vortices in the mixing layer . . . 87
6.4 Characteristics of the mixing layer . . . 89
6.5 Phase-averaged velocity field . . . 92
6.6 Estimation of the seiching amplitude . . . 95
6.7 Mass exchange . . . 97
6.8 Conclusion . . . 98
7 Conclusions and future work 99 7.1 Validation of the 3D-PTV experiments . . . 99
7.2 Investigation of the shallow shear layer . . . 100
7.3 Recommendations on future work . . . 101
References 102 A Comparison between PIV and 3D-PTV measurements 109 A.1 Time-averaged velocity field . . . 109
A.2 Turbulent flow properties . . . 110
A.3 Impact of Eulerian binning procedure on 3D-PTV measurements . . . 113
A.4 Evolution of the mixing layer thickness . . . 114
2.1 Schematic depiction of free-surface flow past a lateral cavity (Akutina, 2015) 4 2.2 Time- and depth-averaged velocity field for free-surface flow past a lateral
cavity (with u and v the velocity in the x- and y-direction and Ub the average,
main channel velocity) (Engelen and De Mulder, 2019) . . . 6 2.3 Secondary recirculation inside a lateral cavity (Akutina, 2015) . . . 6 2.4 Time-averaged transverse velocity field at the cavity interface (with v the
velocity in the transverse direction and Ub the average, main channel velocity),
red (blue) colors indicate outflow (inflow) (flow from left to right) (Engelen and De Mulder, 2019) . . . 7 2.5 Shallow-shear flow (Uijttewaal and van Prooijen, 2005) . . . 8 2.6 Mass exchange coefficient k according to Engelen and De Mulder (2019) . . . 10 2.7 Eulerian (left) and Lagrangian (right) description of flow (Willneff, 2003) . . 11 2.8 Experimental set-up of Particle Image Velocimetry (Raffel et al., 2007) . . . . 12 2.9 Low particle image density (PTV) (a) Medium particle image density (PIV)
(b) High particle image density (LSV) (c) (Raffel et al., 2007) . . . 14 2.10 Correlation plane for double exposed image (autocorrelation) and single
ex-posed image (cross-correlation) (Raffel et al., 2007) . . . 16 2.11 Processes in 3D-PTV (Willneff, 2003) . . . 17 2.12 Collinearity of camera projective center, object point and image point (Maas
et al., 1993) . . . 18 2.13 Intersection of epipolar lines in a three camera setup (Maas, 1993) . . . 20 2.14 Particle tracking (Malik et al., 1993) . . . 21 3.1 Experimental set-up (a) schematic (with the adopted coordinate system) (b)
photograph . . . 24 3.2 PIV set-up (a) laser installed next to the main channel (b) calibration plate . 27 3.3 3D-PTV set-up including main channel, lateral cavity, four digital cameras,
LED panel and downstream calming tank . . . 29 3.4 3D-PTV calibration (a) checkerboard pattern (b) calibration target . . . 30 3.5 Example of an image during 3D-PTV experiments (a) before preprocessing
(b) after preprocessing . . . 31 3.6 Probability density distributions of the residual calibration ∆ error in x-,
y-and z-direction (3D-PTV) . . . 35 3.7 Probability density distributions of the dynamic positional error ∆d and the
velocity error ∆u (3D-PTV) . . . 37 4.1 Convergence of the time-averaged velocity of the PIV measurements in the
main channel (flow case Q1) (x/L = 0.25, y/W =−0.50, z/h = 0.87) . . . 39 4.2 Convergence of the time-averaged velocity of the PIV measurements in the
mixing layer (flow case Q1) (x/L = 0.25, y/W = 0, z/h = 0.87) . . . 39
4.4 Convergence of the root-mean-square velocities of the PIV measurements in the main channel (flow case Q1) (x/L = 0.25, y/W =−0.50, z/h = 0.87) . . 40 4.5 Convergence of the root-mean-square velocities of the PIV measurements in
the mixing layer (flow case Q1) (x/L = 0.25, y/W = 0, z/h = 0.87) . . . 40 4.6 Convergence of the root-mean-square velocities of the PIV measurements in
the cavity (flow case Q1) (x/L = 0.25, y/W = 0.75, z/h = 0.87) . . . 41 4.7 Convergence of the time-averaged velocities of the 3D-PTV measurements in
the main channel (flow case Q1) (x/L = 0.25, y/W =−0.50, z/h = 0.87) . . 42 4.8 Convergence of the time-averaged velocities of the 3D-PTV measurements in
