Investigation into the physical relationship between water-worked ...

Proceedings of the HYDRALAB III Joint User Meeting, Hannover, February 2010

INVESTIGATION INTO THE PHYSICAL RELATIONSHIP BETWEEN WATER-WORKED GRAVEL BED ARMOURS AND TURBULENT IN-CHANNEL FLOW PATTERNS Katinka Koll (1), James R. Cooper (2), Jochen Aberle (3), Simon J. Tait (4), Andrea Marion (5) (1) Leichtweiß-Institute (LWI), TU Braunschweig, Germany, E-mail: [email protected] (2) School of Engineering, Design and Technology, University of Bradford, UK, E-mail: [email protected] (3) Leichtweiß-Institute (LWI), TU Braunschweig, Germany, E-mail: [email protected] (4) School of Engineering, Design and Technology, University of Bradford, UK, E-mail: [email protected] (5) Department of Hydraulic, Maritime, Environmental and Geotechnical Engineering, University of Padova, Italy, E-mail: [email protected]

In flume experiments the near-bed turbulent flow field over two water-worked gravel bed surfaces was investigated. The surfaces were characterized by similar statistical distributions of bed elevations, but with different surface grain orientations. This was achieved by first developing a water-worked static armour layer and then rotating it by 90°. Characteristics of the flow field were measured with a 3D LDA as well as a 3D PIV in order to reflect the effects of the different temporal and spatial resolutions and accuracies of each measurement system. The results show that (1) the shape of the vertical profiles as well as the absolute values obtained by PIV measurements depend only marginally on the number of verticals, (2) PIV and LDA show only good agreement for the longitudinal velocity component, and (3) a representative surface grain size or bed surface roughness height based on simple statistics of bed elevations cannot accurately account for the resistance imposed by a water-worked gravel bed on the flow. 1.

INTRODUCTION

A key problem in river hydraulics has been the adequate evaluation of the resistance imposed by different bed morphologies on the flow. Energy losses due to particle roughness depend on particle size, shape, and arrangement. The equivalent sand roughness height kS, is normally used in studies related to the turbulent flow field, and for practical purposes, kS is usually related to a representative surface grain-size such as D50 or D84. However, recent studies investigating gravel bed structure using statistical methods have shown that grain orientation is different for static and dynamic armour layers (e.g., Aberle & Nikora, 2006). Both bed types may be characterised by the same statistical distribution of bed surface elevations and surface volumetric grain-size distributions but have a very different surface structure in longitudinal and transverse direction. Additionally, further studies have described the presence of organised networks of grain-scale bed structures (e.g., Marion et al., 2003). These observations indicate that the use of a single roughness scale determined from a ‘representative’ surface grain-size may not contain sufficient information to determine, in detail, the influence of the bed on the characteristics of the near-bed flow field (for more details see Cooper et al., 2008a and 2008b). This study was carried out to investigate the influence of grain-arrangement on the near-bed turbulent flow field. Detailed spatially distributed measurements of the flow field were made over two water-worked gravel bed surfaces, characterised by almost the same statistical distribution of bed elevations but with the surface grains arranged in orthogonal directions. This was achieved by rotating a water-worked bed through 90° (see Cooper et al., 2008a for details).


Two of the most common optical methods, Particle Image Velocimetry (PIV) and Laser Doppler Anemometry (LDA) were used to measure the turbulent flow field in the near-bed region. Each technique uses a different physical principle as the fundamental basis and, therefore, has different specific strengths and weaknesses. The main differences are the temporal and spatial resolutions. LDA measures velocities of single seeding particles passing through a small sampling volume at a high temporal resolution, thus providing a high accuracy on estimating mean velocity, Reynolds stresses, and higher-order moments over a large dynamic range. However, information on the spatial structure of the flow can only be obtained by measuring flow velocities subsequently at an abundance of locations or by using more than one system simultaneously. PIV, on the other hand, gives detailed information on the spatial flow structure by measuring the distance travelled by groups of particles within the fluid during a fixed time interval. In order to detect their movement, an area of the flow is illuminated by a laser light sheet. Compared to LDA, PIV measures flow velocities at a lower temporal resolution using a larger measuring volume. However, its advantage over LDA consists in providing velocity vectors at a large number of locations simultaneously (for more details see Koll et al., 2008). For comparison of the two techniques we concentrated on the influence of the number of measurement points on spatial flow characteristics by comparing data measured at identical flow conditions with a 3D-LDA and a 3D-PIV system. Using the double averaging approach, spatially averaged mean flow velocities, turbulence characteristics, and form-induced stresses are used to investigate the possibility to describe spatial flow characteristics by a limited number of single point based measurements. 2.

