Document Type
Thesis - University Access Only
Award Date
2009
Degree Name
Doctor of Philosophy (PhD)
Department / School
Electrical Engineering and Computer Science
Abstract
In the first phase of this research, motion of discrete spherical particles of 1. 58 mm and specific weight 2.5 gm/cc on a 2% and 3% plane slope were studied in a laboratory wave flume under shoaling wave conditions. The range of wave-height-to-water- depth ratio was between 0.237 and 0.813. The range of wave period was between 1.8s and 8.0s. The particle Reynolds number ranged from 96 to 260 and the Keulegan Carpenter number ranged from 166 to 467 in the experiments. Particle image velocimetry technique was used to capture the instantaneous position of the sediment particle and the associated fluid velocity in the wave bottom boundary layer. The measurement plane was parallel to the inclined bed and located at an elevation of ½ particle diameter from bottom of the bed. A few experiments were conducted with the measurement plane parallel to the inclined bed at an elevation of one sediment diameter from bottom to check the sensitivity of measurements with elevation above bed. Gray scale morphological image processing techniques were used to separate the tracer particles (fluid) phase and sediment (discrete spherical particles) phase from the same two-phase particle velocimetry image. The phase separation was based on the signature size registered by the sediment (discrete) particles and tracer particles in the two-phase particle velocimetry image. A sequence of separated image files were then processed using Matlab® to determine the displacement, velocity and acceleration of individual sediment particles and the associated fluid velocity and total acceleration. These experimental measurements were then used to calculate the individual component forces and to check the balance of the momentum equation of motions for bed load conditions under waves. It was found that sediment velocities and fluid velocities were nearly in phase. All the components of modeled forces of equation of motions were one scale smaller than the drag force. The drag force was the dominant force in the equation of motion. The magnitude of drag force varied with the use of model for coefficient of drag to compute the drag force. The model for coefficient of drag by Carty produced a greater drag force and the model for coefficient of drag by Stokes (24 /Res) produced the least drag force respectively. Experimental data suggest that the friction force was greatly underestimated by using the coefficient of sliding or rolling friction which leads to an imbalance in the equation of motion. The imbalance in the equation of motions could not be explained by experimental uncertainties alone. It was suspected that a thin viscous fluid layer was trapped between the sediment and the smooth bed during their motions. The equation of motions was approximately balanced by replacing solid state frictions model and neglecting lift force with the viscous friction force model based on viscous shear stress. The viscous force model took the form Fp = μU 5 < 5, whereμ is the dynamic viscosity, Us is the sediment particle velocity, and 6 is a viscous length scale. When there were noticeable phase lag between fluid and sediment velocities as seen in long period, shallow water waves, Us was replaced with relative velocity, Ur in the viscous friction force model. Much of the drag force was canceled out by this viscous frictional force that reduced the imbalance in equations of bed motions. The study also evaluated several commonly used formulae for the coefficient of drag and lift force using experimental fluid shear rate. The use of Saffman shear lift force did not reduce the bottom friction force as the fluid shear rate over bed was negligible. Use of free stream fluid accelerations to compute fluid acceleration force in accelerating waves coincides with the total fluid accelerations measured at an elevation at half sediment diameter over smooth bed. As the added mass force was one scale smaller than the drag force, no significant variations were noticed for using free stream fluid accelerations over total fluid accelerations measured at an elevation of half sediment diameter over smooth bed. In the second phase of this research, motion of discrete spherical particle (1.58 mm diameter; specific weight 2.5 gm/cc) on a closely glued single sediment layer bed was studied in a laboratory wave flume inclined at 2% slope under shoaling wave conditions. The closely glued single sediment layer (rough bed) was prepared from glass beads of diameter 1.2 to 1.85 mm. The range of wave-height-to-water-depth ratio was between 0.366 and 0.521. Motion of loose discrete spherical (sediment) particle and the associated fluid velocity field were measured simultaneously using particle image velocimetry with the cameras viewing the flow in an oblique direction. The measurement plane was parallel to the bed and located at an elevation of½ particle diameter over rough bed. Morphological image processing techniques were used to separate the tracer (fluid) phase and sediment phases from the same two-phase particle image velocimetry image based on the signature sizes respectively. The displacement, velocity and acceleration of the loose sediment particle were experimentally determined using a sequence of sediment phase images using MatLab® software. The associated fluid velocity and total acceleration was then used to compute the individual terms (inertia, gravity, acceleration, added mass, drag and friction) and check the balance in the equations of motion for bed conditions. The fluid velocity was approximately constant but sediment velocity varied with each trial for same wave-height-to-water-depth ratio and wave period respectively. For the experimental conditions, the loose particle motion experienced only on-shore motions. Sediment inertia, buoyancy, added mass, fluid acceleration and rolling friction force were of the same order of magnitude and all were one order of magnitude smaller than the dominant drag force. It was found that, the drag force governs the shape of resultant force on the right hand side of the equation of motions and is out of phase with the sediment inertia force. The bed load equation of motion was approximately balanced by replacing the rolling frictions with a viscous friction term in equation of motions. The viscous friction force was of the form FR = μU r< 5, whereμ is the dynamic viscosity, Ur is the relative velocity between the fluid and sediment, and t5 is a length scale. Two constant values of o ( one during sediment acceleration and the other during sediment deceleration) were in the viscous friction model to check the balance of equation of motion for rough bed. It was found that the friction model FR = μU r5 did not balance all the trials of rough bed experiment. The friction force model approximately balanced those trials where the relative velocity between fluid and sediment was greater. It was observed that those trials where the relative velocity was greater, a greater drag force was exerted on loose sediment and a greater value of t5 was need to approximately balance the equation of motion. Secondly, it was observed that in those trials where the relative velocity was greater, the sediment displacements were found to be smaller suggesting the sediment moved close to bed. Methodology for oblique PIV techniques are evaluated with bottom parallel PIV and used in this research. Saltation of sediment particles over rough bed encountered with the increases in wave-height-to-water-depth ratio, limits the use of particle image velocimetry measurements, and constrains the use of bed load equation of motion model.
Library of Congress Subject Headings
Sediment transport
Waves -- Analysis
Particle image velocimetry
Format
application/pdf
Number of Pages
406
Publisher
South Dakota State University
Recommended Citation
Havaldar, Sanjay Narayan, "Experimental Study of Particle Motion on a Smooth and Rough Bed Under Shoaling Waves using Particle Image Velocimetry" (2009). Electronic Theses and Dissertations. 1581.
https://openprairie.sdstate.edu/etd2/1581