the mixing layer (flow case Q1) (x/L = 0.25, y/W = 0, z/h = 0.87) . . . 43 4.9 Convergence of the time-averaged velocities of the 3D-PTV measurements in
the cavity (flow case Q1) (x/L = 0.25, y/W = 0.75, z/h = 0.87) . . . 43 4.10 Convergence of the root-mean-square velocities of the 3D-PTV measurements
in the main channel (flow case Q1) (x/L = 0.25, y/W =−0.50, z/h = 0.87) . 44 4.11 Convergence of the root-mean-square velocities of the 3D-PTV measurements
in the mixing layer (flow case Q1) (x/L = 0.50, y/W = 0, z/h = 0.87) . . . . 44 4.12 Convergence of the root-mean-square velocities of the 3D-PTV measurements
in the cavity (flow case Q1) (x/L = 0.25, y/W = 0.75, z/h = 0.87) . . . 45 4.13 Contour plot of|∆u|/Ub and |∆v|/Ub at z/h = 0.87 for flow case Q1 . . . 51
4.14 Probability density distribution of ∆u/Ub and ∆v/Ub at z/h = 0.87 for flow
case Q1 . . . 53 4.15 Cross-sectional profile of the time-averaged longitudinal velocity u across the
main channel and lateral cavity (x/L = 0.5) for flow conditions Q1 and Q2 at different elevations above the bed . . . 55 4.16 Cross-sectional profile of the time-averaged transverse velocity v across the
lateral cavity (y/W = 0.5) for flow conditions Q1 and Q2 at different elevations above the bed . . . 56 4.17 Contour plot of|∆urms|/Ub and|∆vrms|/Ub at z/h = 0.87 for flow case Q1 . 58
4.18 Probability density distribution of ∆urms/Ub and ∆vrms/Ub at z/h = 0.87 for
flow case Q1 . . . 59 4.19 Evolution of mixing layer thickness δm along cavity interface for Q1 . . . 62
4.20 Vertical profiles of the mass exchange coefficient k(z) for flow cases Q1 and Q2 obtained with PIV and 3D-PTV . . . 64 5.1 Vortex indicators based on the velocity gradient (∆, λci, Q and λ2) for three
consecutive time instants (flow case Q1, z/h = 0.87) . . . 74 5.2 Relative λj/Pnj=1λj and cumulativePrj=1λj/Pnj=1λj energy content of the
first 50 modes of u0 and v0 for flow case Q1 at z/h = 0.87 . . . 75 5.3 Γ1 and Γ2vortex indicators using the first 50 POD modes for three consecutive
time instants (flow case Q1, z/h = 0.87) . . . 76
6.2 Transverse velocity component v across the interface (y/W = 0) at z/h = 0.87 for flow cases Q1 and Q2 over a time span of 4 s . . . 79 6.3 Power spectral density of transverse velocity fluctuations v0 in mixing layer
for flow cases Q1 and Q2 and all elevations above the bed . . . 81 6.4 Spatial component of the first three modes of the POD of the transverse
velocity fluctuations v0 of Q1 and Q2 at z/h = 0.13 and z/h = 0.87 . . . 83 6.5 First two seiching modes in transverse (nt= 1, 2 and nl= 0) and longitudinal
direction (nt= 0 and nl= 1, 2) . . . 86
6.6 Propagation of vortices in the mixing layer at z/h = 0.87 for flow case Q1 . . 87 6.7 Reynolds stresses in the mixing layer at z/h = 0.87 for flow case Q1
(corre-sponding to the time instants of Figure 6.6) . . . 89 6.8 Propagation of vortices in the mixing layer at z/h = 0.87 for flow case Q2 . . 89 6.9 Evolution of the mixing layer thickness δm along the cavity interface using
PIV for flow conditions Q1 and Q2 . . . 90 6.10 Power spectral density of the deflection of the center of the mixing layer yM
for all flow cases at z/h = 0.87 for Q1, Q2 and Q4 and z/h = 0.52 for Q3 . . 91 6.11 Contour plot of phase-averaged transverse velocity fluctuations v0 for Q1 and
Q2 at z/h = 0.87 . . . 93 6.12 Contour plot of phase-averaged total velocity √u2+ v2 for Q1 and Q2 at
z/h = 0.87 . . . 94 6.13 Reconstructed surface variations using 3D-PTV over a time interval of 5 s
using the first-order and sinusoidal model at x/L = 0.50 and y/W = 1.00 (flow case Q2) . . . 96 6.14 Reconstructed free-water surface using 3D-PTV at t = t1 and t = t1+ T01/2
using the sinusoidal model (flow case Q2) . . . 97 A.1 Contour plot of|∆u|/Ub and |∆v|/Ub at z/h = 0.87 for flow case Q2 . . . 109
A.2 Probability density distribution of ∆u/Ub and ∆v/Ub at z/h = 0.87 for flow
case Q2 . . . 109 A.3 Contour plot of|∆urms|/Ub and|∆vrms|/Ub at z/h = 0.87 for flow case Q2 . 110
A.4 Probability density distribution of ∆urms/Ub and ∆vrms/Ub at z/h = 0.87 for