EXPERIMENTS

The experiments were carried out in the Total Environment Simulator (TES) at the University of Hull, UK, which is a 14 m long and 6 m wide tank. In the tank, an 11 m long and 1.2 m wide channel was constructed. A coarse gravel sediment mixture (0.71 mm < D < 64 mm) was used as bed material. The bed was water worked with a discharge of Q = 254 l/s to obtain a stable armour layer (D50 = 12.7 mm; D84 = 42.8 mm). Detailed information on bed topography was available from measurements along the 1 m long and 0.6 m wide test section with an Acuity Laser Measurement displacement sensor (AR200-50M). The test section was located 5.39 m from the flume inlet so that neither the scour at the inlet section nor the downstream sill influenced the development of bed topography. Effects of the side walls were minimised by taking the measurements in the middle section of the flume. Longitudinal bed profiles were recorded with a sampling interval of ∆x = 1 mm, a lateral spacing between profiles of ∆y = 0.25 mm, and with a vertical precision of 0.1 mm. Velocity measurements were carried out with a Dantec 3D-LDA and Dantec 3D-PIV system at Q = 200 l/s and 100 l/s. The LDA measurements started 8.5 cm below the water surface. The vertical sampling resolution was z = 2 mm in the near-bed region, z = 5 mm above the roughness layer, and z = 10 mm in the outer flow field. The corresponding sampling times were t = 90 s in the near bed region and t = 60 s above the roughness layer. Sampling frequencies ranged from approximately 10 130 Hz. 20 velocity profiles were measured for the high discharge and 8 profiles for the low discharge. The measuring locations are referenced to bed topography in Figure 1.

Figure 1: Bed scan and location of measuring locations (lines: PIV-Sheets; dots: LDA-profiles); axes are scaled in mm (flow direction from left to right).


The PIV measurements were designed to be taken over the whole water depth, resulting in an area of the stereoscopic measurements of 279 x 252 mm2. 3534 vectors at a spacing of 4.98 mm and 4.13 mm in the streamwise and vertical directions, respectively, could be analysed. The width of the light sheet in the lateral direction was ≈ 2 mm and the measurements were carried out for a duration of 5 min at three different lateral locations within the measurement section of the flume, at a lateral spacing of 5 cm (see Figure 1). For comparison with the LDA data 168 velocity profiles as well as a subset of only 20 profiles were analysed. 3.

RESULTS

An important objective of the comparative LDA - PIV measurements has been the investigation of the ability of both systems to adequately reflect spatial and turbulent flow heterogeneity depending on their spatial resolution. For this purpose, the data were analysed using the double-averaging approach. Figure 2 exemplarily shows double averaged mean velocity profiles, Reynolds stress profiles, as well profiles of form induced stress for the streamwise direction. A good agreement between LDA and PIV data is observed for the longitudinal velocity component, although systematic deviations in the absolute values are evident. Larger deviations are observed between the lateral and vertical velocities (not shown here), which cannot be attributed to the number of measurement points. The PIV results show that the shape of the vertical velocity profiles in longitudinal, lateral, and vertical direction as well as the absolute values of spatially averaged velocities depend only marginally on the number of verticals (168 compared to 20). This is an important result for designing experiments carried out with single point based measuring devices (such as LDA), as spatial flow characteristics may be described by a limited number of measuring locations in planes parallel to the bed. Moreover, the results also clearly indicate that the measuring locations must be separated by a certain spatial scale to avoid a biased spatial average due to spatially correlated measurements. The investigation of the spatially averaged turbulent flow properties revealed major differences in some parameters depending on the measurement technique. The reason for this unexpected result is partly associated with the chosen experimental set up, which aimed at the description of the complete flow field rather than a small section resulting in large interrogation areas for the analysis of the PIV data (4.98 x 4.13 mm2). zWS

0.375

LDA PIV PIV(20)

z [m]

0.315

0.255

0.195

zmax zm

0.135 0.3

0.4

0.5

0.6

[m/s]

0.7

0.8

0.9

0.00

0.01

0.02

0.03 2

2

[m /s ]

0.04

0.000

0.005 2

0.010 2

[m /s ]