flow case Q2 . . . 110 A.5 Contour plot of|∆TKE|/U2
b at z/h = 0.87 for (a) flow case Q1 (b) flow case Q2111
A.6 Probability density distribution of|∆TKE|/U2
b at z/h = 0.87 for (a) flow case
Q1 (b) flow case Q2 . . . 111 A.7 Evolution of mixing layer thickness δm along cavity interface for Q2 . . . 114
2.1 Comparison between PIV and 3D-PTV (Willneff, 2003; Raffel et al., 2007; Alberini et al., 2017) . . . 23 3.1 Overview of experimental flow conditions . . . 26 4.1 Mean absolute difference MAD, standard deviation σ and root-mean-square
error RMSE of the difference between the time-averaged longitudinal u and transverse v velocity obtained with PIV and 3D-PTV . . . 53 4.2 Mean absolute difference MAD, standard deviation σ and root-mean-square
error RMSE of the difference between the longitudinal urms and transverse
vrms root-mean-square velocity obtained with PIV and 3D-PTV . . . 59
4.3 Percentage difference between MAD, σ and RMSE of the difference in time-averaged velocity between PIV and 3D-PTV obtained with a vertical binsize of 1.5 mm and 1 mm, respectively (positive values indicate smaller MAD, σ or RMSE for a binsize of 1.0 mm) . . . 60 4.4 Percentage difference between MAD, σ and RMSE of the difference in
root-mean-square velocity between PIV and 3D-PTV obtained with a vertical bin-size of 1.5 mm and 1 mm, respectively (positive values indicate smaller MAD, σ or RMSE for a binsize of 1.0 mm) . . . 61 6.1 Overview of fundamental vortex shedding properties for the different flow
cases at z/h = 0.87 for Q1, Q2 and Q4 and z/h = 0.52 for Q3 . . . 80 6.2 Strouhal number St = fpλ/Uz for flow case Q1 at z/h = 0.13 and z/h = 0.87 82
A.1 Mean absolute difference MAD, standard deviation σ and root-mean-square error RMSE of the difference between the turbulent kinetic energy TKE ob-tained with PIV and 3D-PTV . . . 112 A.2 Percentage difference between MAD, σ and RMSE of the difference in
turbu-lent kinetic energy between PIV and 3D-PTV obtained with a vertical binsize of 1.5 mm and 1 mm, respectively (positive values indicate smaller mean, standard deviation or RMSE for a binsize of 1.0 mm) . . . 113
2D-PIV two-dimensional Particle Image Velocimetry 3D-PTV three-dimensional Particle Tracking Velocimetry b main channel width
c vortex celerity
dp (mean) particle diameter
Dh hydraulic diameter of the main channel
DMD Dynamic Mode Decomposition E instantaneous exchange velocity
Ev0 power spectral density of transverse velocity fluctuations
EyM power spectral density of deflection of mixing layer centerline
fnlnt natural frequency of the lateral cavity
fs sampling frequency
fp vortex shedding frequency
F r Froude number
g gravitational acceleration h water depth
k mass exchange coefficient l integral length scale of the flow L cavity length
L characteristic length scale LSV Laser Speckle Velocimetry MAD mean absolute difference
POD Proper Orthogonal Decomposition Q discharge in the main channel Q Q-criterion
Re Reynolds number RMSE root-mean-square error St Strouhal number Stk Stokes number
SVD Singular Value Decomposition
t time
td characteristic time scale of the flow
TKE turbulent kinetic energy
u, v, w instantaneous longitudinal, transverse and vertical velocity u, v, w time-averaged longitudinal, transverse and vertical velocity ˜
u periodic velocity component hui phase-averaged velocity
u0, v0, w0 instantaneous longitudinal, transverse and vertical velocity fluctuation urms, vrms, wrms root-mean-square longitudinal, transverse and vertical velocity
U characteristic flow velocity Ub bulk velocity in the main channel
Ui average longitudinal velocity in the cavity interface
Uz average longitudinal velocity in the main channel at elevation z
U1, U2 characteristic flow velocity in lateral cavity and main channel
W cavity width W/L cavity aspect ratio x longitudinal coordinate y transverse coordinate
yM deflection of the centerline of the mixing layer
z vertical coordinate Γ1, Γ2 Γ-criteria
δm mixing layer thickness
∆ ∆-criterion η Kolmogorov scale
rate of dissipation of turbulent kinetic energy λ vortex wavelength
λ2 λ2-criterion
λci λci-criterion
µ mean
µf dynamic fluid viscosity
νf kinematic fluid viscosity
ρf fluid density
ρp particle density
σ standard deviation
φ POD mode
1.1
Research topic
Harbour docks, groyne fields, access channels to locks, natural embayments, cut-off meanders, etc. can be classified as lateral cavities, which are embayments connected to a river, channel or coastal stream. Flow past lateral cavities has been the research topic of many recent investigations, due to ecological, economical and operational reasons. Mass exchange of sediments, nutrients or pollutants between the main channel and the lateral embayment does not only influence the ecological conditions of the cavity and the main stream, but it also has an impact on sedimentation processes, affecting local water depths and requiring regular maintenance dredging. Moreover, flow past a lateral embayment can cause free-surface oscillations inside the cavity, which influence a ship’s manoeuvrability, as well as affecting mooring conditions and loading and unloading operations.
Recent studies have been concentrated on understanding the flow patterns inside such a lateral cavity and the mass exchange between the main stream and lateral embayment. A better understanding of these phenomena can help in optimizing the hydrodynamic design of these structures. Lateral cavities are characterized by flow velocities which are much smaller than those in the main channel. A recirculating gyre has been found to occupy most of a square-shaped cavity, while secondary recirculations and flow instabilities result in a highly three-dimensional flow field. Multiple recirculating gyres have been observed in rectangular cavities with a large width-to-length ratio. Turbulence and vortical structures created at the interface of the main channel and lateral cavity are two of the dominant processes contribut-ing to mass and momentum exchange between main channel and embayment. Moreover, certain flow conditions can result in surface oscillations, also called seiches, increasing the exchange processes even more.
Initial experimental research into this topic was performed using two-dimensional flow mea-surements at the water surface, or at an elevation above the bed which was thought to be representative for the entire water depth. However, the highly three-dimensional character of the flow has resulted in some researchers opting to use three-dimensional measurement techniques, such as is the case in the Hydraulics Laboratory of Ghent University, in which 3D Particle Tracking Velocimetry (3D-PTV) has been adopted. This work uses two-dimensional Particle Image Velocimetry measurements to validate these 3D-PTV results, as well as to study the flow properties in the turbulent mixing layer at the cavity interface, including the creation and propagation of coherent structures and the coupling with the aforementioned surface oscillations.
1.2
Objectives of the master’s dissertation
The objectives of this master’s dissertation are twofold. First of all, Particle Image Ve-locimetry (PIV) measurements are used as an additional validation of 3D Particle Tracking Velocimetry (3D-PTV) measurements which are performed in the Hydraulics Laboratory of Ghent University. In the laboratory, a small-scale flume has been constructed. By per-forming PIV measurements in the same laboratory set-up, the 3D-PTV measurements can be validated and an estimation of the main error sources can be obtained. This validation is mainly focusing on time-averaged flow properties, which can easily be extracted using both measurement techniques. However, also turbulent flow properties, properties of the shallow shear layer and the mass transport across the cavity interface are compared. Since PIV measurements result in a two-dimensional description of the flow, the PIV velocity fields are compared with 2D-slices of the three-dimensional Particle Tracking Velocimetry measurements.