Figure 2: Double averaged mean velocity, double averaged Reynolds stress, and form-induced stress in longitudinal (u) direction (LDA = data measured by LDA, PIV = data measured by PIV, PIV(20) = data measured by PIV reduced to 20 verticals). Note the different scales of the x-axis. A further objective of the investigations has been to examine whether a systematic difference in bed surface topography has a major effect on the vertical velocity distribution in the near bed region. The analysis of the bed structure using 2-D structure functions indicates systematic differences between the two (rotated) bed surfaces in that the streamwise and lateral length scales are different. This indicates the method used to rotate the bed has caused little surface disturbance. PIV data are used to describe the near bed flow field, the vertical distributions of double averaged streamwise velocity, and the typical magnitude of the temporal and spatial fluctuations over the two beds. Figure 3 shows that there is a greater flow retardation over the rotated bed (Bed 2). Preliminary


analysis indicates that this difference is reflected by a change in the turbulence close to the bed rather than by the spatial distribution of the time-averaged velocities. In order to compare hydraulic roughness scales, the equivalent sand roughness ks was calculated using the Clauser method. This method was selected as it is commonly used to describe the vertical velocity distribution in the logarithmic layer. The calculated ks values confirmed that the rotated bed is rougher than the original bed. This result indicates that the use of some representative surface grain size of some simple statistical measure of bed surface elevations is not sufficient to describe the effect that a water-worked bed has on the near bed flow. Estimates of the streamwise length scale of the water-worked beds, obtained by use of 2-D structure functions, may provide an additional means to predict flow resistance. Distance z to steel bottom [m]

Bed 1 h/k = 4.4 0.235

Bed 1 h/k = 3.2 Bed 2 h/k = 4.5

0.215

Bed 2 h/k = 3.3 0.195

zmax

0.175 zm

0.155

z mi n

0.135 0

0.002

0.004 0.006 2 < u~u~ > [( m/s) ]

0.008

0.01

Distance z to steel bottom [m]

0.255

0.255

Bed 1 h/k = 4.4 0.235

Bed 1 h/k = 3.2

0.215

Bed 2 h/k = 4.5 Bed 2 h/k = 3.3

0.195

zmax

0.175 zm

0.155

zmin 0.135 0

2

4

6

8

10

12

< u > u∗ [−]

% % > in the near-bed region and doubleFigure 3: Vertical variability in form-induced stress < uu averaged near-bed streamwise velocity distributions.

ACKNOWLEDGEMENT This work has been supported by European Community's Sixth Framework Programme through the grant to the budget of the Integrated Infrastructure Initiative HYDRALAB III within the Transnational Access Activities, Contract no. 022441. The assistance and contribution of Stuart J. McLelland, Brendan J. Murphy, and Giorgia Massaro is acknowledged. REFERENCES Aberle, J. and Nikora, V. 2006. Statistical properties of armored gravel bed surfaces, Water Resources Research, No.42, doi: 10.1029/2005WR004674. Cooper, J.R., Aberle, J., Koll, K., McLelland, S.J., Murphy, B.M., Tait, S.J. and Marion, A. 2008a. Observation of the near-bed flow field over gravel bed surfaces with different roughness length scales, Proc. Int. Conf. on Fluvial Hydraulics River Flow 2008, 3.-5. September 2008, Çeşme, Turkey. Edited by M. Altinakar, M.A. Kokpinar, Aydin, I., Cokgor, S., and S. Kirkgoz, Kubaba, Vol. 1, 739-746 Cooper, J.R., Aberle, J., Koll, K., Tait, S.J. and Marion, A. 2008b. Different roughness length scales in water worked sediment deposits and their effect on the near bed turbulent flow field, ICHE 2008, Nagoya, Japan, Papers on CD-Rom Koll, K., Tait, S.J., Aberle, J., Cooper, J.R., McLelland, S.J., Murphy, B.J. and Massaro, G. 2008. Estimating flow turbulence characteristics over water-worked gravel beds using LDA and PIV measurement systems, Proc. Int. Conf. on Fluvial Hydraulics River Flow 2008, 3.-5. September 2008, Çeşme, Turkey. Edited by M. Altinakar, M.A. Kokpinar, Aydin, I., Cokgor, S., and S. Kirkgoz, Kubaba, Vol. 1, 747-757 Marion, A., Tait, S.J. and McEwan, I.K. 2003. Analysis of small-scale gravel bed topography during armoring, Water Resources Research, Vol.39, No.12, doi: 10.1029/2003WR002367