Secondly, the properties of turbulent structures in the mixing layer at the interface of a lateral cavity and the main channel are studied, as these play a major role in the mass exchange between the main channel and lateral embayment. The interface of the main channel and lateral cavity is a highly turbulent zone, in which all types of coherent structures are created. As these structures have a large influence on the mass transport, identifying these structures and studying their behaviour can contribute to a better understanding of the general flow patterns in the mixing layer and the transport of mass in and around a lateral cavity. Moreover, a coupling between the formation of coherent structures in the mixing layer and surface oscillations inside the cavity has been reported to contribute significantly to the mass exchange between main stream and cavity. The presence of these surface oscillations is investigated, and their effect on the mass exchange and the characteristics and behaviour of the mixing layer are studied. Due to the lower spatial resolution of the current 3D-PTV measurements, this part of the master’s dissertation will mainly be performed using PIV measurements.
1.3
Dissertation outline
Chapter 2 provides an overview of the available information found in literature related to the research topic of the current master’s dissertation: free-surface flow past a lateral cavity, Particle Image Velocimetry (PIV) and 3D Particle Tracking Velocimetry (3D-PTV). A de-scription of the experimental set-up and an overview of the different flow cases investigated are given in Chapter 3. Moreover, this chapter also includes a description and estimation of the different error sources in the PIV measurements and a validation of the 3D-PTV set-up adopted in this work.
Chapter 4 treats the comparison between the PIV and 3D-PTV measurements performed in the Hydraulic Laboratory of Ghent University, including a comparison of the time-averaged velocity fields, turbulent flow characteristics, some fundamental properties of the shear layer
and the mass exchange associated with free-surface flow past a lateral cavity. In Chapter 5, some mathematical background is provided on the identification of coherent structures in the mixing layer, as well as a thorough comparison between the different techniques proposed in literature. These vortex identifiers are then applied in Chapter 6, which discusses the properties of the flow structures in the turbulent mixing layer. This section also includes a description of the coupling with free-surface oscillations and the influence of these surface fluctuations on the turbulent flow properties in the shallow shear layer. Finally, Chapter 7 summarizes the main results obtained within this master’s dissertation and gives some recommendations for future work.
This chapter provides an overview of the available and most important information found in literature related to the current research topic. At first, free-surface flow past a lateral cavity is described, which includes an overview of the general flow pattern in the lateral embayment and the mixing layer at the interface of the cavity and main channel. Thereafter, the basics of shallow-shear flow and flow instabilities, together with the principles of mass exchange between the main channel and cavity are shortly discussed. To conclude this chapter, an overview of the principles and post-processing techniques of the two measurement techniques adopted during this master’s dissertation is provided.
2.1
Free-surface flow past a lateral cavity
A lateral cavity (Figure 2.1) is an embayment located on the side of a river, channel or coastal main flow, which is characterized by flow velocities which are much smaller than the flow velocities in the main channel and is therefore often called a ‘dead zone’. These cavities are omnipresent in river and channel systems and can be formed by nature or are manmade. Examples of natural cavities are river side arms, bank irregularities, bays, cut-off meanders, etc. Groyne fields, harbour docks and access channels to locks are manmade examples (Weitbrecht and Jirka, 2001; Akutina, 2015; Engelen and De Mulder, 2019; Mignot et al., 2019).
Figure 2.1: Schematic depiction of free-surface flow past a lateral cavity (Akutina, 2015)
Lateral cavities have a major influence on the mass transport in a river or channel. Due to mass exchange between the main river flow and the dead zone, the overall mass trans-port velocity of the river reduces compared to the situation without lateral cavities. Mass transport in rivers includes the transport of sediments, but also the transport of polluting particles, nutrients, etc. The study of mass exchange between the main river and such a lat-eral cavity is important, as it can have a major influence on sedimentation processes inside harbour docks, which influence the corresponding dredging activities and costs, as well as on the maximum concentration and spreading or dispersion of a pollutant cloud in a river
basin (Weitbrecht and Jirka, 2001; Mignot et al., 2019). The mass exchange between the main river flow and the lateral cavity is strongly dependent on the flow structures which develop inside the cavity and at the interface between the cavity and the main flow, the so-called mixing layer. Therefore, the next sections are dedicated to a description of the most important flow patterns in and near a lateral cavity (Mignot et al., 2016).
2.1.1 Description of the time-averaged flow field
In reality, groyne fields or other types of lateral cavities often have a complex shape, with varying dimensions, water depths, orientations with respect to the main channel, etc. In experimental studies, these complex geometries are often simplified towards rectangular or square-shaped planform geometries with constant water depths (Rivi`ere et al., 2010; Akutina, 2015; Engelen and De Mulder, 2019; Mignot et al., 2019). As free-surface flow past a lateral cavity can be considered as a shallow flow, in which the horizontal dimensions are much larger than the vertical dimensions, it was assumed that the flow and mass exchange could easily be investigated by measuring flow velocities at a single horizontal plane, which is then representative for the whole water depth (Weitbrecht and Jirka, 2001). However, Uijttewaal et al. (2001), Tuna et al. (2013), Akutina (2015), Engelen and De Mulder (2019) and Geerinck (2019) indicated that the real flow has a large three-dimensional character, especially near the mixing layer with the main flow.
Many studies have been performed to investigate the flow pattern near and inside a cavity. The cavity is usually characterized by its aspect ratio W/L, which is defined as the ratio of the cavity’s width W perpendicular to the flow, to the cavity’s length L in the direction of the flow. For an approximately square cavity, with an aspect ratio close to one, flow inside the cavity is characterized by a large rotating cell, occupying most of the cavity (Figure 2.1). In the center of this recirculating cell, a slow-moving, ellipsoidal core or dead zone is observed. At the interface with the main flow, a shear or mixing layer develops, due to the interaction between the fast-moving flow in the main channel and the slow-moving recirculating cell inside the cavity (Akutina, 2015). Using 3D Particle Tracking Velocimetry (3D-PTV), Engelen and De Mulder (2019) were able to visualize this flow pattern (Figure 2.2). Also smaller, contra-rotating secondary gyres were observed in the cavity corners and at the upstream cavity wall.
Due to an imbalance between centrifugal and pressure forces, a secondary gyre with a hori-zontal axis is created inside the cavity. This imbalance is created due to the development of a boundary layer near the cavity bed, which causes a deceleration of the flow and a reduction of the centrifugal forces. As a result, a radial inflow is observed near the bed (Ekman, 1905). This effect was extensively studied by Doswell and Burgess (1993), as it also occurs in atmo-spheric flows, such as cyclones and tornadoes. The presence of this secondary recirculation in shallow flow past a lateral embayment was first observed by Gaskin et al. (2002) and later confirmed by Jamieson and Gaskin (2007), whom referred to it as the ‘tea-cup’ effect. Due to mass continuity, a radial inflow has to be compensated by an upward flow in the core, a radial outflow near the free-water surface and a downward flow near the cavity walls (Figure
2.3). Using 3D-PTV, Akutina (2015) was able to confirm the presence of this secondary gyre inside the lateral cavity.
Figure 2.2: Time- and depth-averaged velocity field for free-surface flow past a lateral cavity (with u and v the velocity in the x- and y-direction and Ub the average, main
channel velocity) (Engelen and De Mulder, 2019)
Figure 2.3: Secondary recirculation inside a lateral cavity (Akutina, 2015)
Moreover, Akutina (2015) and Engelen and De Mulder (2019) were able to confirm the observations of Gaskin et al. (2002) and McCoy et al. (2008) that inflow of water and particles from the main stream into the cavity is mainly concentrated in the downstream part of the interface near the channel bed. Outflow on the other hand mainly occurs near the free-water surface at the upstream edge of the cavity. Figure 2.4 shows the transverse velocity component at the interface between the main stream and lateral embayment obtained by (Engelen and De Mulder, 2019), showing the three-dimensional character of the flow at the cavity interface.
Figure 2.4: Time-averaged transverse velocity field at the cavity interface (with v the velocity in the transverse direction and Ub the average, main channel velocity), red (blue)
colors indicate outflow (inflow) (flow from left to right) (Engelen and De Mulder, 2019) Rivi`ere et al. (2010) and Mignot et al. (2019) investigated the influence of the aspect ratio W/L on the main flow patterns inside the cavity. For very small aspect ratios, a single distorted cell is present inside the cavity. For increasing ratios W/L, two contra-rotating cells (orientated along the main flow direction) are present, until 0.5 < W/L < 1.5, when a single gyre occupies the entire cavity. For even larger aspect ratios, again two gyres can be detected, which are aligned in the direction perpendicular to the main flow. If the aspect ratio is increased further, Rivi`ere et al. (2010) even noticed a third or fourth cell, whereas for very long cavities, an area without vorticity and a small surface flow towards the main stream was observed. Next to the influence of the aspect ratio, the presence of multiple lateral cavities close to each other also affects the observed flow patterns. Both the upstream and downstream cavities do influence the flow pattern inside an intermediate embayment: the flow is affected by turbulent structures created in the mixing layers of the upstream cavities and the main flow is directed towards the center of the main stream, away from the cavity (Mignot et al., 2016, 2019). The current study is focusing on an isolated, square cavity. Studies on the effect of multiple lateral cavities were performed by Uijttewaal et al. (2001), Weitbrecht et al. (2008), Erpicum et al. (2009), Meile et al. (2011) and Qin et al. (2017).
2.1.2 Flow instabilities occurring in flow past a lateral cavity
As mentioned before, most studies investigated the flow past a lateral cavity in a single hori-zontal plane at a depth which was assumed to be representative for the entire water depth or analyzed the characteristics of the flow at the free-water surface. Due to the shallowness of the flow, it was assumed that vertical mixing is sufficiently rapid, such that the time neces-sary for this mixing is sufficiently small and that the flow can be considered two-dimensional. However, flow past a lateral cavity also involves large vertical and horizontal velocity gradi-ents, especially in the mixing layer, which can result in a strong three-dimensional character. Velocity gradients exist both due to shear flow and wall-bounded flow (Figure 2.5) (Uijtte-waal and van Prooijen, 2005; Akutina, 2015).
Figure 2.5: Shallow-shear flow (Uijttewaal and van Prooijen, 2005)
Shear flow is characterized by transverse velocity gradients. These transverse velocity gra-dients give rise to so-called Kelvin-Helmholtz instabilities, which are vortices with a vertical axis of rotation. The basic flow was first recognized by von Helmholtz (1868) and Kelvin (1871), while the physical mechanism was first described by Batchelor (1967) (Drazin and Reid, 1981). Kelvin-Helmholtz instabilities arise due to an initial disturbance, which gives rise to small sinusoidal displacements of the vortices created in the shear layer. These dis-placements can grow, leading to an increase in the flow disturbance, until the size of these instabilities is of the same scale as the water depth, after which bottom friction reduces the rate of growth of these disturbances. Kelvin-Helmholtz structures can become as large as the width of the mixing layer. These horizontal eddies dominate the flow pattern at the interface between the main stream and the lateral cavity (Akutina, 2015; Consuegra Mart´ınez, 2017; Geerinck, 2019).
Wall-bounded flow is characterized by Tollmien-Schlichting waves or instabilities, which oc-cur at a rigid boundary. Contrary to the Kelvin-Helmholtz, which have a vertical axis of rotation, Tollmien-Schlichting instabilities near the bed initially have a horizontal axis of rotation which is perpendicular to the main flow direction. They initiate in the viscous boundary layer, whereafter they grow by travelling downstream. When reaching a critical point, they are perturbed, creating three-dimensional turbulence spots (Klebanoff et al., 1962; Akutina, 2015; Consuegra Mart´ınez, 2017). Tollmien-Schlichting instabilities can arise in the viscous boundary layers of the bed, as well as the boundary layers of the cavity walls.
Inside the lateral cavity, another type of flow instability develops. Centrifugal instabilities arise when there is an outward decrease in the magnitude of the angular velocity (Drazin and Reid, 1981). A typical location where centrifugal instabilities may arise is the concave bend of a river, where viscous forces result in the formation of a boundary layer and thus an outward decrease in angular velocity. Centrifugal instabilities which arise in the boundary layer of a curved, concave surface are called G¨ortler instabilities (G¨ortler, 1940) and result in streamwise spiral vortices. In a shallow flow past a lateral embayment, G¨ortler instabilities may be expected in the cavity, where due to wall friction, a boundary layer develops from
